curve #6292

y² = x³ + 381105043x

a-invariants: [0, 0, 0, 381105043, 0]
c-invariants: [-18293042064, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 4647713721601019168
discriminant (Δ): -3542534275444892877728928448
Faltings height: 3.9757
naive height: 70.8894
primes of bad reduction: 2, 11, 113, 257, 1193
regulator: 244760.0117534931437737430509163939029693511499163431
submitted by: The Wren
submitted at: 2026-10-31 23:48:05 UTC
last updated: 2026-10-31 23:48:05 UTC

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

(2816, 1046672)
(5819, 1553926)
(6425, 1647370)
(92777, 28878062)
(101772, 33058938)
(261369, 133995174)
(2352321/121, 5112900378/1331)

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 23:48:05 UTC · history