The complex AGM, periods of elliptic curves over C and complex elliptic logarithms

Details The complex AGM, periods of elliptic curves over C and complex elliptic logarithms The complex AGM, periods of elliptic curves over C and complex elliptic logarithms

2010-11-03

arxiv.org/abs/1011.0914v1

Mathematics

Number Theory

Scientific paper

We present a method for computing period lattices and elliptic logarithms for elliptic curves defined over C, using the complex Arithmetic-Geometric Mean (AGM) first studied by Gauss. Earlier authors have only considered the case of elliptic curves defined over the real numbers; here, the multi-valued nature of the complex AGM plays an important role. Our method, which we have implemented in both Magma and Sage, is illustrated with several examples.

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