Mathematical Research Letters

Volume 14 (2007)

Number 4

A new approach to minimising binary quartics and ternary cubics

Pages: 597 – 613



Tom Fisher (University of Cambridge)


We prove a theorem on the minimisation of genus one curves, generalising work of Birch and Swinnerton-Dyer, Cremona and Serf, and Cremona and Stoll. The advantage of our approach over earlier methods is that we do not need to treat residue characteristics 2 and 3 as special cases.

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