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You searched for: degz=12

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1

New Number: 12.10 |  AESZ:  |  Superseeker: 224 4999008  |  Hash: d0e84951fc25cf38a32ec7fba5893d59  

Degree: 12

\(\theta^4+2^{4} x\left(160\theta^4+32\theta^3+56\theta^2+40\theta+9\right)+2^{13} x^{2}\left(328\theta^4+304\theta^3+442\theta^2+240\theta+57\right)+2^{22} x^{3}\left(416\theta^4+696\theta^3+939\theta^2+738\theta+225\right)+2^{28} 3 x^{4}\left(1120\theta^4+1856\theta^3+3196\theta^2+2832\theta+959\right)+2^{39} 3^{2} x^{5}\left(76\theta^4+128\theta^3+168\theta^2+168\theta+61\right)+2^{45} 3 x^{6}\left(1232\theta^4+2160\theta^3+2420\theta^2+1344\theta+273\right)+2^{54} 3 x^{7}\left(696\theta^4+1272\theta^3+1781\theta^2+554\theta-109\right)+2^{60} 3 x^{8}\left(2608\theta^4+4960\theta^3+8764\theta^2+4440\theta+423\right)+2^{68} 5 x^{9}\left(1216\theta^4+2592\theta^3+4596\theta^2+3456\theta+999\right)+2^{76} 5 x^{10}\left(736\theta^4+2048\theta^3+3128\theta^2+2536\theta+867\right)+2^{84} 5^{2} x^{11}\left(64\theta^4+256\theta^3+412\theta^2+312\theta+93\right)+2^{92} 5^{2} x^{12}\left((2\theta+3)^4\right)\)

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Coefficients of the holomorphic solution: 1, -144, 13584, -80128, -173794032, ...
--> OEIS
Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...

Discriminant

\((256z+1)^2(65536z^2+256z+1)^2(83886080z^3+768z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I\)\(-\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I\) ≈\(-0.00114\)\(0\) ≈\(0.00057-0.003183I\) ≈\(0.00057+0.003183I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(3\)\(3\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(4\)\(0\)\(4\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.10" from ...

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2

New Number: 12.4 |  AESZ:  |  Superseeker: 4 -228/5  |  Hash: c24070a1d4a449404cd7b46398fa6d6e  

Degree: 12

\(5^{2} \theta^4-2^{2} 5^{2} x\left(16\theta^4+32\theta^3+31\theta^2+15\theta+3\right)+2^{4} 5 x^{2}\left(736\theta^4+2368\theta^3+3848\theta^2+2960\theta+915\right)-2^{10} 5 x^{3}\left(304\theta^4+1176\theta^3+2337\theta^2+2313\theta+891\right)+2^{12} 3 x^{4}\left(2608\theta^4+10688\theta^3+21652\theta^2+23580\theta+9945\right)-2^{16} 3 x^{5}\left(2784\theta^4+11616\theta^3+21812\theta^2+22396\theta+9191\right)+2^{21} 3 x^{6}\left(1232\theta^4+5232\theta^3+9332\theta^2+7968\theta+2649\right)-2^{25} 3^{2} x^{7}\left(304\theta^4+1312\theta^3+2472\theta^2+1992\theta+559\right)+2^{30} 3 x^{8}\left(280\theta^4+1216\theta^3+2491\theta^2+2337\theta+827\right)-2^{32} x^{9}\left(1664\theta^4+7200\theta^3+13692\theta^2+11988\theta+3951\right)+2^{38} x^{10}\left(164\theta^4+832\theta^3+1751\theta^2+1731\theta+663\right)-2^{40} x^{11}\left(160\theta^4+928\theta^3+2072\theta^2+2072\theta+777\right)+2^{44} x^{12}\left((2\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 108, 688, 3564, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, -29/5, -228/5, 3724/5, -31856/5, ... ; Common denominator:...

Discriminant

\((16z-1)^2(256z^2-16z+1)^2(4096z^3-768z^2-5)^2\)

Local exponents

≈\(-0.013312-0.074322I\) ≈\(-0.013312+0.074322I\)\(0\)\(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 3}I\)\(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 3}I\)\(\frac{ 1}{ 16}\) ≈\(0.214124\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 3}{ 2}\)
\(3\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(3\)\(\frac{ 3}{ 2}\)
\(4\)\(4\)\(0\)\(1\)\(1\)\(1\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.4" from ...

