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arXiv · 1810.00320

A Necessary and Sufficient Condition for Existence of a Rational Point on an Elliptic Curve

P. Gao
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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.

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P. Gao. 2018-09-30. A Necessary and Sufficient Condition for Existence of a Rational Point on an Elliptic Curve. https://arxiv.org/abs/1810.00320

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