curve #6287

y² = x³ − 295559042x

a-invariants: [0, 0, 0, -295559042, 0]
c-invariants: [14186834016, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 5590729427709296896
discriminant (Δ): 1652390633734968045075333632
Faltings height: 3.9121
naive height: 70.1267
primes of bad reduction: 2, 17, 73, 193, 617
regulator: 200182.8286662463552693463726105021613795161933804303
submitted by: The Wren
submitted at: 2026-10-31 23:44:33 UTC
last updated: 2026-10-31 23:44:33 UTC

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

(-14089, 1169387)
(-11169, 1381233)
(28178, 3747674)
(-1014408/121, 1829146692/1331)
(-14089/25, 50988091/125)
(164050/9, 22081130/27)
(1141209/16, 1183180131/64)

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 23:44:34 UTC · history