curve #4662

y² + xy = x³ + x² − 6379601x + 3572847105

a-invariants: [1, 1, 0, -6379601, 3572847105]
c-invariants: [306220873, -3089236555205]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 667051450707486
discriminant (Δ): 11094515795119330254564
Faltings height: 2.9290
naive height: 58.6195
primes of bad reduction: 2, 3, 13, 23, 73, 127, 673, 2591
regulator: 3893.209328682320069319449315369768125339644300595162
submitted by: The Wren
submitted at: 2026-10-20 18:09:22 UTC
last updated: 2026-10-20 18:09:22 UTC

Witness: 7 independent points log in to add more points →

(2183, -8521)
(3072, 112383)
(-2008, 92063)
(6501, 483477)
(532, 17895)
(2924, 98183)
(2222, 18233)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Seven supplied rational points checked exactly on the displayed model. Rational torsion Z/2Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 18:09:22 UTC · history