#### Vol. 301, No. 1, 2019

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Lifting of Elliptic curves

### Sanoli Gun and V. Kumar Murty

Vol. 301 (2019), No. 1, 101–106
##### Abstract

Suppose that for all but finitely many primes $p$ we are given an elliptic curve ${E}_{p}$ defined over a finite field ${\mathbb{F}}_{p}$ of $p$ elements. We derive a criterion for there to exist an elliptic curve $E$ defined over $ℚ$ for which the reduction of $E$ modulo $p$ is isogenous to ${E}_{p}$ for almost all $p$.

##### Keywords
lifting of elliptic curves, Chebotarev density theorem, generalized Riemann hypothesis, $\ell$-adic representations attached to elliptic curves
##### Mathematical Subject Classification 2010
Primary: 11F11, 11G05
##### Milestones
Received: 9 November 2018
Accepted: 6 April 2019
Published: 16 September 2019
##### Authors
 Sanoli Gun The Institute of Mathematical Sciences HBNI C.I.T Campus, Taramani Chennai India V. Kumar Murty Department of Mathematics University of Toronto Toronto, ON Canada