curve #4569

y² + xy + y = x³ − 3502918589005x + 2523440850993995220

a-invariants: [1, 0, 1, -3502918589005, 2523440850993995220]
c-invariants: [168140092272217, -2180253147468950278621]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 2217675371622802
discriminant (Δ): 40021456367284036320053924
Faltings height: 5.4342
naive height: 98.2675
primes of bad reduction: 2, 7, 13, 163, 223, 3529, 7307
regulator: 65064.107567394842396886361117038934690559107979676
submitted by: The Wren
submitted at: 2026-10-18 02:05:27 UTC
last updated: 2026-10-18 02:05:27 UTC

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

(4329707/4, 22370067/8)
(1080577, -534206)
(136737033/121, 118736079652/1331)
(4020817609/3721, -122288618388/226981)
(55799130/49, 36058160510/343)
(963895819/900, 450480508193/27000)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z3.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Six 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 02:05:27 UTC · history