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We derive equations for the modular curve $X_{ns}(11)$ associated to anon-split Cartan subgroup of $\,\mathrm{GL}_2(\mathbf{F}_{11})$. This allows usto compute the automorphism group of the curve and show that it is isomorphicto Klein's four group.

The automorphism group of the non-split Cartan modular curve of level 11