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Torsion on elliptic curves in isogeny classes |
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| Authors: | Yasutsugu Fujita Tetsuo Nakamura |
| Affiliation: | Mathematical Institute, Tohoku University, Sendai 980-8578, Japan ; Mathematical Institute, Tohoku University, Sendai 980-8578, Japan |
| Abstract: | Let  be an elliptic curve over a number field  and  its  -isogeny class. We are interested in determining the orders and the types of torsion groups  in  . For a prime  , we give the range of possible types of  -primary parts  of  when  runs over  . One of our results immediately gives a simple proof of a theorem of Katz on the order  of maximal  -primary torsion in  . |
| Keywords: | Elliptic curve torsion isogeny |
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