curve #2276

y² + xy = x³ − 15174514376291x + 22750859377945941825

a-invariants: [1, 0, 0, -15174514376291, 22750859377945941825]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2889211710
discriminant (Δ): 23155269969371283012882012265174478400
Faltings height: 6.2309
naive height: 102.6655
primes of bad reduction: 2, 3, 5, 7, 11, 17, 29, 43, 59
regulator: 5.197317586362568152485672027442520922454
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:27 UTC
last updated: 2026-09-26 19:51:27 UTC

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

(2229748, 35291881)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-43, q=34; A=(3q-p)(p+q)^3=-105705, B=-(p+3q)(p-q)^3=26935447. 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 19:51:27 UTC · history