Explicit isogeny descent on elliptic curves

@article{Miller2013ExplicitID,
  title={Explicit isogeny descent on elliptic curves},
  author={Robert L. Miller and Michael Stoll},
  journal={Math. Comput.},
  year={2013},
  volume={82},
  pages={513-529}
}
In this note, we consider an `-isogeny descent on a pair of elliptic curves over Q. We assume that ` > 3 is a prime. The main result expresses the relevant Selmer groups as kernels of simple explicit maps between finitedimensional F`-vector spaces defined in terms of the splitting fields of the kernels of the two isogenies. We give examples of proving the `-part of the Birch and Swinnerton-Dyer conjectural formula for certain curves of small conductor. 
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12 Citations
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