curve #3828

y² + xy = x³ − x² − 353092135629041728179163772615741814535819x + 81191986818542687088740324920880353706680133324628044573750233

a-invariants: [1, -1, 0, -353092135629041728179163772615741814535819, 81191986818542687088740324920880353706680133324628044573750233]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 2637358182216026339930227247387494422820742431210370679141029462588457888044966771641568955530
discriminant (Δ): -30432486880494821838198413545226702284536033607172224312144654734444027305362043575150789260108586288677887816838763060962500
Faltings height: 22.7242
naive height: 298.6270
primes of bad reduction: 2, 5, 7, 11, 19, 29, 41, 47, 67, 101, 103, 113, 139, 8893853, 2344838627, 24230258815823407, 583119375792435382253731558235762198523503
regulator: 34423099844495133624299922.74916748484114377336458390797520827335803423089633864109322465
submitted by: 7fff-zip
submitted at: 2026-10-03 05:22:09 UTC
last updated: 2026-10-03 05:22:09 UTC

Witness: 25 independent points log in to add more points →

(333341473014289143797, -729029868192668751624440098886)
(1846761292888086789748/9, 112557363796899082363202565702853/27)
(3317418610988396116672, -188199130206643640612664779284261)
(3670295073608410182867, 219608803488169551511508286530539)
(-500759774469918609253, -11508067945601849547838141378461)
(-3813267029400678900923/16, -788543530038797366330227985696929/64)
(-268293194339523814068, 12514476716022218323882889312839)
(464138076885834635292, 4158729946426230840936022775789)
(-118060400815715059848, 11010568991769052067514238518659)
(487880889132151352622, 5005424846399830135561606328339)
(11048581200338473390843/36, 284418193997476021558079088734171/216)
(5775852130895334091677/16, -56205591198247832991694345885279/64)
(1366818993317523874963/4, 5287893743124621981775060555237/8)
(542115356655479493587, -7006931590942865003384279208126)
(-496505788973396997703, -11580443120196372965565353879286)
(401333758553437305809438/1849, 305639688191154782154846059217784893/79507)
(79581269838226413090016/225, -2508313423783373937041176889502581/3375)
(295350066651627163272, 1634037384402479564573487697139)
(-97457351997016522503, -10708770598330849315758226052086)
(320383325856401191392, 976244278976110363600376018789)
(66329766494798574237, 7619927484348148631648401883849)
(-667601313030950391778, 4401422587701773152076157966439)
(334498615801991082912, 714128974317217887957915794789)
(725870080576474503997, 14399470490205136828187789573289)
(346963334301652532472, 671298654841957833875492131589)

Commentary

X1008; T=-1128/1847; 2-neighbor step: yes (Q has vector q=[0,2,0,1,-2,1,2,0,2,-1,-1,2,0,-1,1,0,1] in source section basis; h(Q)=12; F'=O+Q-F).

last edited by 7fff-zip at 2026-10-03 05:22:09 UTC · history