We discuss the distribution of Mordell-Weil ranks of the family of elliptic curves y² = (x + αf²)(x + βbg²)(x + γh²) where f,g,h are coprime polynomials that parametrize the projective smooth conic a² + b² = c² and α,β,γ are elements from ℚ̅. In our previous papers we discussed certain special cases of this problem and in this article we complete the picture by proving the general results.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-16,
author = {Bartosz Naskr\k ecki},
title = {Distribution of Mordell-Weil ranks of families of elliptic curves},
journal = {Banach Center Publications},
volume = {108},
year = {2016},
pages = {201-229},
zbl = {06622296},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-16}
}
Bartosz Naskręcki. Distribution of Mordell-Weil ranks of families of elliptic curves. Banach Center Publications, Tome 108 (2016) pp. 201-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-16/