Mathematical Research Letters

Volume 6, Issue 6, November 1999 pp. 735-754.

Pairs of mod~3 and mod~5 representations arising from elliptic curves

Authors: J. Manoharmayum
Author institution: Department of Pure Mathematics and Mathematical Statistics

Summary: For an elliptic curve~$E_0$ over~$\mathbb{Q}$, we study the mod~$3$ representations, restricted to a decomposition group at $3$, of elliptic curves over~$\mathbb{Q}$ whose mod~$5$ representations are equivalent to the mod~$5$ representation given by~$E_0$. Complete lists are obtained describing the mod~$3$ representations up to equivalence and twist by the quadratic unramified character of~$\mathbb{Q}_3.$

Contents Full-Text PDF