curve #2400

y² + xy = x³ − 69149427470x + 6795798242256900

a-invariants: [1, 0, 0, -69149427470, 6795798242256900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 16546530
discriminant (Δ): 1210430171469135434744070144000000
Faltings height: 5.1211
naive height: 86.4922
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29
regulator: 2.171614594174883834648948588518253889284
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:59:14 UTC
last updated: 2026-09-26 19:59:14 UTC

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

(-291260, 47347330)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=16; A=(3q-p)(p+q)^3=-169169, B=-(p+3q)(p-q)^3=1731375. 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 19:59:14 UTC · history