curve #2443

y² + xy + y = x³ − 121333907129x + 16267468435419656

a-invariants: [1, 0, 1, -121333907129, 16267468435419656]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 142159710
discriminant (Δ): 602820353446212270782921300100
Faltings height: 4.9414
naive height: 88.1790
primes of bad reduction: 2, 3, 5, 7, 11, 19, 41, 79
regulator: 4.042171119170903777828343664499875621087
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:55 UTC
last updated: 2026-09-26 20:01:55 UTC

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

(-342234, 133243402)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=19; A=(3q-p)(p+q)^3=-2133, B=-(p+3q)(p-q)^3=2412235. 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 20:01:55 UTC · history