curve #1916

y² + y = x³ − x² + 15906368950552398604847990x + 120164001913749952070571406918783027756

a-invariants: [0, -1, 1, 15906368950552398604847990, 120164001913749952070571406918783027756]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/5ℤ
conductor (N): 70185579173217561441252865 ☆ record for ℤ/5ℤ torsion, rank ≥ 8
discriminant (Δ): -6495384063412917041365137149520120644881812532973939448869909722666343014446875
Faltings height: 13.8034
naive height: 188.8870
primes of bad reduction: 5, 7, 11, 13, 17, 31, 41, 83, 97, 80611965004289
regulator: 3399998.29415128564103900446727106918733939432010604829
submitted by: dujella
submitted at: 2026-09-25 18:48:36 UTC
last updated: 2026-09-25 18:48:36 UTC

(798993694265, 11549162771656912902)
(-420260131525, 10649176656419153352)
(3038751356407, 14019962980015272780)
(6224057434270, 21454119371692021787)
(4815695597570, 17562592743629264012)
(-2851477254860, 7184859913338259652)
(1335032261186, 11990786483392486412)
(698553741652, 11472416216732686715)

found by Klagsbrun (2020)

last edited by dujella at 2026-09-25 18:48:36 UTC · history