[{"author":[{"full_name":"Lombardo, Davide","first_name":"Davide","last_name":"Lombardo"},{"last_name":"Verzobio","first_name":"Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo"}],"day":"26","article_number":"18","title":"On the local-global principle for isogenies of abelian surfaces","arxiv":1,"OA_type":"green","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"TiBr"}],"publication":"Selecta Mathematica","article_type":"original","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","publication_identifier":{"issn":["4321-1234"],"eissn":["1420-9020"],"issnl":["1022-1824"]},"doi":"10.1007/s00029-023-00908-0","quality_controlled":"1","issue":"2","language":[{"iso":"eng"}],"OA_place":"repository","oa_version":"Preprint","month":"01","type":"journal_article","date_updated":"2025-02-13T11:47:12Z","abstract":[{"text":"Let $\\ell$ be a prime number. We classify the subgroups $G$ of $\\operatorname{Sp}_4(\\mathbb{F}_\\ell)$ and $\\operatorname{GSp}_4(\\mathbb{F}_\\ell)$ that act irreducibly on $\\mathbb{F}_\\ell^4$, but such that every element of $G$ fixes an $\\mathbb{F}_\\ell$-vector subspace of dimension 1. We use this classification to prove that the local-global principle for isogenies of degree $\\ell$ between abelian surfaces over number fields holds in many cases -- in particular, whenever the abelian surface has non-trivial endomorphisms and $\\ell$ is large enough with respect to the field of definition. Finally, we prove that there exist arbitrarily large primes $\\ell$ for which some abelian surface\r\n$A/\\mathbb{Q}$ fails the local-global principle for isogenies of degree $\\ell$.","lang":"eng"}],"volume":30,"date_created":"2023-01-16T11:45:53Z","acknowledgement":"It is a pleasure to thank Samuele Anni for his interest in this project and for several discussions on the topic of this paper, which led in particular to Remark 6.30 and to a better understanding of the difficulties with [6]. We also thank John Cullinan for correspondence about [6] and Barinder Banwait for his many insightful comments on the first version of this paper. Finally, we thank the referee for their thorough reading of the manuscript.\r\nOpen access funding provided by Università di Pisa within the CRUI-CARE Agreement. The authors have been partially supported by MIUR (Italy) through PRIN 2017 “Geometric, algebraic and analytic methods in arithmetic\" and PRIN 2022 “Semiabelian varieties, Galois representations and related Diophantine problems\", and by the University of Pisa through PRA 2018-19 and 2022 “Spazi di moduli, rappresentazioni e strutture combinatorie\". The first author is a member of the INdAM group GNSAGA.","year":"2024","_id":"12312","oa":1,"publication_status":"epub_ahead","date_published":"2024-01-26T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/2206.15240","open_access":"1"}],"external_id":{"arxiv":["2206.15240"]},"status":"public","intvolume":"        30"},{"date_published":"2023-11-03T00:00:00Z","ddc":["510"],"publication_status":"published","oa":1,"has_accepted_license":"1","intvolume":"       325","citation":{"mla":"Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic Divisibility  Sequences.” <i>Pacific Journal of Mathematics</i>, vol. 325, no. 2, Mathematical Sciences Publishers, 2023, pp. 331–51, doi:<a href=\"https://doi.org/10.2140/pjm.2023.325.331\">10.2140/pjm.2023.325.331</a>.","ista":"Verzobio M. 2023. Some effectivity results for primitive divisors of elliptic divisibility  sequences. Pacific Journal of Mathematics. 325(2), 331–351.","apa":"Verzobio, M. (2023). Some effectivity results for primitive divisors of elliptic divisibility  sequences. <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pjm.2023.325.331\">https://doi.org/10.2140/pjm.2023.325.331</a>","ama":"Verzobio M. Some effectivity results for primitive divisors of elliptic divisibility  sequences. <i>Pacific Journal of Mathematics</i>. 