Torsion points on elliptic curves over number fields of small degree

Abstract

We determine the set $S(d)$ of possible prime orders of $K$-rational points on elliptic curves over number fields $K$ of degree $d$, for $d=4$, $5$, $6$, and $7$.

v2: Paper almost completely rewritten; exact determination of S(7) is new; added classification of elliptic curves over sextic fields with a point of order 37

Cited by in corpus (11)

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• On the torsion of rational elliptic curves over quartic fields
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• Computing quadratic points on modular curves $X_0(N)$
• On elliptic curves with $p$-isogenies over quadratic fields
• Classification of torsion of elliptic curves over quartic fields
• Towards a classification of isolated $j$-invariants
• Torsion primes for elliptic curves over degree 8 number fields
• A single source theorem for primitive points on curves
• Fermat's Last Theorem over $\mathbb{Q}(\sqrt{2},\sqrt{3})$
• Explicit isogenies of prime degree over number fields