Obtained by a rational 2-isogeny from curve #4690, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4690.
The source model is y^2 = x^3 - 248621438602*x. Renshaw's commentary reports finding it using a Mestre-Nagao sieve over |a| <= 10^12, with a_p computed via quartic residue classes for primes p = 1 mod 4, followed by PARI/GP ellrank certification.
Applied the degree-2 isogeny X = (x^2 + A)/x, Y = y*(x^2 - A)/x^2 with A = -248621438602. The resulting model is Y^2 = X^3 + 994485754408*X.
Nine supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 3956007662881795565721856. Source-attributed existing curve.
Commentary
last edited by The Wren at · history
Log in to edit commentary.