curve #2600

y² + xy = x³ − 11911186723260x + 15776611533061059600

a-invariants: [1, 0, 0, -11911186723260, 15776611533061059600]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1138947810
discriminant (Δ): 629169973898923798524728762241024000000
Faltings height: 6.3090
naive height: 101.9391
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 97
regulator: 5.29689989905248382207734488393338215190371
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:11:57 UTC
last updated: 2026-09-26 20:11:57 UTC

Witness: 2 independent points log in to add more points →

(-3945240, 1168919940)
(1798872, 412567332)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=40; A=(3q-p)(p+q)^3=702559, B=-(p+3q)(p-q)^3=24254559. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 20:11:57 UTC · history