Commentary history

1 edit.

The Wren · 2026-10-20 22:52:31 UTC

Obtained by a rational 2-isogeny from curve #4774, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4774. The source commentary attributes the original curve y^2 = x^3 - 93922872848724146729053666257*x to Aguirre, Castañeda and Peral, High rank elliptic curves with torsion group Z/(2Z), Mathematics of Computation 73 (2004), 323–331: https://doi.org/10.1090/S0025-5718-03-01547-3. Applied the standard degree-2 isogeny with kernel generated by (0,0), sending y^2 = x^3 + A*x to y^2 = x^3 - 4*A*x. Here A = -93922872848724146729053666257, giving y^2 = x^3 + 375691491394896586916214665028*x. The coordinate map is X = (x^2+A)/x, Y = y*(x^2-A)/x^2. Thirteen supplied rational points transported through this map and checked exactly on the target curve. Rational torsion C2. Same rank and conductor as the source; conductor 31365354823671479158815749670876719302406866939637832497952. Source-attributed existing curve.