Resumen de Torsion on elliptic curves in isogeny classes

Yasutsugu Fujita, Tetsuo Nakamura

• 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 .