curve #2242

y² + xy = x³ − x² − 30622821092775x + 65207006677617460425

a-invariants: [1, -1, 0, -30622821092775, 65207006677617460425]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2141143290
discriminant (Δ): 1029710533273794506661528292178167952100
Faltings height: 6.4600
naive height: 104.7719
primes of bad reduction: 2, 3, 5, 11, 13, 43, 53, 73
regulator: 5.749901401040983805944514977377200253442
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:16 UTC
last updated: 2026-09-26 19:49:16 UTC

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

(3391540, 598147565)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-30, q=43; A=(3q-p)(p+q)^3=349323, B=-(p+3q)(p-q)^3=38512683. 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 19:49:16 UTC · history