curve #6293

y² = x³ − 462201817x

a-invariants: [0, 0, 0, -462201817, 0]
c-invariants: [22185687216, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 6836176628419247648
discriminant (Δ): 6319386517976620201357152832
Faltings height: 4.0239
naive height: 71.4681
primes of bad reduction: 2, 7, 11, 37, 53, 3061
regulator: 100817.4285361726538268975748636693491034339443700864
submitted by: The Wren
submitted at: 2026-10-31 23:48:46 UTC
last updated: 2026-10-31 23:48:46 UTC

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

(-16324, 1787478)
(-9317, 1870176)
(-371, 414036)
(21571, 258852)
(28037, 3013368)
(37312, 5890632)
(40700, 6971910)

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 23:48:46 UTC · history