Rank Frequencies for Quadratic Twists of Elliptic Curves

Rubin, Karl; Silverberg, Alice

Experiment. Math., Tome 10 (2001) no. 3, p. 559-570 / Harvested from Project Euclid

Résumé

We give explicit examples of infinite families of elliptic curves $E$ over $\funnyQ$ with (nonconstant) quadratic twists over $\funnyQ(t)$ of rank at least $2$ and $3$. We recover some results announced by Mestre, as well as some additional families. Suppose $D$ is a squarefree integer and let $r_E(D)$ denote the rank of the quadratic twist of $E$ by $D$. We apply results of Stewart and Top to our examples to obtain results of the form {\#\{D : |D|

Publié le : 2001-05-14
Classification:

@article{1069855256,
     author = {Rubin, Karl and Silverberg, Alice},
     title = {Rank Frequencies for Quadratic Twists of Elliptic Curves},
     journal = {Experiment. Math.},
     volume = {10},
     number = {3},
     year = {2001},
     pages = { 559-570},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1069855256}
}

Rubin, Karl; Silverberg, Alice. Rank Frequencies for Quadratic Twists of Elliptic Curves. Experiment. Math., Tome 10 (2001) no. 3, pp.  559-570. http://gdmltest.u-ga.fr/item/1069855256/