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

Jacobo Aguirre, Juan Carlos Peral Alonso, Fernando Castañeda Bravo

• 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