curve #5554

y² + xy = x³ − 1125378537930032743714003012350974165x + 462246539254973183830444025414897429024762252178860001

a-invariants: [1, 0, 0, -1125378537930032743714003012350974165, 462246539254973183830444025414897429024762252178860001]
c-invariants: [54018169820641571698272144592846759921, -399381009916296830910530892689433736224802802771805180745]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 476104570504501398739270545163834259959297573986356551600416936761112424531045295418
discriminant (Δ): -1089229167664457582790386924321632486900844914467639084664044101008568752957713727449034710429641602363097088
Faltings height: 19.5643
naive height: 260.6590
primes of bad reduction: 2, 3, 11, 13, 17, 23, 47, 109, 2907113203012606392757556882232508109, 95291026647437678648324307727994734433
regulator: 2729077779432523759548759.2718364565287489315500480566489342216977101847175279607330127
submitted by: apkorte
submitted at: 2026-10-23 02:16:42 UTC
last updated: 2026-10-23 02:16:42 UTC

Witness: 24 independent points log in to add more points →

(511112210719277578, 143431442834874631660117159)
(26385866248362192034/49, -38177829464463623876920015871/343)
(751158193499226610, 201845735179119711246758071)
(897505206215043666, 418530623119396632135971703)
(-594827502655726958, -959786914347200771986115081)
(295827196498249234, 393977033239132038315973111)
(612016897900652770, 52304617589768508099360391)
(617239355275628050, 52699097243797016955919351)
(-615985741259348990, -960070313501119295600259881)
(519513440126678590, -133457616756453439704105821)
(168686249602181992354/225, 674396850231975063178543784137/3375)
(3703579694729097618, 6862541639804581423541661303)
(72637522720305713410, -619006882068001792854056634329)
(582099789480539842, 66352979322229091532917479)
(503708643713317360, 152268864265039285948145569)
(609327842556898834, 52474372553116689928760311)
(5972700137677987954, 14380740854098320867316909495)
(113247742320590218498/169, -208763285686647636117780550397/2197)
(853575888296641651/4, 3851772466437298568119548323/8)
(145448164799662959010/169, 795720141737408738874732306307/2197)
(48999085065706530460, 342910672861553792371036401271)
(7765782156133246479104842/16410601, -12555205975464132983801743002153925451/66479344651)
(616048201007366224, -52525101820242999909599615)
(16671337227244056274/25, 11408191479230668064104896683/125)

Commentary

Specialization at T = 127/13 of the rank-17 fibration of X1152 given in curve#3926. 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 2026-10-23 02:16:42 UTC · history