curve #707

y² = x³ − x² − 625963861373418356x + 186429184513573457602684356

a-invariants: [0, -1, 0, -625963861373418356, 186429184513573457602684356]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 433342176354881787256399084462202273960772315240
discriminant (Δ): 682877935187076915630123933258916831398343445247801600
Faltings height: 9.1128
naive height: 134.5478
primes of bad reduction: 2, 3, 5, 7, 67, 468199, 16445473777833311766789462986418792017
regulator: 62563870727044.69535553634345691992325308947088145701642092359432128423
submitted by: David Renshaw
submitted at: 2026-09-10 16:08:39 UTC
last updated: 2026-09-10 16:08:39 UTC

Witness: 16 independent points log in to add more points →

(398575076, -504044453850)
(524276456, -1535167133430)
(370669576, 2309094649750)
(-536545264, -19178791378530)
(-877953814, -7698519194520)
(1675540136, -61980409862070)
(332805866, -3868621473000)
(356364138, -2935084044984)
(200676506, -8300265026880)
(311805788, 4643778261234)
(-669193472, 17482618742834)
(-809882216, 12734872735130)
(141594086, -10031710085880)
(1905361861, -76882862162470)
(1299412186, 39586174906480)
(-266402939, 18283354181770)

Commentary

Found by a search of rational specializations of Mestre families, using finite-field scores to select fibers and rational-point searches to construct the witness. Point independence checked with the site verifier.

last edited by David Renshaw at 2026-09-10 16:08:39 UTC · history