curve #1099

y² + xy + y = x³ − 4213613959455x + 3328416232976793662

a-invariants: [1, 0, 1, -4213613959455, 3328416232976793662]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 8682358926885363538
discriminant (Δ): 2040260980471403149530496415360633444 ☆ record for ℤ/3ℤ torsion, rank ≥ 8
Faltings height: 5.9550 ☆ record for ℤ/3ℤ torsion, rank ≥ 8
naive height: 98.8216 ☆ record for ℤ/3ℤ torsion, rank ≥ 8
primes of bad reduction: 2, 7, 13, 43, 61, 97, 251, 349, 547
regulator: 133530.468392000681868842580796388556699882783658068670
submitted by: dujella
submitted at: 2026-09-23 19:07:45 UTC
last updated: 2026-09-23 19:07:45 UTC

(137177, 1659144070)
(-563615, -2350086962)
(960817, 408055152)
(1245950, 111922021)
(-1065128, -2570083998)
(1154661, 50052976)
(1168285, 16589026)
(-537260, -2331499659)

found by Dujella (2001)

last edited by dujella at 2026-09-23 19:07:46 UTC · history