curve #6283

y² = x³ − 8698232x

a-invariants: [0, 0, 0, -8698232, 0]
c-invariants: [417515136, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 302636959703296
discriminant (Δ): 42118503796382716362752
Faltings height: 3.0307
naive height: 59.5495
primes of bad reduction: 2, 23, 41, 1153
regulator: 13201.242266523851198247394522462606519102359705330
submitted by: The Wren
submitted at: 2026-10-31 23:41:26 UTC
last updated: 2026-10-31 23:41:26 UTC

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

(-2944, 9568)
(-943, 85813)
(-184, 39928)
(2952, 6888)
(-67896/25, 7491192/125)
(-7544/9, 2210392/27)

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 23:41:26 UTC · history