curve #6280

y² = x³ − 6096577x

a-invariants: [0, 0, 0, -6096577, 0]
c-invariants: [292635696, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1189384035741728
discriminant (Δ): 14502342712940393730112
Faltings height: 2.9419
naive height: 58.4833
primes of bad reduction: 2, 41, 241, 617
regulator: 15807.039659536792777230640182190741449122763435694
submitted by: The Wren
submitted at: 2026-10-31 23:40:07 UTC
last updated: 2026-10-31 23:40:07 UTC

Witness: 6 independent points log in to add more points →

(-2468, 3702)
(-2401, 28224)
(-2169, 54948)
(-148697/121, 99924384/1331)
(88929/25, 19090092/125)
(1338273/289, 1309723176/4913)

Commentary

Quartic twist y^2 = x^3 + ax (j = 1728) of rank 6. Rank proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file families/family_Z2.add_2026-10-24.part1.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 23:40:08 UTC · history