curve #6224

y² = x³ + x² − 58688527466280191366935634849293x + 172828260414429225351633173655215433532259221775

a-invariants: [0, 1, 0, -58688527466280191366935634849293, 172828260414429225351633173655215433532259221775]
c-invariants: [2817049318381449185612910472766080, -149323616998066867606106972326801248249334804210048]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 32736769003255761661213081100841716671044
discriminant (Δ): 33509280434380543360357017041321430555282471573413743534292586529714061858761810356196810904832
Faltings height: 17.0382
naive height: 231.0630
primes of bad reduction: 2, 3, 11, 17, 19, 29, 37, 41, 43, 101, 107, 127, 401, 523, 5653, 174367, 1430569993
regulator: 36160012338.8015505411981558718880256143257825410716899367730
submitted by: apkorte
submitted at: 2026-10-31 05:26:14 UTC
last updated: 2026-10-31 05:26:14 UTC

Witness: 11 independent points log in to add more points →

(3895655569767581, 57610380159491195845638)
(4287874121782562, 3938879900303750591409)
(4290876981013577, 2242297379148899056974)
(-31872933962943807478/6241, 287214642001257889806446942229/493039)
(-7608955894950968875/961, 11192054601994201351278045270/29791)
(16140342961911413/4, 331199125566333659392527/8)
(16650741910130525/4, 205085247482993351439195/8)
(116675491030211501/25, 3011546511560158776028674/125)
(117102686112454121/25, 3303051665851967332418406/125)
(223292894023447634/49, 1390298597139014097249231/343)
(1774749874632616474937/414736, 1831172193952016802485747317749/267089984)

Commentary

Specialization at T = 5332/6817 of the fibration given in curve#6191. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-31 05:26:14 UTC · history