High rank elliptic curves of the form y2=x3 + Bx

  1. Aguirre, Jacobo
  2. Peral Alonso, Juan Carlos
  3. Castañeda Bravo, Fernando
Journal:
Revista matemática complutense

ISSN: 1139-1138,  1988-2807

Year of publication: 2000

Volume: 13

Issue: 1

Pages: 17-32

Type: Article

DOI: 10.5209/REV_REMA.2000.V13.N1.17088 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista matemática complutense

Abstract

Seven elliptic curves of the form y2 = x3 + B x and having rank at least 8 are presented. To find them we use the double descent method of Tate. In particular we prove that the curve with B = 14752493461692 has rank exactly 8

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