curve #6285

y² = x³ − 16748536x

a-invariants: [0, 0, 0, -16748536, 0]
c-invariants: [803929728, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1122053832573184
discriminant (Δ): 300684144140639117737984
Faltings height: 3.1945
naive height: 61.5151
primes of bad reduction: 2, 7, 17, 73, 241
regulator: 13906.450692708505366463691876317197647733342103100
submitted by: The Wren
submitted at: 2026-10-31 23:43:11 UTC
last updated: 2026-10-31 23:43:11 UTC

Witness: 6 independent points log in to add more points →

(-4088, 12264)
(-952, 122808)
(-119, 44625)
(4232, 70104)
(11169, 1098285)
(-4599/4, 1065435/8)

Commentary

Quartic twist y^2 = x^3 + ax (j = 1728) of rank 6. 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 23:43:11 UTC · history