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3

New Number: 12.12 |  AESZ:  |  Superseeker: 48 3184  |  Hash: 2b1c995b5f2826ce90fc016ad86fd66f  

Degree: 12

\(\theta^4-2^{4} x\left(27\theta^4+42\theta^3+37\theta^2+16\theta+3\right)+2^{9} x^{2}\left(139\theta^4+430\theta^3+579\theta^2+376\theta+103\right)-2^{14} x^{3}\left(369\theta^4+1638\theta^3+2992\theta^2+2481\theta+819\right)+2^{19} x^{4}\left(667\theta^4+2870\theta^3+6158\theta^2+6571\theta+2559\right)-2^{24} x^{5}\left(1263\theta^4+3066\theta^3+2692\theta^2+4295\theta+2110\right)+2^{29} 3 x^{6}\left(787\theta^4+1842\theta^3-1598\theta^2-3339\theta-1652\right)-2^{34} x^{7}\left(3087\theta^4+9750\theta^3+2942\theta^2-13117\theta-9816\right)+2^{39} x^{8}\left(3227\theta^4+6254\theta^3+14286\theta^2+4793\theta-1948\right)-2^{44} x^{9}\left(3906\theta^4+1440\theta^3+5279\theta^2+7593\theta+3747\right)+2^{49} x^{10}\left(3896\theta^4+6208\theta^3+3391\theta^2+725\theta+525\right)-2^{54} 5 x^{11}\left(408\theta^4+1536\theta^3+2230\theta^2+1460\theta+361\right)+2^{59} 5^{2} x^{12}\left((2\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 2704, 179968, 14147856, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 46, 3184, 409910, -3351792, ... ; Common denominator:...

Discriminant

\((16z-1)(32z-1)(4096z^2-192z+1)(64z-1)^2(163840z^3+1024z^2+32z-1)^2\)

Local exponents

≈\(-0.009802-0.019I\) ≈\(-0.009802+0.019I\)\(0\)\(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) ≈\(0.013353\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 32}\)\(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(3\)\(3\)\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(4\)\(4\)\(0\)\(2\)\(4\)\(1\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.12" from ...

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4

New Number: 12.13 |  AESZ:  |  Superseeker: 92/5 -76/5  |  Hash: dba247c75acfa39c7b95fa5054ec0315  

Degree: 12

\(5^{2} \theta^4-2^{2} 5 x\left(204\theta^4+456\theta^3+413\theta^2+185\theta+35\right)+2^{4} x^{2}\left(15584\theta^4+68672\theta^3+112204\theta^2+80560\theta+23355\right)-2^{8} x^{3}\left(31248\theta^4+175968\theta^3+412240\theta^2+410040\theta+153195\right)+2^{12} x^{4}\left(51632\theta^4+209728\theta^3+475320\theta^2+630640\theta+291767\right)-2^{17} x^{5}\left(49392\theta^4+140352\theta^3+11864\theta^2-35120\theta-12789\right)+2^{22} 3 x^{6}\left(12592\theta^4+46080\theta^3+11800\theta^2-52224\theta-39545\right)-2^{27} x^{7}\left(20208\theta^4+72192\theta^3+95128\theta^2+2176\theta-35669\right)+2^{32} x^{8}\left(10672\theta^4+18112\theta^3+35960\theta^2+24560\theta+3975\right)-2^{37} x^{9}\left(5904\theta^4+9216\theta^3+9640\theta^2+6720\theta+2709\right)+2^{42} x^{10}\left(2224\theta^4+6464\theta^3+8328\theta^2+5360\theta+1507\right)-2^{47} x^{11}\left(432\theta^4+1920\theta^3+3400\theta^2+2816\theta+915\right)+2^{53} x^{12}\left((2\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 28, 876, 30512, 1161964, ...
--> OEIS
Normalized instanton numbers (n0=1): 92/5, -342/5, -76/5, 75394/5, -2156752/5, ... ; Common denominator:...

Discriminant

\((64z-1)(32z-1)(256z^2-48z+1)(16z-1)^2(32768z^3-1024z^2-32z-5)^2\)

Local exponents

≈\(-0.020941-0.040594I\) ≈\(-0.020941+0.040594I\)\(0\)\(\frac{ 1}{ 64}\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 16}\) ≈\(0.073133\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(3\)\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(4\)\(4\)\(0\)\(2\)\(2\)\(2\)\(1\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.13" from ...

