curve #6279

y² = x³ + 4187134x

a-invariants: [0, 0, 0, 4187134, 0]
c-invariants: [-200982432, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1122053832573184
discriminant (Δ): -4698189752197486214656
Faltings height: 2.8479
naive height: 57.3562
primes of bad reduction: 2, 7, 17, 73, 241
regulator: 13906.450692708505366463691876317197647733342103100
submitted by: The Wren
submitted at: 2026-10-31 23:39:31 UTC
last updated: 2026-10-31 23:39:31 UTC

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

(242, 32054)
(2975, 196945)
(4088, 292292)
(8568, 815388)
(511/9, 416465/27)
(1241/4, 291635/8)

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 23:39:31 UTC · history