curve #4150

y² = x³ − x² − 233824729x + 1154819670169

a-invariants: [0, -1, 0, -233824729, 1154819670169]
c-invariants: [11223587008, -997696853504000]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 15560960576448
discriminant (Δ): 242143494061768872452296704 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 6
Faltings height: 3.7831 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 6
naive height: 69.4239 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 6
primes of bad reduction: 2, 3, 7, 17, 31, 47, 61, 79, 97
regulator: 935.54530992377022159622975831745397354329473428745
submitted by: NDElkies
submitted at: 2026-10-11 03:48:47 UTC
last updated: 2026-10-11 03:48:47 UTC

(4155, -504968)
(34517, -5848680)
(1469, -902496)
(83256, -23638415)
(5725, 61488)
(11767, 180420)

2, 3, 7, 17, 31, 47, 61, 79, 97

last edited by NDElkies at 2026-10-11 03:48:47 UTC · history