Torsion subgroups of elliptic curves over quintic and sextic number fields

Abstract

Let ${\Phi }^{\infty }(d)$ denote the set of finite abelian groups that occur infinitely often as the torsion subgroup of an elliptic curve over a number field of degree $d$. The sets ${\Phi }^{\infty }(d)$ are known for $d\le 4$. In this article we determine ${\Phi }^{\infty }(5)$ and ${\Phi }^{\infty }(6)$.

Minor edits. 10 pages

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