curve #6275

y² = x³ − 2961922x

a-invariants: [0, 0, 0, -2961922, 0]
c-invariants: [142172256, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 334010020096
discriminant (Δ): 1663032844554620764672
Faltings height: 2.7614
naive height: 56.3176
primes of bad reduction: 2, 41, 881
regulator: 1677.33247833761453881946402652794027570632730391
submitted by: The Wren
submitted at: 2026-10-31 23:35:42 UTC
last updated: 2026-10-31 23:35:42 UTC

Witness: 5 independent points log in to add more points →

(-1681, 15129)
(-1312, 40344)
(2050, 50430)
(-881/49, 2502921/343)
(6929/4, 65559/8)

Commentary

Quartic twist y^2 = x^3 + ax (j = 1728) of rank 5. 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 23:35:43 UTC · history