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University of Cambridge > Talks.cam > Number Theory Seminar > Ranks of elliptic curves with prescribed torsion over number fields

## Ranks of elliptic curves with prescribed torsion over number fieldsAdd to your list(s) Download to your calendar using vCal - Johan Bosman (Warwick)
- Tuesday 28 February 2012, 14:30-15:30
- MR13.
If you have a question about this talk, please contact Tom Fisher. Let E(K), where K is a number field of degree
d and E is an elliptic curve over K. T is known by Mazur’s theorem,
_{1}T is known as well, and for _{2}d equal to 3 or 4, it is known which
groups occur infinitely often.We shall study the following problem: given a E, where
E is an elliptic curve over a number field K of degree d with the torsion subgroup of E(K)
isomorphic to T. For d = 2 and T = or Z/13ZT = , and also for Z/18Zd = 4 and
T = , it turns out that the rank is always even. This will be
explained by a phenomenon we call “false complex multiplication”.Z/22ZThis is joint work with Peter Bruin, Andrej Dujella, and Filip Najman. This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
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