curve #3888

y² + xy + y = x³ − x² − 5673102070833309040932775322x + 161845970216562658658356775277031088670169

a-invariants: [1, -1, 1, -5673102070833309040932775322, 161845970216562658658356775277031088670169]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 306314872341656438707158563818134116664412159478955001255014491670
discriminant (Δ): 369492108858344119479694549317886877821333777644294599311675308560613850436678400000
Faltings height: 14.8300
naive height: 203.3302
primes of bad reduction: 2, 3, 5, 7, 11, 13, 61, 101, 9017256817, 5563821183544832374537474127540468597592946909
regulator: 2136941348892071180.11553286788796527267755130459186544807080412500682530801962
submitted by: 7fff-zip
submitted at: 2026-10-04 14:08:44 UTC
last updated: 2026-10-04 14:08:44 UTC

(135473067070817, -1370993910459534654889)
(38511022891927, -22015049989220183689)
(269537498231300689/7225, -28310087590591138106478133/614125)
(13198464916078777/361, 394215085683854951470349/6859)
(-86639980491743, 54786933473636260631)
(395727251169804907/2116, 231197727472393349091225071/97336)
(47902310940817, -3068790006979704889)
(4177613096977, -371777965789749365689)
(113388563250265817/841, -33153186325372609171059421/24389)
(4437038891292637/121, 74387047632826003831441/1331)
(332176938290319377/2809, -159281886358022351285072189/148877)
(108266760762991693/2209, 4062157738392100723663453/103823)
(148818199106483977/249001, -49460149160234366790259458211/124251499)
(49622401225153177/121, 10879082014895587456946341/1331)
(5160929821281847/49, -293608196807533683738601/343)
(7279508829927547/324, -1247099158910733738680899/5832)
(-669633611357528927/7744, -52060855676407519534450483/681472)
(109743597945935683/49, -36335086650090052573436197/343)
(40521726598148569/841, -462972131969026203392477/24389)
(123297491059361130007/1540081, 898075584346631487611436458281/1911240521)

X1008, t=15/2

last edited by 7fff-zip at 2026-10-04 14:08:44 UTC · history