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ON THE NUMBER OF ELLIPTIC CURVES WITH PRESCRIBED ISOGENY OR TORSION GROUP OVER NUMBER FIELDS OF PRIME DEGREE

Part of: Arithmetic algebraic geometry Curves

Published online by Cambridge University Press:  18 December 2014

FILIP NAJMAN
FILIP NAJMAN*
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička Cesta 30, 10000 Zagreb, Croatia e-mail: fnajman@math.hr
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Abstract

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Let p be a prime and K a number field of degree p. We determine the finiteness of the number of elliptic curves, up to K-isomorphism, having a prescribed property, where this property is either that the curve contains a fixed torsion group as a subgroup or that it has a cyclic isogeny of prescribed degree.

MSC classification

Primary: 11G05: Elliptic curves over global fields
Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties 14H52: Elliptic curves
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 2 , May 2015 , pp. 465 - 473
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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