Optimal curves differing by a 3-isogeny
Volume 158 / 2013
Acta Arithmetica 158 (2013), 219-227
MSC: Primary 11G05; Secondary 14K02.
DOI: 10.4064/aa158-3-2
Abstract
Stein and Watkins conjectured that for a certain family of elliptic curves $E$, the $X_0(N)$-optimal curve and the $X_1(N)$-optimal curve of the isogeny class $\mathcal {C}$ containing $E$ of conductor $N$ differ by a 3-isogeny. In this paper, we show that this conjecture is true.
