Torsion of rational elliptic curves over cubic fields and sporadic points on $X_1(n)$

By Filip Najman. 2012

90 citations recorded by the source corpus.

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 $X_1(21)$ of degree 3, which is the lowest possible degree of a sporadic point on a modular curve $X_1(n)$.

Subfields: Geometry and Topology, Information Systems, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/992e3bcee2cc68f3f4514e1306e3689414c37f73

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In Geometry and Topology

1. David Zureick-Brown
2. 'Alvaro Lozano-Robledo

In Information Systems

1. David Zureick-Brown

In Mathematical Physics

1. David Zureick-Brown
2. 'Alvaro Lozano-Robledo

Citations in the corpus

• Sporadic cubic torsion (2020, background): “It was formally conjectured in [Wan15, Conjecture 1.1.2] that the only possible torsion structures for elliptic curves over K are the ones identified by Jeon–Kim–Schweizer and Najman [JKS04, Naj16].”