curve #347

y² + xy = x³ − 7825076977946661057500886536x + 267129303320099174770669569025143803236416

a-invariants: [1, 0, 0, -7825076977946661057500886536, 267129303320099174770669569025143803236416]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 71980039431687992091942838657160225518541452772249974246307039430
naive height: 204.3002
Faltings height: 14.8349
discriminant (Δ): -161481963868349728343894906983811129192119744590010308336788056503431538562144665600
primes of bad reduction: 2, 3, 5, 11, 13, 23, 230409719, 3357805369, 5404168209821, 7586019315246809018734444433
regulator: 45658817351372557765.84762731104967074203942269027872702843322079565992891893
submitted by: Christopher R. Hill
submitted at: 2026-08-25 10:35:51 UTC
last updated: 2026-08-25 10:35:51 UTC

Witness: 19 independent points

(-269994352556697044/6241, -357134263261356806167547912/493039)
(116376796986928330/2209, 3447125899280579992778348/103823)
(109949136054695176, -36457559385201629517042248)
(50651785940488, 26973562694658330040)
(3345494618949049/64, -15558487284249269508271/512)
(39821135577616, 136642346228325331192)
(21976186516757717606416/55815841, -3181849994888976637542194777854328/417000148111)
(1356345325443624995728/4618201, -47908038480877346820268958188520/9924513949)
(567470333332610202640/20784481, 25748064756758868215010767826824/94756448879)
(665466253719971970064/12496225, -1676272119194302949301420634232/44174155375)
(40599832698126693136/844561, 35163261579684769171697428168/776151559)
(53895044707600, -44091570678290354696)
(1575222637383952/49, 75768315498008614494280/343)
(-93011338658384, 436232723071273845592)
(-1413589876209776/25, 90898929294398079112472/125)
(63046635759478, -156164138942821557530)
(1128212607856144, 37782265650034032051448)
(6147660794800, 468247503506462889304)
(340862584566325456/11881, -333314762136602848125876392/1295029)

Commentary

Found with Rank Hunter v0.7.21; family=Mestre/Fermigier sextuple, generic rank >=11; parameter=14829/16; local status: rigorous rank lower bound >= 19.

last edited by Christopher R. Hill at 2026-08-25 10:35:52 UTC · history