curve #4148

y² + xy + y = x³ − x² − 67584371126469131084x + 205095005548870533421285214799

a-invariants: [1, -1, 1, -67584371126469131084, 205095005548870533421285214799]
c-invariants: [3244049814070518292017, -177202084779625916712673093272489]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 28983994238784137252911395913008815756940462042
discriminant (Δ): 1585268876387152693646945013370953417023744892958902046654464
Faltings height: 10.3126
naive height: 148.5933
primes of bad reduction: 2, 3, 13, 37, 155660977841, 24164676092959, 889979331228497771
regulator: 710532322183450.2077706888017073115790825328044670966027533706719944328
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:08:20 UTC
last updated: 2026-10-11 01:08:20 UTC

(1282476508623221/229441, 4870236935275824760875/109902239)
(183047979797, 78237639543487797)
(2145838403, 264480764317311)
(65900575631, 16791331636162443)
(2494290897, 228117411562205)
(-1122952809457/121, -241724878315875975/1331)
(5576380401, -40277723158755)
(-230342292291/25, 26701112293216017/125)
(6648850709, -222857064399051)
(348822048269/25, 175822457691002337/125)
(3929066759, -14379910915101)
(34054401557, -6115286140170315)
(-8835502227, 335390270449581)
(2155868513, 263460431215521)
(3486481109, 108825962850549)
(3688956629, 77328568511541)

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