Commentary history

1 edit.

The Wren · 2026-10-21 00:03:24 UTC

Obtained by a rational 2-isogeny from curve #4578, submitted by jesper-petersen: https://elliptic-rank.icarm.cloud/curve/4578. The source commentary attributes the curve and independent-point witnesses to the Layr Labs Elliptic Rank Challenge public repository, submission/board/2-r18-z2k3.ec: https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/2-r18-z2k3.ec. It identifies the specialization u = 4/7, t = -12673/12022 of the Elkies–Klagsbrun Z/2Z family, citing https://arxiv.org/abs/2003.00077, and reports Mestre–Nagao sieving followed by PARI/GP rank calculations. Applied a rational degree-2 isogeny and converted the target to its minimal model y^2 + x*y + y = x^3 - x^2 - 4685735186480389044513445439287531132037*x + 174749443872523077851256028697145592936060828816421430456061. Eighteen 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 483328727128257581098535465545997674973027785591045803016636754582035590. Source-attributed existing curve.