curve #4570

y² + xy + y = x³ + x² − 643658x + 197016806

a-invariants: [1, 1, 1, -643658, 197016806]
c-invariants: [30895585, -170454237425]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 908423747925
discriminant (Δ): 252510007091972625
Faltings height: 2.1639
naive height: 51.7384
primes of bad reduction: 3, 5, 29, 71, 109, 1861
regulator: 864.30240764734887499599623415292546429566361206994
submitted by: The Wren
submitted at: 2026-10-18 02:06:36 UTC
last updated: 2026-10-18 02:06:36 UTC

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

(-144, 17005)
(-810, 14107)
(-925, 1882)
(1800, 68917)
(-5840/9, 508054/27)
(-630, 19102)

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 02:06:37 UTC · history