A Necessary and Sufficient Condition for Existence of a Rational Point on an Elliptic Curve
Number Theory
2018-12-05 v1
Abstract
In this paper, the proof of the existence of a rational point on an elliptic curve is transformed into the proof of the existence of an integer solution for a Diophantine equation. By a new formula for calculating the number of elements in intersection of two finite sets, a necessary and sufficient condition for existence of a rational point on an elliptic curve is established. This condition is different from L-function in the Birch and Swinnerton-Dyer conjecture.
Keywords
Cite
@article{arxiv.1810.00320,
title = {A Necessary and Sufficient Condition for Existence of a Rational Point on an Elliptic Curve},
author = {P. Gao},
journal= {arXiv preprint arXiv:1810.00320},
year = {2018}
}