Optimal curves differing by a 3-isogeny

Dongho Byeon, Donggeon Yhee
2013 Acta Arithmetica  
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 C containing E of conductor N differ by a 3-isogeny. In this paper, we show that this conjecture is true.
doi:10.4064/aa158-3-2 fatcat:vpiuwqwys5e3jp4geemorjbhta