curve #3890

y² + xy + y = x³ − x² − 3180500270674869680127777404333x + 2170019692568909691401222674055996506446789781

a-invariants: [1, -1, 1, -3180500270674869680127777404333, 2170019692568909691401222674055996506446789781]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 692089487209325040912098756417715265619080868468064126679060391190
discriminant (Δ): 24765395379326661716507074536028724127488321873128244901778480064595742738001905242543513600
Faltings height: 16.3701
naive height: 222.3174
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 41, 157, 8060861, 143105126774126833, 1810416608988774858248545146967
regulator: 1068590285018073676.18444992404561682453192714999575506048086457985244243447336
submitted by: 7fff-zip
submitted at: 2026-10-04 14:08:58 UTC
last updated: 2026-10-04 14:08:58 UTC

(64500551781396565/9, -15915661887770055031214716/27)
(916946027270455, -4963030826193520703368)
(-13946560446495594281/7225, -20522906519142495994920353992/614125)
(227765999264041511/361, -139644451852149161078627896/6859)
(81705622123699855, -23349377060070414505907368)
(2477703459748210645/529, -3650569414862545204668330206/12167)
(-612294813803425, 62352796264131998677912)
(850352146263263, -8964544724623888242280)
(9984155478814092175/7569, 10817466674812919504119415336/658503)
(-1650558658194389, 54064153143187180279736)
(21974776524537610627/25281, -31701423759474321561757036376/4019679)
(238943032239529987/2209, 4438062322938933338032007740/103823)
(283364245230531973351/249001, 613424809212362725422211632008/124251499)
(36890863409893615, 7077494979181890486500792)
(11274170537929483/49, -13062917345407742411607532/343)
(807251156569913293/729, 48000326822991654385251898/19683)
(1921118792468557171963655/1736305561, 169699914125306332831587411622743208/72350116421309)
(3030039308681903, 142661095257819378767096)
(63619729599794783/49, -5193755081914774466054872/343)
(936218645094943, -3602317911322182091624)

X1008, t=48/47

last edited by 7fff-zip at 2026-10-04 14:08:58 UTC · history