curve #4086

y² + xy + y = x³ − x² + 1682744314x + 47509035811260

a-invariants: [1, -1, 1, 1682744314, 47509035811260]
c-invariants: [-80771727087, -41048170413700761]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 5685053598081
discriminant (Δ): -1280042158010253426194181901983 ☆ record for ℤ/4ℤ torsion, rank ≥ 6
Faltings height: 4.4609 ☆ record for ℤ/4ℤ torsion, rank ≥ 6
naive height: 76.5070 ☆ record for ℤ/4ℤ torsion, rank ≥ 6
primes of bad reduction: 3, 11, 13, 103, 181, 313, 757
regulator: 6841.4054649121522938897416510391352805236559529685
submitted by: jesper-petersen
submitted at: 2026-10-09 06:39:52 UTC
last updated: 2026-10-09 06:39:52 UTC

(-69153/4, 29189515/8)
(-61189/4, 34178961/8)
(4115, 7380570)
(-6511/64, 3522713853/512)
(2051306/169, 18331573164/2197)
(30174939/25, 165778581778/125)

Found using a Tate-normal-form discriminant sieve.

last edited by jesper-petersen at 2026-10-09 06:39:52 UTC · history