curve #4574

y² = x³ + x² − 598329x + 177034456

a-invariants: [0, 1, 0, -598329, 177034456]
c-invariants: [28719808, -153130088800]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 489394393228
discriminant (Δ): 138923407616845904
Faltings height: 2.1298
naive height: 51.5193
primes of bad reduction: 2, 13, 17, 29, 53, 103, 269
regulator: 579.18521058778640913846333011950037166919868142681
submitted by: The Wren
submitted at: 2026-10-18 02:09:36 UTC
last updated: 2026-10-18 02:09:36 UTC

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

(-217, 17225)
(525, 2809)
(1161, 32383)
(-867, 6695)
(485, 1079)
(-853, -8215)

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 02:09:36 UTC · history