curve #2370

y² + xy = x³ − 153419985170x + 21821346803664900

a-invariants: [1, 0, 0, -153419985170, 21821346803664900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 195418230
discriminant (Δ): 25407560191203515733703593984000000
Faltings height: 5.3524
naive height: 88.8829
primes of bad reduction: 2, 3, 5, 7, 17, 19, 43, 67
regulator: 3.535957078435470946116200558225303080538
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:21 UTC
last updated: 2026-09-26 19:57:21 UTC

Witness: 1 independent point log in to add more points →

(-173060, 207906430)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-43, q=8; A=(3q-p)(p+q)^3=-2872625, B=-(p+3q)(p-q)^3=-2520369. 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 19:57:21 UTC · history