curve #6320

y² = x³ − 146422126525x

a-invariants: [0, 0, 0, -146422126525, 0]
c-invariants: [7028262073200, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 27442482094211978976800
discriminant (Δ): 200909329267937667795582481981000000
Faltings height: 5.4635
naive height: 88.7429
primes of bad reduction: 2, 5, 101, 181, 421, 761
regulator: 14952198702.7726711019318160276378563519080316222024569
submitted by: The Wren
submitted at: 2026-11-01 00:09:07 UTC
last updated: 2026-11-01 00:09:07 UTC

Witness: 8 independent points log in to add more points →

(89775625/196, 467522887875/2744)
(1363455625/2916, -28933175103875/157464)
(9878449/16, -24365790057/64)
(23887248025/51984, 2044096056603325/11852352)
(145225777225/379456, -1055043496342725/233744896)
(3801509811268225/24068836, 234386664629920725368775/118081709416)
(1804172808025/712336, 2395539094947591075/601211584)
(9730987019209/329476, -30352808857483034973/189119224)

Commentary

Quartic twist y^2 = x^3 + ax (j = 1728) of rank 8: the rational 2-isogenous partner (a -> -4a, reduced by 16) of y^2 = x^3 + 585688506100x, from M. Rubinstein's elliptic-curves-by-rank collection (families/family_Z2.add_2026-10-24.part1.tsv.gz). The eight generators were transported through the 2-isogeny and checked exactly on this model; rank is preserved under isogeny. https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-11-01 00:09:07 UTC · history