curve #6291

y² = x³ − 368172726x

a-invariants: [0, 0, 0, -368172726, 0]
c-invariants: [17672290848, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 8675273994897348864
discriminant (Δ): 3193999275498267021431883264
Faltings height: 3.9671
naive height: 70.7858
primes of bad reduction: 2, 3, 73, 673, 1249
regulator: 232768.1801136081166728541544257120410197264998680114
submitted by: The Wren
submitted at: 2026-10-31 23:47:31 UTC
last updated: 2026-10-31 23:47:31 UTC

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

(-16152, 1316388)
(-3650, 1138070)
(-1752, 799788)
(26499, 2975115)
(50475, 10488705)
(-162866/9, 23171390/27)
(81433/4, 7765747/8)

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 23:47:31 UTC · history