2023;325(2):331-351. doi:<a href=\"https://doi.org/10.2140/pjm.2023.325.331\">10.2140/pjm.2023.325.331</a>","short":"M. Verzobio, Pacific Journal of Mathematics 325 (2023) 331–351.","ieee":"M. Verzobio, “Some effectivity results for primitive divisors of elliptic divisibility  sequences,” <i>Pacific Journal of Mathematics</i>, vol. 325, no. 2. Mathematical Sciences Publishers, pp. 331–351, 2023.","chicago":"Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic Divisibility  Sequences.” <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/pjm.2023.325.331\">https://doi.org/10.2140/pjm.2023.325.331</a>."},"status":"public","external_id":{"isi":["001104766900001"],"arxiv":["2001.02987"]},"volume":325,"date_created":"2023-01-16T11:46:19Z","file_date_updated":"2023-11-13T09:50:41Z","page":"331-351","type":"journal_article","oa_version":"Published Version","month":"11","date_updated":"2023-12-13T11:18:14Z","abstract":[{"text":"Let P be a nontorsion point on an elliptic curve defined over a number field K and consider the sequence {Bn}n∈N of the denominators of x(nP). We prove that every term of the sequence of the Bn has a primitive divisor for n greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve.","lang":"eng"}],"_id":"12313","acknowledgement":"This paper is part of the author’s PhD thesis at Università of Pisa. Moreover, this\r\nproject has received funding from the European Union’s Horizon 2020 research\r\nand innovation programme under the Marie Skłodowska-Curie Grant Agreement\r\nNo. 101034413. I thank the referee for many helpful comments.","year":"2023","doi":"10.2140/pjm.2023.325.331","quality_controlled":"1","publication_identifier":{"eissn":["0030-8730"]},"isi":1,"issue":"2","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"title":"Some effectivity results for primitive divisors of elliptic divisibility  sequences","arxiv":1,"author":[{"first_name":"Matteo","last_name":"Verzobio","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","full_name":"Verzobio, Matteo"}],"file":[{"file_size":389897,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_name":"2023_PacificJourMaths_Verzobio.pdf","success":1,"date_created":"2023-11-13T09:50:41Z","access_level":"open_access","file_id":"14525","date_updated":"2023-11-13T09:50:41Z","checksum":"b6218d16a72742d8bb38d6fc3c9bb8c6"}],"day":"03","publication":"Pacific Journal of Mathematics","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"scopus_import":"1","ec_funded":1,"article_processing_charge":"Yes (in subscription journal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Mathematical Sciences Publishers","department":[{"_id":"TiBr"}]},{"author":[{"full_name":"Naskręcki, Bartosz","last_name":"Naskręcki","first_name":"Bartosz"},{"first_name":"Matteo","last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo"}],"date_updated":"2023-05-08T10:42:09Z","day":"03","abstract":[{"text":"In this note we prove a formula for the cancellation exponent $k_{v,n}$ between division polynomials $\\psi_n$ and $\\phi_n$ associated with a sequence $\\{nP\\}_{n\\in\\mathbb{N}}$ of points on an elliptic curve $E$ defined over a discrete valuation field $K$. The formula is identical with the result of Yabuta-Voutier for the case of finite extension of $\\mathbb{Q}_{p}$ and\r\ngeneralizes to the case of non-standard Kodaira types for non-perfect residue fields.","lang":"eng"}],"type":"preprint","oa_version":"Preprint","month":"03","arxiv":1,"title":"Common valuations of division polynomials","article_number":"2203.02015","date_created":"2023-01-16T11:45:22Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2022","publication":"arXiv","_id":"12311","article_processing_charge":"No","publication_status":"submitted","oa":1,"date_published":"2022-03-03T00:00:00Z","doi":"10.48550/arXiv.2203.02015","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2203.02015"}],"status":"public","external_id":{"arxiv":["2203.02015"]},"extern":"1","citation":{"short":"B. Naskręcki, M. Verzobio, ArXiv (n.d.).","ieee":"B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” <i>arXiv</i>. .","chicago":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2203.02015\">https://doi.org/10.48550/arXiv.2203.02015</a>.","mla":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>ArXiv</i>, 2203.02015, doi:<a href=\"https://doi.org/10.48550/arXiv.2203.02015\">10.48550/arXiv.2203.02015</a>.","ista":"Naskręcki B, Verzobio M. Common valuations of division polynomials. arXiv, 2203.02015.","apa":"Naskręcki, B., &#38; Verzobio, M. (n.d.). Common valuations of division polynomials. