curve #2473

y² + xy + y = x³ − 25272107099x + 1546343526323666

a-invariants: [1, 0, 1, -25272107099, 1546343526323666]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 53232270
discriminant (Δ): 17704246688884492064760240900
Faltings height: 4.5801
naive height: 83.4725
primes of bad reduction: 2, 3, 5, 7, 13, 17, 31, 37
regulator: 7.781036609039836517566201139495069982870
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:03:47 UTC
last updated: 2026-09-26 20:03:47 UTC

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

(-90066, 55649872)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=17; A=(3q-p)(p+q)^3=1755, B=-(p+3q)(p-q)^3=1102267. 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 20:03:47 UTC · history