curve #3836

y² = x³ + x² − 842413012324305578666836977637273856269360x + 288403922980116612503775562807381925521173299446585945542092900

a-invariants: [0, 1, 0, -842413012324305578666836977637273856269360, 288403922980116612503775562807381925521173299446585945542092900]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 80662291558091086630925743317546342370769850891985789314852157830969102561050813838967415842236967920 ★ record for rank ≥ 27
discriminant (Δ): 2328511854544640581030412035762402985599595952010310555461882432941015485621869825520107512315594086647537166434513599312000000
Faltings height: 23.0185
naive height: 301.2249
primes of bad reduction: 2, 3, 5, 11, 19, 31, 37, 61, 101, 248222033, 1275337899542452782523469351, 718840946137689476159565722112843792814402522693208117
regulator: 34757576355194834706300098444.174202940723992968522862396258706321352229540878617440821369526
submitted by: Matej Jurasić
submitted at: 2026-10-03 16:40:00 UTC
last updated: 2026-10-03 16:40:00 UTC

Witness: 27 independent points log in to add more points →

(612614466748340604680, 1497190904315369442271245745350)
(-388514297428088081800, -23601901817763575379471855745530)
(1717665920843473221830, -62523439442222741249761090839000)
(4320292159750175342690, 278005143663178844812138831963140)
(643230595574310100280, 3559765084599911442148931602950)
(1455499630870420885970, 46321892798072018714504662708260)
(-842562988236964991920, -20001101069386465152588742682250)
(1781581362350012160245/4, 9970478390541243267530973591225/8)
(1042006929732795758930, 23280729944622086061347289252900)
(136747059541439781830, -13257584907744548119535330841000)
(373201261197892409480, 5098381162017919253392725246150)
(-763338192893179347550, -22060464282974778814588397396220)
(713690650213142803520, -7120608511113451045085430337290)
(439685019141837097838, -1734569565737449514284639499544)
(-9466726025406932920, 17215631494965267249936269480250)
(411211535998759793330, 3395255371447527565471701553500)
(743852773413453730928, 8564987690158565938049745151734)
(28909415448266958310145/64, -109101735682930910665526100811425/512)
(-1050285062483142570670, -3822254061238350322416264766500)
(-49811771960223439342, 18172573132301264207326097276964)
(-56686916858673110061470/441, -183957423664920134071039166827148500/9261)
(38754861415271121793145/64, 293664809062456861838887237245075/512)
(106039487297871757290320/169, 5752509141012588890375859656557650/2197)
(1049214496083293023880, -23655038948874175432450266058950)
(424315506905272581038, 2711149385866733789253283146744)
(27885548871032427326840/169, 27254794951234895842401713414843010/2197)
(547788879685495619317520/1369, -198704036985963788016442048541513250/50653)

Commentary

Specialization at T = -336/1045 of a rank-16 fibration of X1008 (two neighbour steps from the one in curve#751).

last edited by Matej Jurasić at 2026-10-03 16:40:01 UTC · history