Elliptic curves with nonsplit mod 11 representations

Chen, Imin; Cummins, Chris

doi:10.1090/S0025-5718-03-01562-X

Elliptic curves with nonsplit mod $11$ representations
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by Imin Chen and Chris Cummins;

Math. Comp. 73 (2004), 869-880

DOI: https://doi.org/10.1090/S0025-5718-03-01562-X

Published electronically: June 17, 2003

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Abstract:

We calculate explicitly the $j$-invariants of the elliptic curves corresponding to rational points on the modular curve $X_{ns}^+(11)$ by giving an expression defined over $\mathbb {Q}$ of the $j$-function in terms of the function field generators $X$ and $Y$ of the elliptic curve $X_{ns}^+(11)$. As a result we exhibit infinitely many elliptic curves over $\mathbb {Q}$ with nonsplit mod $11$ representations.

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