Explicit isogenies of prime degree over number fields

par Barinder Banwait (Ruprecht-Karls-Universität Heidelberg)

jeudi 7 avr. 2022, 14:00 → 15:00 Europe/Paris

M7.411 (ENS Lyon, UMPA)

We provide an explicit and algorithmic version of a theorem of Momose classifying isogenies of prime degree of elliptic curves over number fields, which we implement in Sage and PARI/GP. Combining this algorithm with recent work of Box-Gajović-Goodman we determine the first instances of isogenies of prime degree for cubic number fields, as well as for several quadratic fields not previously known. While the correctness of the general algorithm relies on the Generalised Riemann Hypothesis, the algorithm is unconditional for the restricted class of semistable elliptic curves. This is joint work with Maarten Derickx.

Link to the preprint: https://arxiv.org/pdf/2203.06009.pdf