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On the Existence of Elliptic Curves of Mordell–Weil Rank 6 with Four Parameters

✍ Scribed by Hizuru Yamagishi


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
92 KB
Volume
181
Category
Article
ISSN
0021-8693

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✦ Synopsis


We construct an elliptic curve defined over Q with Mordell᎐Weil rank G 6 as a generic twist by a certain quadratic extension. Moreover, since they have four independent parameters, they give us rather a large supply of elliptic curves defined over Q with rank G 6. As an application, we find infinitely many pairs Ž .

a ,b of rational numbers such that the elliptic curve by s x q ax q ax q 1 is of Mordell᎐Weil rank G 6.