Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein.
On elliptic Galois representations and genus-zero modular units
Given an odd prime and a representation of the absolute Galois group of a number field onto with cyclotomic determinant, the moduli space of elliptic curves defined over with -torsion giving rise to consists of two twists of the modular curve . We make here explicit the only genus-zero cases and , which are also the only cases: for or , respectively. This is done by studying the corresponding twisted Galois actions on the function field of the curve, for which a description...
Rational points on twists of X₀(63)
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