curve #4151

y² + xy = x³ − 2645847709956652990162877004373777240000716x + 1775600707383853135236937359191378179281909580978893451088403600

a-invariants: [1, 0, 0, -2645847709956652990162877004373777240000716, 1775600707383853135236937359191378179281909580978893451088403600]
c-invariants: [127000690077919343527818096209941307520034369, -1534119011179649108844904379376467625914861605110078853701660761953]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 69091304515521739790555844408634859091978684938104067510692172291844813570793753812938746648481730
discriminant (Δ): -176565248542306523589198087600131146361431611790759882980759253544622393301416241264208232341482798789979567091426210929777049600
Faltings height: 23.3528
naive height: 304.7971
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 23, 31, 41, 47, 209101903, 1677932941, 863199191831, 76788778919518891, 1560453966943905930921631799961719291443
regulator: 764139365779751881291723604.284899547962773524012705442512950592533518130714354451343063768
submitted by: apkorte
submitted at: 2026-10-11 04:55:13 UTC
last updated: 2026-10-11 04:55:13 UTC

Witness: 26 independent points log in to add more points →

(-1838923491275586039144, 20555673272608031171407406351220)
(1870673544196978779438, 58071980246419782447665575689456)
(-1242162818353792198632, 56085259166870343615354577379316)
(2968945376760728164248, 141740601491874165469286067306996)
(185180790893745131808, 35944272724793191927840792268916)
(921626952033487828308, 10951831511524145237833160257416)
(4894409999185346689008, -325687808545072594187402148947724)
(-1077245040811849116456, -58101037983531821620720782735564)
(1214559704689451737368, 18807574293421085267880220470516)
(988310886712645564248, -11225933375939102205822644693004)
(25424610984552216007608, 4045893002728227425381745410764116)
(1015762816504187296296, 11665536878356541921641682800500)
(-383035752871288152456, 52276738180975987992541653964020)
(5102272971977045170200, 348000290959915146340297518907380)
(10096918913947882489224, -1002207101241206870611725456498684)
(-1019030061744306252604, 58426154726246085763005632890904)
(1091763370788863972496, 13721714503909154662282028070900)
(-172394387254588457064, 47186931147730345194210103214580)
(-684855295130943926992, -57152498204518719885611732405284)
(4493465830468878284058, 283928159466992230898551263571776)
(1232530164398921980200, -19669465936476024616777219348620)
(-1713001324912675132584, 35796027429884170367488075364340)
(278101492383452087904, -32577522963518103251323551633804)
(921793869258505211350134534/6889, 27984579920976372539353461691260467984190/571787)
(-709344509845426947312, -57406425051024933871589360541444)
(1619934133888998398508, 41719433516101114330412548129776)

Commentary

Specialization at T = 1407/4685 of the rank-17 fibration of X1152 given in curve#3856. 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 2026-10-11 04:55:13 UTC · history