curve #415

y² = x³ − 427670503289292x + 3399885724607313599540

a-invariants: [0, 0, 0, -427670503289292, 3399885724607313599540]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 1621900754394200788355711211547589920632
discriminant (Δ): 12611900266169305330254010380994059222834432
Faltings height: 7.1721
naive height: 112.6817
primes of bad reduction: 2, 3, 74357, 260069807, 1164876769745932667975669
regulator: 1873537079052523.3264756279843828205045950748499482784825281925579750
submitted by: Rayan Hatout
submitted at: 2026-08-29 05:38:00 UTC
last updated: 2026-08-29 05:38:00 UTC

(-23844716, 6337646946)
(4853162, 37929393542)
(11471458, 1860255846)
(788125420, 22117953962070)
(44864161/4, 30028319343/8)
(107290529/4, 847632994031/8)
(311735017/9, 4687602508817/27)
(603130228/49, 274060080594/343)
(659415220/841, 1350242944932330/24389)
(1794637828/169, 16421817245274/2197)
(2745074761/1681, 3585120476082417/68921)
(21862803994/2025, 583719402377278/91125)
(27902123386/49, 4657719080833398/343)
(41106617842/11881, 57357091233687582/1295029)
(43837849222/841, 8544460904609562/24389)

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