Non-divisible point on a two-parameter family of elliptic curves
Number Theory
2021-08-23 v2
Abstract
Let n be a positive integer and t a non-zero integer. We consider the elliptic curve over Q given by E : y 2 = x 3 + tx 2 -- n 2 (t + 3n 2)x + n 6. It is a special case of an elliptic surface studied recently by Bettin, David and Delaunay [2] and it generalizes Washington's family. The point (0, n 3) belongs to E(Q) and we obtain some results about its nondivisibility in E(Q). Our work extends to this two-parameter family of elliptic curves a previous study of Duquesne (mainly stated for n = 1 and t > 0).
Keywords
Cite
@article{arxiv.2101.08067,
title = {Non-divisible point on a two-parameter family of elliptic curves},
author = {Valentin Petit},
journal= {arXiv preprint arXiv:2101.08067},
year = {2021}
}