curve #4572

y² + xy = x³ + x² − 2955555x + 1954475325

a-invariants: [1, 1, 0, -2955555, 1954475325]
c-invariants: [141866665, -1689730680725]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 302611538850
discriminant (Δ): 23204252799018000
Faltings height: 2.3113
naive height: 56.3112
primes of bad reduction: 2, 3, 5, 29, 71, 89, 101, 109
regulator: 728.31645142688892432048648090659209258292178568104
submitted by: The Wren
submitted at: 2026-10-18 02:08:25 UTC
last updated: 2026-10-18 02:08:25 UTC

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

(810, -10035)
(-1566, 53181)
(1170, -10575)
(1010, -1475)
(986, -179)
(999, -855)

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 02:08:25 UTC · history