curve #6278

y² = x³ + 2174558x

a-invariants: [0, 0, 0, 2174558, 0]
c-invariants: [-104378784, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 302636959703296
discriminant (Δ): -658101621818479943168
Faltings height: 2.6841
naive height: 55.3906
primes of bad reduction: 2, 23, 41, 1153
regulator: 13201.242266523851198247394522462606519102359705330
submitted by: The Wren
submitted at: 2026-10-31 23:38:51 UTC
last updated: 2026-10-31 23:38:51 UTC

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

(722, 44118)
(736, 44712)
(943, 53751)
(2738, 162726)
(7544, 667644)
(9016, 867468)

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 23:38:51 UTC · history