curve #105

y² + xy + y = x³ − x² − 46496231372x + 3827433258938575

a-invariants: [1, -1, 1, -46496231372, 3827433258938575]
c-invariants: [2231819105841, -3306892292536952745]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 1264178492449062735461483178
discriminant (Δ): 104856020877695059530117260716032
Faltings height: 4.9650
naive height: 85.3015
primes of bad reduction: 2, 3, 655657, 107117194614550556453
regulator: 703896103.94797884020123281580587091171576593109950500826130294
submitted by: David Renshaw
submitted at: 2026-06-24 00:01:15 UTC
last updated: 2026-07-01 22:46:38 UTC

(1009, 61485425)
(33409, 48059585)
(44917, 42751157)
(74813, 27668797)
(105061, 10053317)
(107167, 8626907)
(110005, 6562229)
(111421, 5423237)
(133741, 1003877)
(141443, 8905789)
(146971, 12905837)
(234613, 76254389)

Found by Zev Klagsbrun.

last edited by David Renshaw at 2026-06-24 02:36:13 UTC · history