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2203.02015\">https://doi.org/10.48550/arXiv.2203.02015</a>","ama":"Naskręcki B, Verzobio M. Common valuations of division polynomials. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2203.02015\">10.48550/arXiv.2203.02015</a>"},"language":[{"iso":"eng"}]},{"abstract":[{"text":"Let P and Q be two points on an elliptic curve defined over a number field K. For α∈End(E), define Bα to be the OK-integral ideal generated by the denominator of x(α(P)+Q). Let O be a subring of End(E), that is a Dedekind domain. We will study the sequence {Bα}α∈O. We will show that, for all but finitely many α∈O, the ideal Bα has a primitive divisor when P is a non-torsion point and there exist two endomorphisms g≠0 and f so that f(P)=g(Q). This is a generalization of previous results on elliptic divisibility sequences.","lang":"eng"}],"date_updated":"2023-05-08T12:00:17Z","month":"05","type":"journal_article","oa_version":"Published Version","volume":7,"date_created":"2023-01-16T11:44:39Z","year":"2021","_id":"12308","publication_status":"published","oa":1,"date_published":"2021-05-20T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s40993-021-00267-9"}],"status":"public","extern":"1","intvolume":"         7","citation":{"short":"M. Verzobio, Research in Number Theory 7 (2021).","ieee":"M. Verzobio, “Primitive divisors of sequences associated to elliptic curves with complex multiplication,” <i>Research in Number Theory</i>, vol. 7, no. 2. Springer Nature, 2021.","chicago":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves with Complex Multiplication.” <i>Research in Number Theory</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s40993-021-00267-9\">https://doi.org/10.1007/s40993-021-00267-9</a>.","ista":"Verzobio M. 2021. Primitive divisors of sequences associated to elliptic curves with complex multiplication. Research in Number Theory. 7(2), 37.","mla":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves with Complex Multiplication.” <i>Research in Number Theory</i>, vol. 7, no. 2, 37, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s40993-021-00267-9\">10.1007/s40993-021-00267-9</a>.","apa":"Verzobio, M. (2021). Primitive divisors of sequences associated to elliptic curves with complex multiplication. <i>Research in Number Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40993-021-00267-9\">https://doi.org/10.1007/s40993-021-00267-9</a>","ama":"Verzobio M. Primitive divisors of sequences associated to elliptic curves with complex multiplication. <i>Research in Number Theory</i>. 2021;7(2). doi:<a href=\"https://doi.org/10.1007/s40993-021-00267-9\">10.1007/s40993-021-00267-9</a>"},"author":[{"full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","last_name":"Verzobio","first_name":"Matteo"}],"day":"20","title":"Primitive divisors of sequences associated to elliptic curves with complex multiplication","article_number":"37","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Research in Number Theory","scopus_import":"1","article_processing_charge":"No","article_type":"original","publication_identifier":{"issn":["2522-0160","2363-9555"]},"doi":"10.1007/s40993-021-00267-9","quality_controlled":"1","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"issue":"2"},{"year":"2021","_id":"12309","type":"journal_article","oa_version":"Preprint","month":"01","date_updated":"2023-05-08T11:58:14Z","abstract":[{"text":"Take a rational elliptic curve defined by the equation y2=x3+ax in minimal form and consider the sequence Bn of the denominators of the abscissas of the iterate of a non-torsion point. We show that B5m has a