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5

New Number: 12.14 |  AESZ:  |  Superseeker: 7/2 237/2  |  Hash: 614b95fc4275078df0800c7546870e7f  

Degree: 12

\(2^{2} \theta^4+2 x\left(74\theta^4+22\theta^3+77\theta^2+66\theta+18\right)+3^{2} x^{2}\left(97\theta^4+1206\theta^3+2235\theta^2+1750\theta+642\right)+3^{4} x^{3}\left(126\theta^4+3910\theta^3+7341\theta^2+8588\theta+3750\right)+3^{6} x^{4}\left(832\theta^4+6078\theta^3+26372\theta^2+37719\theta+21825\right)+3^{8} x^{5}\left(442\theta^4+12544\theta^3+62654\theta^2+116087\theta+78828\right)-3^{10} x^{6}\left(1032\theta^4-5126\theta^3-73629\theta^2-192529\theta-165306\right)-2 3^{12} x^{7}\left(1432\theta^4+11737\theta^3+11907\theta^2-41634\theta-71496\right)-3^{14} x^{8}\left(1871\theta^4+35422\theta^3+145979\theta^2+220752\theta+99504\right)+2 3^{17} x^{9}\left(151\theta^4-2094\theta^3-20341\theta^2-54972\theta-48672\right)+2^{3} 3^{19} x^{10}(\theta+3)(86\theta^3+414\theta^2+181\theta-936)+2^{3} 3^{22} x^{11}(\theta+4)(\theta+3)(21\theta^2+137\theta+224)+2^{4} 3^{24} x^{12}(\theta+3)(\theta+5)(\theta+4)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -9, -18, 747, -5751, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...

Discriminant

\((9z+1)(z+1)(324z^2-18z+1)(81z^2+9z+1)^2(486z^2-27z-2)^2\)

Local exponents

\(-1\)\(-\frac{ 1}{ 9}\)\(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 3}I\)\(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 3}I\)\(\frac{ 1}{ 36}-\frac{ 1}{ 108}\sqrt{ 57}\)\(0\)\(\frac{ 1}{ 36}-\frac{ 1}{ 36}\sqrt{ 3}I\)\(\frac{ 1}{ 36}+\frac{ 1}{ 36}\sqrt{ 3}I\)\(\frac{ 1}{ 36}+\frac{ 1}{ 108}\sqrt{ 57}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(3\)
\(1\)\(1\)\(0\)\(0\)\(1\)\(0\)\(1\)\(1\)\(1\)\(4\)
\(1\)\(1\)\(-1\)\(-1\)\(3\)\(0\)\(1\)\(1\)\(3\)\(4\)
\(2\)\(2\)\(1\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(5\)

Note:

This is operator "12.14" from ...

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6

New Number: 12.15 |  AESZ:  |  Superseeker: 27/5 1619/5  |  Hash: f7297f2850190f8613d1cbc3a7363a23  

Degree: 12

\(5^{2} \theta^4-5 x\left(296\theta^4+574\theta^3+457\theta^2+170\theta+25\right)-x^{2}\left(4531\theta^4+24118\theta^3+37791\theta^2+23710\theta+5550\right)+2^{2} x^{3}\left(559\theta^4+9744\theta^3+19448\theta^2+14280\theta+4055\right)+x^{4}\left(1455\theta^4-636\theta^3+151398\theta^2+254100\theta+114136\right)+x^{5}\left(80304\theta^4+79818\theta^3-776517\theta^2-952026\theta-338569\right)-x^{6}\left(18597\theta^4-67050\theta^3-680097\theta^2-608202\theta-164470\right)-2 x^{7}\left(19086\theta^4+454818\theta^3+525507\theta^2-112266\theta-235189\right)-2^{2} x^{8}\left(52779\theta^4-252492\theta^3-39867\theta^2+316368\theta+192050\right)-2^{3} x^{9}\left(27325\theta^4+45630\theta^3-118827\theta^2-223839\theta-101599\right)+2^{2} 17 x^{10}\left(8047\theta^4+9182\theta^3-8905\theta^2-20876\theta-9476\right)+2^{5} 17^{2} x^{11}(\theta+1)(19\theta^3+129\theta^2+246\theta+145)-2^{4} 17^{3} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 109, 3329, 122581, ...
--> OEIS
Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...

Discriminant

\(-(4z+1)(z+1)(68z^2+61z-1)(z-1)^2(34z^3-12z^2+3z-5)^2\)

Local exponents

\(-1\)\(-\frac{ 61}{ 136}-\frac{ 11}{ 136}\sqrt{ 33}\)\(-\frac{ 1}{ 4}\) ≈\(-0.126959-0.475615I\) ≈\(-0.126959+0.475615I\)\(0\)\(-\frac{ 61}{ 136}+\frac{ 11}{ 136}\sqrt{ 33}\) ≈\(0.606859\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(2\)\(4\)\(4\)\(0\)\(2\)\(4\)\(1\)\(2\)

Note:

This is operator "12.15" from ...

