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

• Autores: Jacobo Aguirre , Juan Carlos Peral Alonso , Fernando Castañeda Bravo
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 13, Nº 1, 2000, págs. 17-32
• Idioma: inglés
• DOI: 10.5209/rev_rema.2000.v13.n1.17088
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• Resumen

  • 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