curve #3823

y² + xy = x³ − 3566862264456040453402777542072091898501806667020x + 2775901981222520606682346408401398903774337983509368021559821883366036112

a-invariants: [1, 0, 0, -3566862264456040453402777542072091898501806667020, 2775901981222520606682346408401398903774337983509368021559821883366036112]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 35028452381048333097288650748033085143072638987206133544804164145215073041337797548040177444704405110
discriminant (Δ): -424549547339235029040354547781271362824832182694995470563855770666650760826491803500187219547148542194169808584580566456001996206744068513792000000
Faltings height: 26.8803
naive height: 347.1374
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 31, 43, 67, 73, 83, 107, 127, 167, 1783, 57299756815703, 286481625038538515530015390454545956513705132401042916934583
regulator: 515477345969573634903960664.630114060384131195700968465853262644942430218375163819440651177
submitted by: 7fff-zip
submitted at: 2026-10-03 05:21:43 UTC
last updated: 2026-10-03 05:21:43 UTC

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

(1010031683874810802760464, -451282668965645377784307021586425932)
(-6167087796599106963556430824/2809, 23270860068044762456178025024628034500836/148877)
(1015216799127759715521944, -448455197257618597458975580353974092)
(2083724993444729656090264, 2095444583565922429628459849795769268)
(31908821945252665645387064, 179937933401784147608157206479552462868)
(1573518966602523592807064, 1029247116719403743508268183409670068)
(572541448183937966488664, 959899320573430470038688091454367668)
(-2197547590223604198424936, -42671599098702246018286592027053132)
(1044372560984366328824564, 435753055157825978146272943957462568)
(1699241690773764187491224, 1273330007283705505251878218564418228)
(-1369228036860208144341736, 2256710225391916496065722213227564468)
(116698284975006349176316664, -1260492333579488586607289152465314620332)
(629758190966845492768664, 882836588849627718906650199271167668)
(656528521124198199956024, -846840282794599718466417879045795052)
(-1077575315573731916928616, 2316941547209860100514806223978011828)
(2452864653685404062098904, 2963889707594417111924937680375460788)
(263450683376412115718467736/49, 4044194379892136547580113858749539985324/343)
(1226901947865848990090264, -496541014003271372720456429339859532)
(982643032339809209163704, -468804106960239646567290462867080812)
(321424781253304647553544, 1289430766890388300474059690107383748)
(3389286114154150417562264, 5442462427725093906816413838619436468)
(2201682098525301293656664, 2365427643241658996467354069523463668)
(814564519742343231616664, 641044929595838848288930790449503668)
(-1751006234856361897351336, 1911249577038684896861475935629983668)
(-1670191880489172432313936, 2018459259729801526313383540296294068)
(117027511262553175862564, -1536256394768723657335634123798171932)

Commentary

X1092; T=-1781/2571; 2-neighbor step: yes (Q has vector q=[-1,-1,0,-1,1,-1,-1,-2,0,0,0,1,-1,0,0,1,1] in source section basis; h(Q)=12; F'=O+Q-F).

last edited by 7fff-zip at 2026-10-03 05:21:43 UTC · history