curve #4571

y² + xy = x³ + x² − 332882x + 73626240

a-invariants: [1, 1, 0, -332882, 73626240]
c-invariants: [15978361, -63732909005]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 407479401186
discriminant (Δ): 10138902460310052
Faltings height: 1.9489
naive height: 49.7602
primes of bad reduction: 2, 3, 11, 13, 29, 313, 52321
regulator: 293.58975855152314742564726472581463313024140866820
submitted by: The Wren
submitted at: 2026-10-18 02:07:24 UTC
last updated: 2026-10-18 02:07:24 UTC

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

(146, 5234)
(294, -1278)
(-538, 10136)
(386, 1490)
(262, -2248)
(958, -25680)

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 02:07:24 UTC · history