curve #2634

y² + xy = x³ − 855476764990x + 304547227464748100

a-invariants: [1, 0, 0, -855476764990, 304547227464748100]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 200255730
discriminant (Δ): 1049828475589738701972148224000000
Faltings height: 5.4723
naive height: 94.0384
primes of bad reduction: 2, 3, 5, 29, 43, 53, 101
regulator: 29.7512881996809609315402896943575493075809
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:14:13 UTC
last updated: 2026-09-26 20:14:13 UTC

Witness: 2 independent points log in to add more points →

(144080, 429207710)
(535730, 623960)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=24; A=(3q-p)(p+q)^3=-12625, B=-(p+3q)(p-q)^3=6401711. 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 20:14:13 UTC · history