curve #6282

y² = x³ + 6592314x

a-invariants: [0, 0, 0, 6592314, 0]
c-invariants: [-316431072, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 2781350647974144
discriminant (Δ): -18335536815549021129216
Faltings height: 2.9614
naive height: 58.7178
primes of bad reduction: 2, 3, 47, 97, 241
regulator: 16369.230631562898502801173830873377584321514555990
submitted by: The Wren
submitted at: 2026-10-31 23:40:45 UTC
last updated: 2026-10-31 23:40:45 UTC

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

(94, 24910)
(1128, 94188)
(2350, 168730)
(2619, 187695)
(5547, 455241)
(40608, 8199432)

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 23:40:45 UTC · history