curve #6431

y² + xy + y = x³ − x² − 1695359888094491956853475147x + 29944056110728141925223118735007297506395

a-invariants: [1, -1, 1, -1695359888094491956853475147, 29944056110728141925223118735007297506395]
c-invariants: [81377274628535613928966807041, -25871664479668748425656946176783624694893825]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 521607499184196718927790415750303151660290282153131005511627601550903657094
discriminant (Δ): -75486970516177053586049806210210656069473797116045003516874041008113778738975571968
Faltings height: 14.6341
naive height: 199.9234
primes of bad reduction: 2, 11, 73, 419, 38651, 2658353, 14045622808963, 21980863642663754071, 2221429011520003046814119
regulator: 7197633666354132230096.681541073571850718038427112903571182182113458810303565889592
submitted by: apkorte
submitted at: 2026-11-02 22:50:19 UTC
last updated: 2026-11-02 22:50:19 UTC

(47472361156267, -237584161727724371958)
(-2976197904677, 186985081717911067402)
(17558761761303, -74760824630311101478)
(-38560355004597, 194890515930824917674)
(-41307490771389, -171731701192182566838)
(-23364068433813, -238328731934858524918)
(37437602508331, -137642380888086903798)
(-43172995843581, -150556770806379351630)
(92251359809117, 811561894447329780742)
(1237297933923531/49, 19508479822946086230630/343)
(-11499407331189, -218904197421725264374)
(53763583723501, -306920708223379240058)
(14149036594091, 93749215544686773322)
(19018473215195, 67675136881804696330)
(110942963590627, -1098808342702359014838)
(64403991266475, 433469412417712697354)
(-31091701867685, -229345838995906692710)
(559584299678419/49, 37686766254436025905086/343)
(26993645446507, 62042054886957512970)
(45761600789369, -219527117100324685610)
(24068332466247, -55515646645863359650)
(-46405963309637, 93182637582541301562)

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