curve #4320

y² + xy = x³ − 94805771283683614x + 10689892431384258800958404

a-invariants: [1, 0, 0, -94805771283683614, 10689892431384258800958404]
c-invariants: [4550677021616813473, -9236067067542015136453281265]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 189292828310363778
discriminant (Δ): 5169846354648601229958756882314292516800196038648064 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 6
Faltings height: 8.6785 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 6
naive height: 128.8854 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 6
primes of bad reduction: 2, 3, 7, 11, 13, 67, 89, 97, 163, 353, 947
regulator: 14796.483660929702341085581394419453680535228506782
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:50:23 UTC
last updated: 2026-10-17 09:50:23 UTC

(-74090450/9, -91441046192846/27)
(-143844976, 4620772701182)
(144737396, 6500896442)
(-186706366, -4677757263256)
(2224574275/4, 91203764604491/8)
(17973077969/64, 1276163450175229/512)

Curve 4x2-6.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 09:50:23 UTC · history