Testing equivalence of ternary cubics

Authors:
Tom Fisher
Affiliations:
DPMMS, Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK
Venue:
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Year:
2006

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Abstract

Let C be a smooth plane cubic curve with Jacobian E. We give a formula for the action of the 3-torsion of E on C, and explain how it is useful in studying the 3-Selmer group of an elliptic curve defined over a number field.