Three elliptic curves with rank at least seven
HTML articles powered by AMS MathViewer
- by David E. Penney and Carl Pomerance PDF
- Math. Comp. 29 (1975), 965-967 Request permission
Abstract:
Three rational elliptic curves whose ranks are at least 7 are exhibited. The arithmetical details are given for one of the curves, namely ${y^2} = {x^3} + 1692602{x^2} - 530052723915x$ .References
- André Néron, Problèmes arithmétiques et géométriques rattachés à la notion de rang d’une courbe algébrique dans un corps, Bull. Soc. Math. France 80 (1952), 101–166 (French). MR 56951
- David E. Penney and Carl Pomerance, A search for elliptic curves with large rank, Math. Comp. 28 (1974), 851–853. MR 376686, DOI 10.1090/S0025-5718-1974-0376686-X
- A. Wiman, Über rationale Punkte auf Kurven dritter Ordnung vom Geschlechte Eins, Acta Math. 80 (1948), 223–257 (German). MR 28603, DOI 10.1007/BF02393650
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 965-967
- MSC: Primary 14G25; Secondary 10B10, 14G05
- DOI: https://doi.org/10.1090/S0025-5718-1975-0376687-2
- MathSciNet review: 0376687