curve #4565

y² + xy + y = x³ − 60541x + 5811054

a-invariants: [1, 0, 1, -60541, 5811054]
c-invariants: [2905945, -5025109789]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 147300958
discriminant (Δ): -412284923073982
Faltings height: 1.6034
naive height: 44.6754
primes of bad reduction: 2, 7, 19, 239, 331
regulator: 145.9492786919904033913223497421896983563227433
submitted by: The Wren
submitted at: 2026-10-18 02:02:16 UTC
last updated: 2026-10-18 02:02:16 UTC

Witness: 4 independent points log in to add more points →

(-309/4, 25639/8)
(2014, 88737)
(-38, 2857)
(-1472/9, 93134/27)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z3.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Four supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C3. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 02:02:16 UTC · history