SELF-POINTS ON ELLIPTIC CURVES OF PRIME CONDUCTOR

Author:

DELAUNAY CHRISTOPHE1,WUTHRICH CHRISTIAN2

Affiliation:

1. Université de Lyon, Université Lyon 1, Institut Camille Jordan, CNRS, UMR5208, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France

2. School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom

Abstract

Let E be an elliptic curve of conductor p. Given a cyclic subgroup C of order p in E[p], we construct a modular point PC on E, called self-point, as the image of (E,C) on X0(p) under the modular parametrization X0(p) → E. We prove that the point is of infinite order in the Mordell–Weil group of E over the field of definition of C. One can deduce a lower bound on the growth of the rank of the Mordell–Weil group in its PGL 2(ℤp)-tower inside ℚ(E[p]).

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Root numbers and parity phenomena;Bulletin of the London Mathematical Society;2023-10-05

2. Kolyvagin derivatives of modular points on elliptic curves;Journal of Number Theory;2021-12

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