curve #6450

y² + xy = x³ + x² − 6096267602075189303093101x + 5785531476056422506086348176729968721

a-invariants: [1, 1, 0, -6096267602075189303093101, 5785531476056422506086348176729968721]
c-invariants: [292620844899609086548468873, -4998699195314943701595351892843806491429]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 3588763787204356219879878373767701986968559902837420633478815610398
discriminant (Δ): 40069100353759866665816703544385952910609964473404838335568532027697671292
Faltings height: 13.0206
naive height: 182.8228
primes of bad reduction: 2, 3, 7, 11, 13, 1770169, 692685551, 487313773571710268544210335130940619855879640107
regulator: 24147016952306966734.0273485011235496240103137794219090098942235586315374303395
submitted by: apkorte
submitted at: 2026-11-03 14:29:42 UTC
last updated: 2026-11-03 14:29:42 UTC

(986082275314, 856115905176857257)
(1341977607964, -145772994095253593)
(1474511204764, -48726667325989721)
(-750356769572, 3152369294786043901)
(1601490997099, -360382996770905033)
(882464093920, 1045469232023923639)
(1316026133389, 204797467200240457)
(1349579222556, -127321142407653977)
(1791464157619, 783396199671440287)
(1374327592228, -55319109328292969)
(-2466849852551, -2410904823168984683)
(474410210553, -1732100995279011854)
(256701320011, 2058525318340196638)
(-209609140605, -2655965915975338034)
(2122355475519, 1551452192426820187)
(17271909764245, 71084644403194355866)
(1483726615364, -81726064330906921)
(72106713150844/49, 11666299410177487489/343)
(13331450887891, 47894460452564199406)
(1102966765309, 635097353033213002)

No commentary yet.