Rank parity for congruent supersingular elliptic curves

Jeffrey Hatley

doi:10.1090/proc/13545

Rank parity for congruent supersingular elliptic curves

Number Theory 2017-06-19 v4

Authors: Jeffrey Hatley

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

A recent paper of Shekhar compares the ranks of elliptic curves $E_1$ and $E_2$ for which there is an isomorphism $E_1[p] \simeq E_2[p]$ as $\mathrm{Gal}(\bar{\mathbf{Q}}/\mathbf{Q})$ -modules, where $p$ is a prime of good ordinary reduction for both curves. In this paper we prove an analogous result in the case where $p$ is a prime of good supersingular reduction.

Keywords

elliptic curves rank parity supersingular reduction ordinary reduction galois modules isomorphism number theory

Cite

@article{arxiv.1605.08382,
  title  = {Rank parity for congruent supersingular elliptic curves},
  author = {Jeffrey Hatley},
  journal= {arXiv preprint arXiv:1605.08382},
  year   = {2017}
}

Comments

fixed a persistent typo in the results of Section 3. this typo led to the original example for p=3 being incorrect; it has been replaced with a correct example

Rank parity for congruent supersingular elliptic curves

Abstract

Keywords

Cite

Comments

Related papers