curve #2357

y² + xy = x³ − 220591104875x + 38733902194640625

a-invariants: [1, 0, 0, -220591104875, 38733902194640625]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 946506990
discriminant (Δ): 38843018848487476853944886601000000
Faltings height: 5.4106
naive height: 89.9723
primes of bad reduction: 2, 3, 5, 11, 13, 37, 67, 89
regulator: 5.027127620832177198606491020821412546767
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:33 UTC
last updated: 2026-09-26 19:56:33 UTC

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

(-163250, 265401625)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-11, q=26; A=(3q-p)(p+q)^3=300375, B=-(p+3q)(p-q)^3=3393751. 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 19:56:33 UTC · history