On families of 9-congruent elliptic curves

• Autorzy: Tom Fisher
• Języki publikacji: EN

Abstrakty

EN

We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.

Kategorie tematyczne

• 11F80: Galois representations
• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 171
• Numer: 4
• Strony: 371-387

Daty

wydano

2015

Twórcy

autor

Tom Fisher

• DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK

Identyfikatory

DOI

10.4064/aa171-4-5