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arXiv · 1110.4232

The class group pairing and $p$-descent on elliptic curves

Jean Gillibert·Christian Wuthrich
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Abstract

We give explicit formulae for the logarithmic class group pairing on an elliptic curve defined over a number field. Then we relate it to the descent relative to a suitable cyclic isogeny. This allows us to connect the resulting Selmer group with the logarithmic class group of the base. These constructions are explicit and suitable for computer experimentation. From a conceptual point of view, the questions that arise here are analogues of "visibility" questions in the sense of Cremona and Mazur.

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Jean Gillibert, Christian Wuthrich. 2011-10-19. The class group pairing and $p$-descent on elliptic curves. https://doi.org/10.1112/plms%2Fpds044

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