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1

New Number: 16.3 |  AESZ:  |  Superseeker: 68 1294532/3  |  Hash: ed2a3fd88f95da59e82dcb7b2feb1eb1  

Degree: 16

\(\theta^4+2^{2} x\left(4\theta^4-136\theta^3-345\theta^2-277\theta-78\right)-2^{7} x^{2}\left(200\theta^4+1736\theta^3+5488\theta^2+6235\theta+2661\right)-2^{12} x^{3}\left(1753\theta^4+4110\theta^3+20372\theta^2+22839\theta+8793\right)-2^{16} 3 x^{4}\left(2348\theta^4-19892\theta^3-14072\theta^2-33415\theta-43923\right)+2^{20} 3^{2} x^{5}\left(7876\theta^4+135496\theta^3+165125\theta^2+164459\theta+135000\right)+2^{26} 3^{2} x^{6}\left(35570\theta^4+273894\theta^3+190975\theta^2-89697\theta-119673\right)+2^{30} 3^{4} x^{7}\left(26487\theta^4+106022\theta^3-140553\theta^2-488804\theta-337095\right)+2^{36} 3^{4} x^{8}\left(16757\theta^4-83170\theta^3-787090\theta^2-1456680\theta-830376\right)-2^{41} 3^{4} x^{9}\left(35072\theta^4+724464\theta^3+3034063\theta^2+4788747\theta+2542968\right)-2^{46} 3^{5} x^{10}\left(66016\theta^4+658784\theta^3+2080330\theta^2+2614218\theta+968913\right)-2^{50} 3^{6} x^{11}\left(73120\theta^4+498112\theta^3+780920\theta^2-812872\theta-2147843\right)-2^{56} 3^{7} x^{12}\left(544\theta^4-88512\theta^3-765688\theta^2-2198712\theta-2138531\right)+2^{63} 3^{7} x^{13}\left(7104\theta^4+111552\theta^3+620932\theta^2+1494292\theta+1329663\right)+2^{69} 3^{8} x^{14}\left(1856\theta^4+26624\theta^3+142124\theta^2+335916\theta+297185\right)+2^{74} 3^{9} x^{15}\left(400\theta^4+5664\theta^3+30008\theta^2+70536\theta+62089\right)+2^{80} 3^{10} x^{16}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, 312, 86184, 21412224, 5052550824, ...
--> OEIS
Normalized instanton numbers (n0=1): 68, 3884, 1294532/3, 70075068, 14264173344, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.3" from ...

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2

New Number: 21.5 |  AESZ:  |  Superseeker: 68 1294532/3  |  Hash: 4366cc0350a0cd6b6cada2d063210cca  

Degree: 21

\(3^{42} \theta^4+2^{2} 3^{40} x\left(84\theta^4+2744\theta^3+2767\theta^2+1395\theta+266\right)-2^{7} 3^{38} x^{2}\left(28632\theta^4-64616\theta^3-401808\theta^2-457195\theta-145577\right)-2^{12} 3^{36} x^{3}\left(1796465\theta^4+4387486\theta^3-13907708\theta^2-38720521\theta-16882079\right)-2^{16} 3^{34} x^{4}\left(12888324\theta^4+883132620\theta^3-376920528\theta^2-4705538121\theta-2356225465\right)+2^{20} 3^{32} x^{5}\left(15110087508\theta^4-59416327992\theta^3-93935305179\theta^2+473636919819\theta+276322691378\right)+2^{26} 3^{30} x^{6}\left(368607593226\theta^4+2752098222\theta^3-4203192602301\theta^2+7661991124374\theta+5590781200123\right)+2^{30} 3^{28} x^{7}\left(8976035576583\theta^4+86869344212022\theta^3-352928067611241\theta^2+324848061028908\theta+304756694298380\right)-2^{36} 3^{26} x^{8}\left(287345565585063\theta^4-2058497615772744\theta^3+5114776744081692\theta^2-2723154486628800\theta-3338412865794115\right)-2^{42} 3^{24} x^{9}\left(8086348524095191\theta^4-26542274634468426\theta^3+57031331334711288\theta^2-10359594846687183\theta-28531041907407590\right)-2^{48} 3^{22} x^{10}\left(9138167063224382\theta^4-210786417171295732\theta^3+385718056174963201\theta^2+135920796138151506\theta-109222517440189964\right)-2^{56} 3^{20} x^{11}\left(69459893095336185\theta^4-302456301362585951\theta^3-20357692020292143\theta^2+272843233489824071\theta+56730080742496994\right)+2^{63} 3^{18} x^{12}\left(743025570226011919\theta^4+1722851886386622743\theta^3+4279395328918008662\theta^2+2387785701116330890\theta+460663159312368262\right)+2^{70} 3^{16} x^{13}\left(5328543651426881559\theta^4+12106074639731324439\theta^3+27206670237984316473\theta^2+23454463830806413755\theta+7973392735071986314\right)-2^{77} 3^{14} x^{14}\left(12814290043833983598\theta^4+29486286695176916655\theta^3+54559002172004010549\theta^2+47244767076328000884\theta+16349527240751334310\right)-2^{84} 3^{12} x^{15}\left(11241006670596368517\theta^4+140148225681755811675\theta^3+426004004156158265613\theta^2+568862491428556891473\theta+288735461646223842494\right)-2^{91} 3^{10} x^{16}\left(149313501026215021737\theta^4+1160889124895193502299\theta^3+3499844598801376071558\theta^2+4848134454175048557246\theta+2583172451610721942964\right)-2^{98} 3^{8} x^{17}\left(399191805902016390924\theta^4+3365435815479226427853\theta^3+11022203202943884018777\theta^2+16468321771715730056394\theta+9401073993084275038112\right)-2^{104} 3^{6} x^{18}(\theta+2)(1049708323072676363423\theta^3+7841867367394433134508\theta^2+20281913557507730486849\theta+18053683715529608744540)-2^{113} 3^{4} 5 13 x^{19}(\theta+2)(\theta+3)(2756169614187243177\theta^2+15979386173427193195\theta+24003427310340038070)-2^{125} 3^{2} 5^{2} 13^{2} 277 x^{20}(\theta+2)(\theta+3)(\theta+4)(1612801380441\theta+5372303849908)-2^{135} 5^{3} 13^{3} 197 277^{2} 7477 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)

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Coefficients of the holomorphic solution: 1, -1064/9, 255160/27, -518636416/729, 324919050152/6561, ...
--> OEIS
Normalized instanton numbers (n0=1): 68, 3884, 1294532/3, 70075068, 14264173344, ... ; Common denominator:...

Discriminant

\(109418989131512359209+4084975594243128077136z-4950731056692878015007744z^2-1104444452859181162116157440z^3-14086368208628838120839970816z^4+29359391068800421521682310627328z^5+5093095342081091319195606592782336z^6+220485263163106300057279729565171712z^7-50192284838132100451263027094405251072z^8-10044362703958757259932921898715614019584z^9-80717274527134170593908162833297627414528z^10-17451749161604119395832822379227954450268160z^11+2655070586111688069582739058208370586894204928z^12+270799775431202616087302711154595543168409665536z^13-9261936133799538427872587248902083856235877105664z^14-115552646865652918948418180372226694538155159191552z^15-21829371470305145024674994388194566220201357815578624z^16-830025110000015829298726502169762402902552084496777216z^17-15520857732060386886664917231765204268675241738734927872z^18-150693259232882498736033526949465598164668992007710965760z^19-722569018226175667213867459118067348751195156761909657600z^20-1351893965595951422473559533993541733676791231112282112000z^21\)

No data for singularities

Note:

This is operator "21.5" from ...

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