curve #6440

y² + y = x³ − 54872726324722077900626958943x + 5204113203472990972902171190518498960670314

a-invariants: [0, 0, 1, -54872726324722077900626958943, 5204113203472990972902171190518498960670314]
c-invariants: [2633890863586659739230094029264, -4496353807800664200587475908607983102019151512]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 9964293167936890687448052389303611340484958564398895810204256359145593394190227185
discriminant (Δ): -1125516734784311487600694757633789418964478494641677276241621777047290501840757111681675
Faltings height: 15.4581
naive height: 210.2392
primes of bad reduction: 5, 19, 29, 41, 3253, 14723, 807514633, 575704150870581013, 3961967418985549758530425483213375084186657
regulator: 1881115647704999795239067.906000806685750884802995559764790531865232126910354747168
submitted by: apkorte
submitted at: 2026-11-03 07:36:59 UTC
last updated: 2026-11-03 07:36:59 UTC

(181613965908299, 1108489099783115770952)
(548605125244699, 11841157591886160004872)
(4445939748581974/25, 129301517815682860692507/125)
(-235532152929693, -2249925629410663746648)
(209748474154306, 1709504476737547648283)
(-2908604222443, 2315964516185164598972)
(216207552753009, 1856607120322312697667)
(21038848765049886/25, 2944871721454836013273491/125)
(-16213867586504951/64, 863700795895607802850971/512)
(-109759360997501, 3147161368827140799272)
(-200587376451053469/2809, -440594950706536823773101336/148877)
(115984131505719, -632458066275967395928)
(87141263763599, -1041225418847577467448)
(-3289509991530754/25, -398163443297907883082544/125)
(-53742113152254, 2828050690488490700891)
(1545458399393455724/289, -1919447829893822390971690467/4913)
(292179107784001/4, -10073904305695137818549/8)
(4656828593888634, 317392345290421760297667)
(2337340000245319, -112455352309055256200728)
(240878595911011, 2441889795703437871016)
(1857872730867969/16, -40379892195832471097377/64)
(1327274302411849, -47650552120862911163428)

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