Torsion of rational elliptic curves over cubic fields and sporadic points on X₁(n)

2012/11/09 by Najman, Filip · 2 citations
#11G05 #11G18 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1211.2188

Abstract

We classify the possible torsion structures of rational elliptic curves over cubic fields. Along the way we find a previously unknown torsion structure over a cubic field, \Z /21 \Z, which corresponds to a sporadic point on X₁(21) of degree 3, which is the lowest possible degree of a sporadic point on a modular curve X₁(n).

Cited by

• Stability of torsion subgroups of elliptic curves over non-Galois extensions of odd prime degree
• Rational isolated j-invariants from X₁(ℓⁿ) and X₀(ℓⁿ)

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