curve #6284

y² = x³ + 8903883x

a-invariants: [0, 0, 0, 8903883, 0]
c-invariants: [-427386384, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 2536932239286048
discriminant (Δ): -45177095675061949848768
Faltings height: 3.0365
naive height: 59.6196
primes of bad reduction: 2, 3, 73, 109, 373
regulator: 13344.427839360105639026736177474809880484870685333
submitted by: The Wren
submitted at: 2026-10-31 23:42:23 UTC
last updated: 2026-10-31 23:42:23 UTC

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

(109, 31174)
(327, 54282)
(5341, 447118)
(73/4, 101981/8)
(7957/9, 2498498/27)
(7957/169, 44988878/2197)

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 23:42:23 UTC · history