curve #4568

y² + xy = x³ + x² − 344476x + 76995100

a-invariants: [1, 1, 0, -344476, 76995100]
c-invariants: [16534873, -66647777885]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 845072108562
discriminant (Δ): 45567978237880164
Faltings height: 2.0146
naive height: 49.8629
primes of bad reduction: 2, 3, 11, 19, 43, 2113, 7417
regulator: 392.24891414110502866784617650096669323053848426057
submitted by: The Wren
submitted at: 2026-10-18 02:04:52 UTC
last updated: 2026-10-18 02:04:52 UTC

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

(-263, 12358)
(-453, 12073)
(-109, 10697)
(402, -2120)
(-582, 9278)
(-668, 3430)

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 02:04:52 UTC · history