Torsion subgroups of elliptic curves over quintic and sextic number fields. (English) Zbl 1421.11049
Summary: 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 \( d \leq 4\). In this article we determine \(\Phi^\infty (5)\) and \(\Phi^\infty (6)\).
MSC:
| 11G05 | Elliptic curves over global fields |
| 11G18 | Arithmetic aspects of modular and Shimura varieties |
| 14G35 | Modular and Shimura varieties |
| 14H51 | Special divisors on curves (gonality, Brill-Noether theory) |
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