Calculating the j-invariants of elliptic curves with non-split mod 11 representation using Magma

Imin Chen, CECM

We calculate explicitly using Magma the $j$-invariants of the elliptic
curves classified by modular curve $X_{ns}^+(11)$ by giving an expression
defined over $\q$ 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 $\q$ with non-split
mod $11$ galois structure. This is joint work with Chris Cummins.