curve #6295

y² = x³ + 1425207908x

a-invariants: [0, 0, 0, 1425207908, 0]
c-invariants: [-68409979584, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 4062435162051472928
discriminant (Δ): -185274070998176663041072467968
Faltings height: 4.3054
naive height: 74.8464
primes of bad reduction: 2, 73, 89, 173, 317
regulator: 357390.4419809387962901888953489700670378513044541824
submitted by: The Wren
submitted at: 2026-10-31 23:50:09 UTC
last updated: 2026-10-31 23:50:09 UTC

Witness: 7 independent points log in to add more points →

(4325, 2498985)
(12816, 4513368)
(22784, 6655776)
(56052, 15999732)
(58473/4, 39157419/8)
(103952/49, 597360168/343)
(4495924/169, 16549496244/2197)

Commentary

Quartic twist y^2 = x^3 + ax (j = 1728) of rank 7. 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 23:50:09 UTC · history