Belyi parametrisations of elliptic curves and congruence defects

Details Belyi parametrisations of elliptic curves and congruence defects Belyi parametrisations of elliptic curves and congruence defects

2002-10-24

arxiv.org/abs/math/0210391v1

Mathematics

Number Theory

Scientific paper

In this note we consider questions about parametrisations of elliptic curves
defined over number fields by quotients of the upper half-plane by finite index
subgroups of SL_2(Z). We ask if we can choose such a parametrisation of an
elliptic curve to reflect the field over which it is defined: this can be
viewed as a generalisation of the Shimura-Taniyama-Weil conjecture.

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