curve #4564

y² + xy + y = x³ − 11713476x + 15429402098

a-invariants: [1, 0, 1, -11713476, 15429402098]
c-invariants: [562246825, -13331846783125]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 147253752950
discriminant (Δ): 96451208182250000
Faltings height: 2.5878
naive height: 60.4424
primes of bad reduction: 2, 5, 41, 61, 89, 101, 131
regulator: 632.36447306396571468380243528606764690486328839360
submitted by: The Wren
submitted at: 2026-10-18 02:01:04 UTC
last updated: 2026-10-18 02:01:04 UTC

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

(1957, 471)
(-643, 150971)
(1982, -529)
(2501, 40931)
(1877, 6611)
(2222, 18226)

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 02:01:04 UTC · history