curve #1913

y² + xy + y = x³ − 6731612366192377228520404x + 3182900810959595258205766071715171806

a-invariants: [1, 0, 1, -6731612366192377228520404, 3182900810959595258205766071715171806]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 4688824384798005181241330 ☆ record for ℤ/6ℤ torsion, rank ≥ 8
discriminant (Δ): 15146052294464339624035702590983548157409454838226727000961168811139827402500 ☆ record for ℤ/6ℤ torsion, rank ≥ 8
Faltings height: 13.3130 ☆ record for ℤ/6ℤ torsion, rank ≥ 8
naive height: 183.1202 ☆ record for ℤ/6ℤ torsion, rank ≥ 8
primes of bad reduction: 2, 5, 7, 13, 19, 29, 47, 67, 73, 139, 379, 421, 719, 2551
regulator: 9074742.91844786475147596172385118190296768466372118493
submitted by: dujella
submitted at: 2026-09-25 18:32:43 UTC
last updated: 2026-09-25 18:32:43 UTC

(71245230500, 1644283142159898882)
(336545034178, 977510982171662398)
(2321008034964, 249451111998060642)
(53011446939, 1681129734303793317)
(-1340852485347, -3130223106305263327)
(5163116922911, 10298735949654325017)
(-22717663328123/9, -54616556850967347829/27)
(382252340914, 815830511061642718)

found by Klagsbrun (2020)

last edited by dujella at 2026-09-25 18:32:43 UTC · history