curve #6294

y² = x³ + 1012640008x

a-invariants: [0, 0, 0, 1012640008, 0]
c-invariants: [-48606720384, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 4101759143208960256
discriminant (Δ): -66457686585491114548920352768
Faltings height: 4.2200
naive height: 73.8211
primes of bad reduction: 2, 113, 593, 1889
regulator: 567451.1731139740831190049013628738219611872399540727
submitted by: The Wren
submitted at: 2026-10-31 23:49:31 UTC
last updated: 2026-10-31 23:49:31 UTC

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

(200, 450040)
(593, 775051)
(1889/4, 5532881/8)
(177184/9, 141759856/27)
(241792/9, 184305952/27)
(4172801/16, 8587180543/64)
(8577152/121, 27534802208/1331)

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 23:49:31 UTC · history