curve #2601

y² + xy + y = x³ − x² − 10502359794383x + 11981922511786747031

a-invariants: [1, -1, 1, -10502359794383, 11981922511786747031]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 154143990
discriminant (Δ): 12117276757899925864380814126433145753600
Faltings height: 6.4294
naive height: 101.5615
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 59
regulator: 14.3605716429321031080540278548152005871228
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:01 UTC
last updated: 2026-09-26 20:12:01 UTC

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

(2311513, 235919620)
(2522955, 1241439982)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-15, q=44; A=(3q-p)(p+q)^3=3585183, B=-(p+3q)(p-q)^3=24029343. 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 20:12:01 UTC · history