Stein and Watkins conjectured that for a certain family of elliptic curves E, the X₀(N)-optimal curve and the X₁(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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-2,
author = {Dongho Byeon and Donggeon Yhee},
title = {Optimal curves differing by a 3-isogeny},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {219-227},
zbl = {1294.11087},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-2}
}
Dongho Byeon; Donggeon Yhee. Optimal curves differing by a 3-isogeny. Acta Arithmetica, Tome 161 (2013) pp. 219-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-2/