curve #6290

y² = x³ − 356301977x

a-invariants: [0, 0, 0, -356301977, 0]
c-invariants: [17102494896, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 4062435162051472928
discriminant (Δ): 2894907359346510360016757312
Faltings height: 3.9589
naive height: 70.6875
primes of bad reduction: 2, 73, 89, 173, 317
regulator: 178695.2209904693981450944476744850335189256522270912
submitted by: The Wren
submitted at: 2026-10-31 23:46:59 UTC
last updated: 2026-10-31 23:46:59 UTC

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

(-14308, 1472702)
(-2853, 996648)
(23141, 2036408)
(53573, 11604736)
(-2059549/121, 1416969712/1331)
(-1382437/169, 3380255956/2197)
(-103952/9, 43321996/27)

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 23:46:59 UTC · history