Mathematical Research Letters
Volume 14 (2007)
A new approach to minimising binary quartics and ternary cubics
Pages: 597 – 613
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.