curve #2623

y² + xy = x³ − 467718249810x + 121138138800548100

a-invariants: [1, 0, 0, -467718249810, 121138138800548100]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 770861910
discriminant (Δ): 208999743585264061567440174144000000
Faltings height: 5.5718
naive height: 92.2270
primes of bad reduction: 2, 3, 5, 7, 13, 41, 71, 97
regulator: 18.8202883223838300972532314324995925686617
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:23 UTC
last updated: 2026-09-26 20:13:23 UTC

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

(-675780, 358944390)
(207720, 181407390)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=28; A=(3q-p)(p+q)^3=327375, B=-(p+3q)(p-q)^3=4893391. 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 20:13:23 UTC · history