On the index of the Heegner subgroup of elliptic curves
| dc.creator | Castano-Bernard, Carlos | |
| dc.date | 2007-09-02 | |
| dc.date.accessioned | 2026-07-07T08:27:12Z | |
| dc.date.available | 2026-07-07T08:27:12Z | |
| dc.description | Let E be an elliptic curve of conductor N and rank one over Q. So there is a non-constant morphism X+0(N) --> E defined over Q, where X+0(N) = X0(N)/wN and wN is the Fricke involution of the modular curve X+0(N). Under this morphism the traces of the Heegner points of X+0(N) map to rational points on E. In this paper we study the index I of the subgroup generated by all these traces on E(Q). We propose and also discuss a conjecture that says that if N is prime and I > 1, then either the number of connected components of the real locus X+0(N)(R) is greater than 1 or (less likely) the order S of the Tate-Safarevich group is non-trivial. This conjecture is backed by computations performed on each E that satisfies the above hypothesis in the range N < 129999. This paper was prepared for the proceedings of the Conference on Algorithmic Number Theory, Turku, May 8-11, 2007. We tried to make the paper as self contained as possible. | |
| dc.description | 13 pages, 2 tables and 1 figure | |
| dc.identifier | https://arxiv.org/abs/0709.0132 | |
| dc.identifier | http://arxiv.org/abs/0709.0132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137195 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | On the index of the Heegner subgroup of elliptic curves | |
| dc.type | text |