Summary

You searched for: inst=68

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1

New Number: 3.17 |  AESZ: 387  |  Superseeker: 68 125636/3  |  Hash: 06864aab02693f4b84eb494138bb3428  

Degree: 3

\(\theta^4-2^{2} x\left(228\theta^4+456\theta^3+385\theta^2+157\theta+26\right)+2^{11} x^{2}(\theta+1)^2(132\theta^2+264\theta+109)-2^{18} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, 104, 18600, 3925760, 906368680, ...
--> OEIS
Normalized instanton numbers (n0=1): 68, 204, 125636/3, 841384, 123715360, ... ; Common denominator:...

Discriminant

\(-(400z-1)(-1+256z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 400}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "3.17" from ...

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2

New Number: 6.5 |  AESZ:  |  Superseeker: -11 -3422/3  |  Hash: 6a4aeb5833b7673c962d5598842d3f2c  

Degree: 6

\(\theta^4-x\left(12+64\theta+125\theta^2+122\theta^3+61\theta^4\right)-2^{3} x^{2}\left(193\theta^4+772\theta^3+1033\theta^2+522\theta+72\right)+2^{9} 3 x^{3}\left(146\theta^4+876\theta^3+1838\theta^2+1572\theta+405\right)-2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{16} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{19} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, 12, 324, 5760, 215460, ...
--> OEIS
Normalized instanton numbers (n0=1): -11, 68, -3422/3, 30735, -1014993, ... ; Common denominator:...

Discriminant

\(-(24z-1)(27648z^3-1728z^2+27z+1)(-1+32z)^2\)

Local exponents

≈\(-0.016119\)\(0\)\(\frac{ 1}{ 32}\) ≈\(0.03931-0.026431I\) ≈\(0.03931+0.026431I\)\(\frac{ 1}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(2\)\(0\)\(1\)\(2\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.5" from ...

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3

New Number: 7.16 |  AESZ:  |  Superseeker: 22/5 68  |  Hash: 660211ce6175f36772066594bfc33cbb  

Degree: 7

\(5^{2} \theta^4-2 5 x\theta(15+71\theta+112\theta^2+38\theta^3)-2^{2} x^{2}\left(4364\theta^4+15872\theta^3+24679\theta^2+19360\theta+6000\right)-2^{4} 3^{2} 5 x^{3}\left(92\theta^4+224\theta^3+103\theta^2-176\theta-165\right)+2^{6} 3^{2} x^{4}\left(1228\theta^4+10496\theta^3+30154\theta^2+35736\theta+14715\right)+2^{9} 3^{4} x^{5}(\theta+1)(38\theta^3+74\theta^2-304\theta-495)-2^{10} 3^{4} x^{6}(2\theta+13)(2\theta+3)(17\theta+39)(\theta+1)-2^{12} 3^{6} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 0, 60, 480, 16524, ...
--> OEIS
Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...

Discriminant

\(-(-1+36z)(12z+5)^2(12z+1)^2(4z-1)^2\)

Local exponents

\(-\frac{ 5}{ 12}\)\(-\frac{ 1}{ 12}\)\(0\)\(\frac{ 1}{ 36}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 2}\)
\(4\)\(1\)\(0\)\(2\)\(1\)\(3\)

Note:

This is operator "7.16" from ...

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4

New Number: 8.79 |  AESZ:  |  Superseeker: 22/5 68  |  Hash: 064e5b590dd8b6a4daa1e905fbe693c2  

Degree: 8

\(5^{2} \theta^4-2 5 x\left(338\theta^4+412\theta^3+371\theta^2+165\theta+30\right)+2^{2} x^{2}\left(46396\theta^4+103408\theta^3+125291\theta^2+76370\theta+19080\right)-2^{4} 3 x^{3}\left(115508\theta^4+357896\theta^3+524149\theta^2+375205\theta+106530\right)+2^{6} 3^{2} x^{4}\left(173456\theta^4+669024\theta^3+1118292\theta^2+883484\theta+269049\right)-2^{11} 3^{3} x^{5}\left(20272\theta^4+91616\theta^3+168594\theta^2+142006\theta+45053\right)+2^{14} 3^{4} x^{6}\left(5792\theta^4+29504\theta^3+58300\theta^2+51220\theta+16641\right)-2^{21} 3^{5} x^{7}(\theta+1)^2(58\theta^2+208\theta+201)+2^{26} 3^{6} x^{8}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, 12, 204, 4368, 112140, ...
--> OEIS
Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...

Discriminant

\((-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3\)

Local exponents

\(0\)\(\frac{ 1}{ 48}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 12}\)\(\frac{ 5}{ 48}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)\(3\)\(2\)
\(0\)\(2\)\(1\)\(2\)\(4\)\(2\)

Note:

This is operator "8.79" from ...

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5

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

Degree: 16

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

Maple   LaTex

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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6

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)\)

Maple   LaTex

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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