Elementary 3-descent with a 3-isogeny
Henri Cohen, Fabien Pazuki
TL;DR
This paper explains how to perform 3-descent with a 3-isogeny on elliptic curves with rational 3-torsion, providing practical methods and geometric insights for estimating their rank.
Contribution
It offers a practical approach and geometric interpretation for 3-descent with a 3-isogeny on elliptic curves with rational 3-torsion.
Findings
Method for estimating elliptic curve rank using 3-descent with 3-isogeny
Geometric interpretation of the descent computations
Practical procedures for elliptic curves with rational 3-torsion
Abstract
In this expository paper, we show how to use in practice 3-descent with a 3-isogeny to find an estimate for the rank of an elliptic curve having a rational 3-torsion subgroup, and we also give a geometric interpretation of these computations.
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Taxonomy
TopicsFinite Group Theory Research · DNA and Nucleic Acid Chemistry