Functions and differentials on the non-split Cartan modular curve of level 11

Fernández, Julio; González, Josep

doi:10.1090/mcom/3109

Functions and differentials on the non-split Cartan modular curve of level 11
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by Julio Fernández and Josep González PDF

Math. Comp. 86 (2017), 437-454 Request permission

Abstract:

The genus $4$ modular curve $X_{ns}(11)$ attached to a non-split Cartan group of level $11$ admits a model defined over $\mathbb {Q}$. We compute generators for its function field in terms of Siegel modular functions. We also show that its Jacobian is isomorphic over $\mathbb {Q}$ to the new part of the Jacobian of the classical modular curve $X_0(121)$.

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