curve #4567

y² = x³ + x² − 20959x + 26245281

a-invariants: [0, 1, 0, -20959, 26245281]
c-invariants: [1006048, -22681959040]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 1033441474688
discriminant (Δ): -297137159685243136
Faltings height: 2.0319
naive height: 47.6897
primes of bad reduction: 2, 7, 71, 113, 233, 617
regulator: 2558.2518299870590879545153791969956994068508736542
submitted by: The Wren
submitted at: 2026-10-18 02:04:18 UTC
last updated: 2026-10-18 02:04:18 UTC

Witness: 6 independent points log in to add more points →

(145, 5126)
(1543, 60580)
(1776, 74793)
(-1051/4, 29591/8)
(71, 5012)
(-159, 5058)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Six supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C2. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 02:04:18 UTC · history