curve #3844

y² = x³ + x² − 16744331720913321791617976286840815878340x − 176317709298239536353235999960548557122770538403695034073312

a-invariants: [0, 1, 0, -16744331720913321791617976286840815878340, -176317709298239536353235999960548557122770538403695034073312]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 17618290971556207682545290958840926789835323960 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 12
discriminant (Δ): 287027776706153309882255269451273073151758737877395409053855082219809339347866878492762578968425142373197378482734404000000
Faltings height: 22.1880
naive height: 289.4702
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 31, 43, 71, 73, 83, 227, 233, 359, 479, 1093, 1163, 1307, 1427, 4943, 71387
regulator: 12786281092845026.120694800597699928142249535443908915917123328
submitted by: jesper-petersen
submitted at: 2026-10-03 18:49:01 UTC
last updated: 2026-10-03 18:49:01 UTC

(645425488796636470697809/4624, -142696276429257250148356925724143745/314432)
(205205572015786612156, -2242480905666180232741019671920)
(-10119285877693429650831944099/155500900, -1548541214745000717810994893706364230241949/1939096223000)
(-208399857028157718175331/2500, -100018012479921039538176236938435053/125000)
(-30543938866646986781271671/1774224, -772467153496885575510123405172059221075/2363266368)
(-26789219791743347037943523/487204, 258571714076780583615452031804369235101/340068392)
(29751423097213808370781/196, -2422640571480192109784919853870605/2744)
(169414748210684529933084/169, 69141608778099566772556371940778640/2197)
(9835508164753258239907324/27889, -28627618508602920202963932499832394480/4657463)
(-11288119599487019862109412/426409, 138774946679014045560130396095147490320/278445077)
(95550867576621574220943640972044/23296832689, 933544754843091654571792440828946426401784211400/3555865463820137)
(259946394145269858430523079841/1800814096, -49195264908175696487554745726605716147438375/76419346977856)

2-isogenous to curve #3704 (rank 12, torsion Z/4Z).

last edited by jesper-petersen at 2026-10-03 18:49:01 UTC · history