curve #4318

y² + xy + y = x³ + x² − 707689811309x + 6240890917555791626

a-invariants: [1, 1, 1, -707689811309, 6240890917555791626]
c-invariants: [33969110942833, -5392130007536536036265]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 277520551027421169
discriminant (Δ): -16803164956096087181955292609440115093071 ☆ record for ℤ/4ℤ torsion, rank ≥ 7
Faltings height: 6.3977 ☆ record for ℤ/4ℤ torsion, rank ≥ 7
naive height: 100.0785 ☆ record for ℤ/4ℤ torsion, rank ≥ 7
primes of bad reduction: 3, 13, 17, 23, 43, 79, 101, 103, 107, 4813
regulator: 56674.66441777488322382069554646653534683849563158307
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:50:18 UTC
last updated: 2026-10-17 09:50:18 UTC

(-165406, -2520516775)
(10487457, -33950795993)
(26791454/25, -323940939152/125)
(-81124594/49, -581250025705/343)
(7841, 2497062839)
(-1258608, -2266051850)
(445686845, 9408787925137)

Curve 4-7.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 09:50:18 UTC · history