primitive divisor for every m. Then, we show how to generalize this method to the terms of the form Bmp with p a prime congruent to 1 modulo 4.","lang":"eng"}],"page":"129-168","date_created":"2023-01-16T11:44:54Z","volume":198,"external_id":{"arxiv":["2001.09634"]},"status":"public","citation":{"chicago":"Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>. Institute of Mathematics, Polish Academy of Sciences, 2021. <a href=\"https://doi.org/10.4064/aa191016-30-7\">https://doi.org/10.4064/aa191016-30-7</a>.","ieee":"M. Verzobio, “Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728,” <i>Acta Arithmetica</i>, vol. 198, no. 2. Institute of Mathematics, Polish Academy of Sciences, pp. 129–168, 2021.","short":"M. Verzobio, Acta Arithmetica 198 (2021) 129–168.","ama":"Verzobio M. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. <i>Acta Arithmetica</i>. 2021;198(2):129-168. doi:<a href=\"https://doi.org/10.4064/aa191016-30-7\">10.4064/aa191016-30-7</a>","apa":"Verzobio, M. (2021). Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. <i>Acta Arithmetica</i>. Institute of Mathematics, Polish Academy of Sciences. <a href=\"https://doi.org/10.4064/aa191016-30-7\">https://doi.org/10.4064/aa191016-30-7</a>","mla":"Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>, vol. 198, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2021, pp. 129–68, doi:<a href=\"https://doi.org/10.4064/aa191016-30-7\">10.4064/aa191016-30-7</a>.","ista":"Verzobio M. 2021. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. Acta Arithmetica. 198(2), 129–168."},"intvolume":"       198","extern":"1","publication_status":"published","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2001.09634","open_access":"1"}],"date_published":"2021-01-04T00:00:00Z","publisher":"Institute of Mathematics, Polish Academy of Sciences","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","scopus_import":"1","article_processing_charge":"No","publication":"Acta Arithmetica","day":"04","author":[{"first_name":"Matteo","last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo"}],"title":"Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728","arxiv":1,"issue":"2","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"publication_identifier":{"issn":["0065-1036","1730-6264"]},"quality_controlled":"1","doi":"10.4064/aa191016-30-7"},{"external_id":{"arxiv":["2102.07573"]},"status":"public","language":[{"iso":"eng"}],"citation":{"short":"M. Verzobio, ArXiv (n.d.).","chicago":"Verzobio, Matteo. “A Recurrence Relation for Elliptic Divisibility Sequences.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2102.07573\">https://doi.org/10.48550/arXiv.2102.07573</a>.","ieee":"M. Verzobio, “A recurrence relation for elliptic divisibility sequences,” <i>arXiv</i>. .","apa":"Verzobio, M. (n.d.). A recurrence relation for elliptic divisibility sequences. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2102.07573\">https://doi.org/10.48550/arXiv.2102.07573</a>","ista":"Verzobio M. A recurrence relation for elliptic divisibility sequences. arXiv, 2102.07573.","mla":"Verzobio, Matteo. “A Recurrence Relation for Elliptic Divisibility Sequences.” <i>ArXiv</i>, 2102.07573, doi:<a href=\"https://doi.org/10.48550/arXiv.2102.07573\">10.48550/arXiv.2102.07573</a>.","ama":"Verzobio M. A recurrence relation for elliptic divisibility sequences. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2102.07573\">10.48550/arXiv.2102.07573</a>"},"extern":"1","publication_status":"submitted","oa":1,"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2102.07573"}],"date_published":"2021-02-15T00:00:00Z","doi":"10.48550/arXiv.2102.07573","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","publication":"arXiv","_id":"12314","abstract":[{"text":"In literature, there are two different definitions of elliptic divisibility\r\nsequences. The first one says that a sequence of integers $\\{h_n\\}_{n\\geq 0}$\r\nis an elliptic divisibility sequence if it verifies the recurrence relation\r\n$h_{m+n}h_{m-n}h_{r}^2=h_{m+r}h_{m-r}h_{n}^2-h_{n+r}h_{n-r}h_{m}^2$ for every\r\nnatural number $m\\geq n\\geq r$. The second definition says that a sequence of\r\nintegers $\\{\\beta_n\\}_{n\\geq 0}$ is an elliptic divisibility sequence if it is\r\nthe sequence of the square roots (chosen with an appropriate sign) of the\r\ndenominators of the abscissas of the iterates of a point on a rational elliptic\r\ncurve. It is well-known that the two sequences are not equivalent. Hence, given\r\na sequence of the denominators $\\{\\beta_n\\}_{n\\geq 0}$, in general does not\r\nhold\r\n$\\beta_{m+n}\\beta_{m-n}\\beta_{r}^2=\\beta_{m+r}\\beta_{m-r}\\beta_{n}^2-\\beta_{n+r}\\beta_{n-r}\\beta_{m}^2$\r\nfor $m\\geq n\\geq r$. We will prove that the recurrence relation above holds for\r\n$\\{\\beta_n\\}_{n\\geq 0}$ under some conditions on the indexes $m$, $n$, and $r$.","lang":"eng"}],"day":"15","date_updated":"2023-02-21T10:22:57Z","month":"02","oa_version":"Preprint","type":"preprint","author":[{"id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo","first_name":"Matteo","last_name":"Verzobio"}],"date_created":"2023-01-16T11:46:36Z","title":"A recurrence relation for elliptic divisibility sequences","arxiv":1,"article_number":"2102.07573"},{"issue":"4","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"publication_identifier":{"issn":["0022-314X"]},"quality_controlled":"1","doi":"10.1016/j.jnt.2019.09.003","publisher":"Elsevier","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","article_processing_charge":"No","scopus_import":"1","publication":"Journal of Number Theory","day":"01","author":[{"first_name":"Matteo","last_name":"Verzobio","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","full_name":"Verzobio, Matteo"}],"arxiv":1,"title":"Primitive divisors of sequences associated to elliptic curves","status":"public","external_id":{"arxiv":["1906.00632"]},"citation":{"ama":"Verzobio M. Primitive divisors of sequences associated to elliptic curves. <i>Journal of Number Theory</i>. 2020;209(4):378-390. doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.09.003\">10.1016/j.jnt.2019.09.003</a>","ista":"Verzobio M. 2020. Primitive divisors of sequences associated to elliptic curves. Journal of Number Theory. 209(4), 378–390.","mla":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves.” <i>Journal of Number Theory</i>, vol. 209, no. 4, Elsevier, 2020, pp. 378–90, doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.09.003\">10.1016/j.jnt.2019.09.003</a>.","apa":"Verzobio, M. (2020). Primitive divisors of sequences associated to elliptic curves. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2019.09.003\">https://doi.org/10.1016/j.jnt.2019.09.003</a>","ieee":"M. Verzobio, “Primitive divisors of sequences associated to elliptic curves,” <i>Journal of Number Theory</i>, vol. 209, no. 4. Elsevier, pp. 378–390, 2020.","chicago":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves.” <i>Journal of Number Theory</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jnt.2019.09.003\">https://doi.org/10.1016/j.jnt.2019.09.003</a>.","short":"M. Verzobio, Journal of Number Theory 209 (2020) 378–390."},"intvolume":"       209","extern":"1","oa":1,"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1906.00632"}],"date_published":"2020-04-01T00:00:00Z","year":"2020","_id":"12310","oa_version":"Preprint","month":"04","type":"journal_article","date_updated":"2023-05-10T11:14:56Z","abstract":[{"text":"Let  be a sequence of points on an elliptic curve defined over a number field K. In this paper, we study the denominators of the x-coordinates of this sequence. We prove that, if Q is a torsion point of prime order, then for n large enough there always exists a primitive divisor. Later on, we show the link between the study of the primitive divisors and a Lang-Trotter conjecture. Indeed, given two points P and Q on the elliptic curve, we prove a lower bound for the number of primes p such that P is in the orbit of Q modulo p.","lang":"eng"}],"page":"378-390","date_created":"2023-01-16T11:45:07Z","volume":209}]