Tamagawa numbers of elliptic curves with prescribed torsion subgroup or isogeny

نویسندگان

چکیده

We study Tamagawa numbers of elliptic curves with torsion Z/2Z?Z/14Z over cubic fields and an n-isogeny Q, for n?{6,8,10,12,14,16,17,18,19,37,43,67,163}. Bruin Najman [3] proved that every curve a field is base change defined Q. find Q are always divisible by 142, each factor 14 coming from rational prime split multiplicative reduction type I14k, one which p=2. The only exception the 1922.e2, cE=c2=14. same they have subgroup turn out to number 143. As n-isogenies, 18-isogeny must be 4, while remaining n mentioned set 2, except finite sets specified curves.

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ژورنال

عنوان ژورنال: Journal of Number Theory

سال: 2022

ISSN: ['0022-314X', '1096-1658']

DOI: https://doi.org/10.1016/j.jnt.2021.09.007