curve #4315

y² = x³ − x² − 567553808246049x + 2655925051270455158049

a-invariants: [0, -1, 0, -567553808246049, 2655925051270455158049]
c-invariants: [27242582795810368, -2294719080842176481692160]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 7751841093349428163776 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 9
discriminant (Δ): 8653109808461883529988557689980524859315257344 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 9
Faltings height: 7.5110 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 9
naive height: 113.5307 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 9
primes of bad reduction: 2, 3, 41, 73, 79, 311, 337, 953, 1193, 1433
regulator: 3980874.3394949963683710649200908981580004614199222398327
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:50:05 UTC
last updated: 2026-10-17 09:50:05 UTC

(24450193, 58272991680)
(-3395193831/169, 169463419567200/2197)
(15675845/4, -177429119459/8)
(62019099/25, 4442734772532/125)
(-25538893, 22209436780)
(-22258143, 65279242080)
(4442751, -14903555400)
(-24425824, 44112779585)
(1991093641/9, 88340255736128/27)

Curve 2x2-9.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 09:50:05 UTC · history