curve #6270

y² = x³ − 241142x

a-invariants: [0, 0, 0, -241142, 0]
c-invariants: [11574816, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 3721565706496
discriminant (Δ): 897425797595858432
Faltings height: 2.1343
naive height: 48.7930
primes of bad reduction: 2, 11, 97, 113
regulator: 1227.20211403219162544585333082499748513450208965
submitted by: The Wren
submitted at: 2026-10-31 23:31:29 UTC
last updated: 2026-10-31 23:31:29 UTC

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

(-352, 6424)
(-226, 6554)
(-88, 4532)
(2825/4, 107915/8)
(5537/4, 385217/8)

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 23:31:29 UTC · history