curve #6300

y² = x³ + 34229404990x

a-invariants: [0, 0, 0, 34229404990, 0]
c-invariants: [-1643011439520, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 74985738622043961606400
discriminant (Δ): -2566717215768227303409476575936000
Faltings height: 5.1001
naive height: 84.3827
primes of bad reduction: 2, 5, 11, 29, 53, 193, 1049
regulator: 2888515.48731536691286538129629997444190086377682238340
submitted by: The Wren
submitted at: 2026-10-31 23:53:19 UTC
last updated: 2026-10-31 23:53:19 UTC

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

(150626, 92591954)
(228536, 140565964)
(334631, 221191091)
(760815, 682958265)
(888386, 855306686)
(1846240/9, 3378157640/27)
(3224626/9, 6516969146/27)
(4892536/9, 11431410364/27)

Commentary

Quartic twist y^2 = x^3 + ax (j = 1728) of rank 8. 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 23:53:19 UTC · history