curve #6149

y² + xy = x³ − 43307516470667909397368942149568998097988x + 3499115631376721680996306429665710510429089489717769207422992

a-invariants: [1, 0, 0, -43307516470667909397368942149568998097988, 3499115631376721680996306429665710510429089489717769207422992]
c-invariants: [2078760790592059651073709223179311908703425, -3023235905509487532383926896417061970487343882950921563076520225]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 1971884938673174193750900402502247077454485322961163350472203675043968633295043896460563650
discriminant (Δ): -90924598737824018417998700543665943399245461384465041304786004702462641090746514971852231123714681828437063890385950720000
Faltings height: 22.2202
naive height: 292.3384
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 43, 67, 191, 41763087850759017300427000716247995895821453556481507935971679278357271245437
regulator: 10469462711792200807376844.45293009580512022838213710366322439163551107900209668238839141
submitted by: Ritik Jain
submitted at: 2026-10-29 13:48:17 UTC
last updated: 2026-10-29 13:48:17 UTC

Witness: 25 independent points log in to add more points →

(57153550796485605863598553969699560488139849192/28451414059674017917057081, 13593037491661830488746615644744651433070057782170197109480437067790284/151759464040868231365318512969019511021)
(26254220253896575292163/4, -4251899333964033913253231430175353/8)
(43501035467636437639452, -9072864641805683756160356791642056)
(-4141379699513867764632/169, 4684125448666349633972983348559148/2197)
(208672244310348277939242/1681, 13076370226518368713094379940056744/68921)
(35054001577906781295212, 6562945036438582379257084728251564)
(17105838178285279970148/169, -858244426484094550065823073843952/2197)
(1276041678803248773477642/10201, 203793124764374446724307941547634374/1030301)
(10833547186098540170232, 1127395963092828365660149566266364)
(19254277632104775121182, -2671564001883075902520818607283446)
(199337942770547475552, 1669461058371040955064166359804)
(30771343357875235997448/289, 1514645088587436429203822925775932/4913)
(1831290699263602082226476/6241, -1975595127509058541300584988727395180/493039)
(-12332279031104110428, -2007814845210449619824765907216)
(41602066789937719492644/169, 6118312214745413915614341719652060/2197)
(454897704886424081268, 8827880953294776705651952392480)
(440347591768815780130409655768/3210015649, -67972252239731015735453144219757750607009428/181869856625393)
(189932320022370798254676/625, -67028832233477740332478739696058624/15625)
(106422788072675274312, 309084523036893004221320556924)
(153062092976033194032, -675511578172227257403026628996)
(10375562601695274041235912/58081, -16933185772472112661356296552470987716/13997521)
(7742680586673250158638187/45796, -9848626891511685766058681374621011339/9800344)
(21636141803712485185416/25, -3097968948053527240142966336493876/125)
(16535887057207889983006248/2209, 67216387814195403294433387599977395812/103823)
(1426125867444597523272, -53312679873307917563102719885956)

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