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Elliptic curves with nonsplit mod $11$ representations
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 …