curve #4322

y² + xy + y = x³ + x² − 553051180885x + 127120073721139490

a-invariants: [1, 1, 1, -553051180885, 127120073721139490]
c-invariants: [26546456682481, -109831942793489638121]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 979984404735
discriminant (Δ): 3845262521437766622745935159462800625 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 5
Faltings height: 5.7354 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 5
naive height: 92.7298 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 5
primes of bad reduction: 3, 5, 7, 17, 19, 59, 389, 1259
regulator: 24825.2738554759352191429757725593561250008136996
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:50:30 UTC
last updated: 2026-10-17 09:50:30 UTC

(2349971/4, 562131285/8)
(-538553902/1681, 35917568580633/68921)
(13475557/9, 43980253231/27)
(196814683/36, 2735955237643/216)
(12131211373/15376, 812404214108877/1906624)

Curve cell-4x2-5.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 09:50:30 UTC · history