Rank frequencies for quadratic twists of elliptic curves
| dc.creator | Rubin, Karl | |
| dc.creator | Silverberg, Alice | |
| dc.date | 2000-10-05 | |
| dc.date | 2001-06-04 | |
| dc.date.accessioned | 2026-07-07T04:37:52Z | |
| dc.date.available | 2026-07-07T04:37:52Z | |
| dc.description | We give explicit examples of infinite families of elliptic curves E over Q with (nonconstant) quadratic twists over Q(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| < x, r_E(D) >= 2} >> x^{1/3}, #{D : |D| < x, r_E(D) >= 3} >> x^{1/6} for all sufficiently large x. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0010056 | |
| dc.identifier | http://arxiv.org/abs/math/0010056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60063 | |
| dc.subject | Number Theory | |
| dc.title | Rank frequencies for quadratic twists of elliptic curves | |
| dc.type | text |