curve #2470

y² + xy + y = x³ − 3155478554x + 46708275010556

a-invariants: [1, 0, 1, -3155478554, 46708275010556]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 23993970
discriminant (Δ): 1068342456988102491347171619600
Faltings height: 4.4667
naive height: 77.2308
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 47
regulator: 3.071025107342691890251725966033087393369
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:03:36 UTC
last updated: 2026-09-26 20:03:36 UTC

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

(-59514, 4899121)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-4, q=17; A=(3q-p)(p+q)^3=120835, B=-(p+3q)(p-q)^3=435267. 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 20:03:36 UTC · history