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Calculating the j-invariants of elliptic curves with non-split mod 11 representation using MagmaImin 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. |