curve #6033

y² + xy + y = x³ − 711386760194875075232620917118x + 221990158614264542997161297566829380381098908

a-invariants: [1, 0, 1, -711386760194875075232620917118, 221990158614264542997161297566829380381098908]
c-invariants: [34146564489354003611165804021641, -191799497042724616369394095128746001397975489189]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 101164411429739150871932825580925108907114527197963443603225211803566536418110
discriminant (Δ): 1751986579203881860685957837715627579477435566986429832485519444642983239939944370900062500
Faltings height: 16.0792
naive height: 217.8246
primes of bad reduction: 2, 3, 5, 7, 13, 17, 13317956467, 135981212614783, 13226906932995318982937522899361934859799666221
regulator: 29354168927690873506652.10044386869012860099435843994809686283635608640820391325164
submitted by: apkorte
submitted at: 2026-10-28 14:32:25 UTC
last updated: 2026-10-28 14:32:25 UTC

Witness: 22 independent points log in to add more points →

(565363806355219, 713154483832540064015)
(-509643659831396, 21264307641557153887700)
(316993292046484, 5323374560417789885255)
(4799351924389894, 327650735129897642700665)
(-493269620455796, 21280878478761423285620)
(-864127418933831, -13836943750347764605285)
(4802670340679719, 327997117576655359374515)
(338780664106744, 4457435031894743807915)
(570931081927609, 1392606885066309435755)
(2583357643089094, -124999491201269771521735)
(2253007628936104, -100277589907893174528805)
(402265615162594, 957805848076257379640)
(1308742885990219, 39148345488185010200765)
(-950875158055406, -6219604232915722584235)
(2335621805997169, -106308883634360696501785)
(2826159087719839, 144168392305153246605275)
(-133095542249981, 17728927118916351270815)
(2435592855251131/4, -30548405722480172927525/8)
(-29280710321774159/64, 10881571160052062865446605/512)
(10406853173250769, 1058256993787289135772815)
(1463307848164579, -48107685339438911893825)
(1576440824146969, -54938581478418935573485)

Commentary

Specialization at T = -25/31 of the rank-17 fibration of X1008 given in curve#3594. 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 2026-10-28 14:32:25 UTC · history