curve #6347

y² = x³ − 81783696325945424019764939463x + 9004356313886901178717592607052557230552362

a-invariants: [0, 0, 0, -81783696325945424019764939463, 9004356313886901178717592607052557230552362]
c-invariants: [3925617423645380352948717094224, -7779763855198282618412000012493409447197240768]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 73401058978526659423039514633498831407012791265270374650673277773268733988360
discriminant (Δ): -16844697455372435710471015193179403901371626808024175067613541492805226394513074092800
Faltings height: 15.3352
naive height: 211.3357
primes of bad reduction: 2, 3, 5, 13, 23, 41, 1753, 10391, 304357679456195830823726300032917252694824417642794415285466531
regulator: 10300553648050306826069.51322037506969443036026351225007389640683198203955267502800
submitted by: apkorte
submitted at: 2026-11-01 04:57:48 UTC
last updated: 2026-11-01 04:57:48 UTC

(170374080504761, 126643008720586936110)
(1380024410276734/9, -7102389414405440579840/27)
(172773297221661, -178062180802227434390)
(674247186182673/4, -720409554957635973599/8)
(76624871406801, -1785380671263186600070)
(165448339124201, 47141026244223277470)
(234788537457809, 1656911079255011618118)
(1630391784319039/9, 9876715328465144522740/27)
(159267251478221, -137382772624517739930)
(192155380280321, -619890935361478843530)
(-16074868292586151/49, 249176663888640715211790/343)
(160041275293721, -121490806352665059570)
(173505476436737, 194092936270975368822)
(3689225719942409/25, 48278178745579830665202/125)
(26298322831257/16, -190607616566808650380093/64)
(111026145535121, 1137024796682127545670)
(211526513274846, 1081372046841331077820)
(5787328730810381969/35344, 369263071931382224809627065/6644672)
(166741784877671, 59068747647802408620)
(164447350917671, -48810917212352506380)
(165707692135901, 48402075800475760170)
(149782094601371, -339021704959101695580)

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