No 17-torsion on elliptic curves over cubic number fields
نویسنده
چکیده
Consider, for d an integer, the set S(d) of prime numbers p such that: there exists a number field K of degree d, an elliptic curve E overK, and a point P in E(K) of order p. It is a well-known theorem of Mazur, Kamienny, Abramovich and Merel that S(d) is finite for every d; moreover S(1) and S(2) are known. In [7], we tried to answer a question of Kamienny and Mazur by determining S(3), and we proved S(3) = {2, 3, 5, 7, 11, 13 and may be 17}. (Actually in loc. cit. we made for some p’s the arithmetic assumption (called (∗)p there) that J1(p)’s winding quotient has rank 0 over Q. This is now known to be true for every p, by Kato’s almost published work
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