curve #6276

y² = x³ + 11847688x

a-invariants: [0, 0, 0, 11847688, 0]
c-invariants: [-568689024, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 334010020096
discriminant (Δ): -106434102051495728939008
Faltings height: 3.1080
naive height: 60.4765
primes of bad reduction: 2, 41, 881
regulator: 3354.66495667522907763892805305588055141265460783
submitted by: The Wren
submitted at: 2026-10-31 23:36:20 UTC
last updated: 2026-10-31 23:36:20 UTC

Witness: 5 independent points log in to add more points →

(200, 48760)
(4961, 425293)
(11849, 1343119)
(2009/4, 623651/8)
(16072/9, 4424392/27)

Commentary

Quartic twist y^2 = x^3 + ax (j = 1728) of rank 5. 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 23:36:20 UTC · history