curve #2236

y² + xy + y = x³ − 16981360652009x + 13560057947959993496

a-invariants: [1, 0, 1, -16981360652009, 13560057947959993496]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 29730862590
discriminant (Δ): 233964782750564963318137716355690090628100
Faltings height: 6.6343
naive height: 103.0030
primes of bad reduction: 2, 3, 5, 11, 13, 17, 41, 61, 163
regulator: 5.126823677285206335833736378353686776171
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:55 UTC
last updated: 2026-09-26 19:48:55 UTC

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

(3749873, 1614025128)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=51; A=(3q-p)(p+q)^3=11234123, B=-(p+3q)(p-q)^3=32458283. 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 19:48:55 UTC · history