curve #2450

y² + xy = x³ − 98739671380x + 11942190477568400

a-invariants: [1, 0, 0, -98739671380, 11942190477568400]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 62478570
discriminant (Δ): 379257389127539592538176000000
Faltings height: 4.8938
naive height: 87.5609
primes of bad reduction: 2, 3, 5, 7, 11, 17, 37, 43
regulator: 5.715907829332912940415043444647665982205
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:20 UTC
last updated: 2026-09-26 20:02:20 UTC

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

(135032, 32663276)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=20; A=(3q-p)(p+q)^3=2079, B=-(p+3q)(p-q)^3=2178079. 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 20:02:20 UTC · history