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7

New Number: 12.16 |  AESZ:  |  Superseeker: 288 -8252768  |  Hash: e5412f8624ff9afc10459abda2d297d0  

Degree: 12

\(\theta^4-2^{4} x\left(160\theta^4+224\theta^3+200\theta^2+88\theta+17\right)+2^{12} x^{2}\left(992\theta^4+1184\theta^3+1664\theta^2+1368\theta+399\right)-2^{22} x^{3}\left(1172\theta^4+1104\theta^3+542\theta^2+912\theta+331\right)+2^{28} x^{4}\left(16624\theta^4+15104\theta^3+5408\theta^2-752\theta-1829\right)-2^{37} x^{5}\left(23072\theta^4+16784\theta^3+23748\theta^2+1100\theta-4281\right)+2^{47} x^{6}\left(12696\theta^4+8556\theta^3+18218\theta^2+6591\theta+144\right)-2^{52} x^{7}\left(167440\theta^4+175808\theta^3+289048\theta^2+160176\theta+37033\right)+2^{61} x^{8}\left(96496\theta^4+172672\theta^3+241896\theta^2+158752\theta+44823\right)-2^{70} x^{9}\left(36784\theta^4+100224\theta^3+148008\theta^2+108576\theta+32891\right)+2^{79} x^{10}\left(8720\theta^4+32704\theta^3+54968\theta^2+44784\theta+14529\right)-2^{91} x^{11}\left(144\theta^4+696\theta^3+1352\theta^2+1222\theta+427\right)+2^{99} x^{12}\left((2\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 272, 85264, 30040320, 11678489872, ...
--> OEIS
Normalized instanton numbers (n0=1): 288, 59200, -8252768, -1223488576, 585571467872, ... ; Common denominator:...

Discriminant

\((512z-1)(65536z^2-768z+1)(134217728z^3-655360z^2+256z-1)^2(256z-1)^3\)

Local exponents

\(0\) ≈\(3.7e-05-0.001244I\) ≈\(3.7e-05+0.001244I\)\(\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(\frac{ 1}{ 512}\)\(\frac{ 1}{ 256}\) ≈\(0.004808\)\(\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(3\)\(3\)\(1\)\(1\)\(0\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(4\)\(4\)\(2\)\(2\)\(0\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.16" from ...

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8

New Number: 12.17 |  AESZ:  |  Superseeker: 4 52  |  Hash: e65be092d4832d3740d2a3078755f447  

Degree: 12

\(\theta^4+2^{2} x\left(24\theta^4+6\theta^3+11\theta^2+8\theta+2\right)+2^{4} x^{2}\left(209\theta^4+2\theta^3+23\theta^2-10\right)+2^{7} x^{3}\left(223\theta^4-1218\theta^3-2225\theta^2-2088\theta-776\right)-2^{10} x^{4}\left(1409\theta^4+9634\theta^3+19337\theta^2+18420\theta+6872\right)-2^{13} x^{5}\left(6527\theta^4+35858\theta^3+78357\theta^2+78428\theta+30414\right)-2^{17} x^{6}\left(6276\theta^4+37704\theta^3+91143\theta^2+97914\theta+40036\right)-2^{21} x^{7}\left(2923\theta^4+22130\theta^3+61939\theta^2+73401\theta+32138\right)-2^{24} x^{8}\left(602\theta^4+10928\theta^3+42765\theta^2+60182\theta+29287\right)+2^{26} x^{9}\left(2352\theta^4+7392\theta^3-7024\theta^2-31968\theta-21891\right)+2^{29} x^{10}\left(1584\theta^4+11904\theta^3+24696\theta^2+19776\theta+4915\right)-2^{35} x^{11}\left(16\theta^4-176\theta^3-784\theta^2-1036\theta-449\right)-2^{39} x^{12}\left((2\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 112, -1152, 19216, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...

Discriminant

\(-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3\)

Local exponents

\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 1}{ 16}\) ≈\(-0.057187-0.018391I\) ≈\(-0.057187+0.018391I\)\(0\)\(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) ≈\(0.270624\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(0\)\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(0\)\(4\)\(4\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.17" from ...

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9

New Number: 12.7 |  AESZ:  |  Superseeker: -24/7 117  |  Hash: fedf397077a0af56af404f5156e1b5c0  

Degree: 12

\(7^{2} \theta^4+2 3 7 x\left(111\theta^4+120\theta^3+102\theta^2+42\theta+7\right)+2^{2} 3 x^{2}\left(16827\theta^4+34008\theta^3+38464\theta^2+20846\theta+4494\right)+3^{3} x^{3}\left(178553\theta^4+439878\theta^3+528099\theta^2+313502\theta+74536\right)+2 3^{3} x^{4}\left(1355053\theta^4+3438698\theta^3+3854711\theta^2+2221354\theta+519896\right)+2^{2} 3^{4} x^{5}\left(2406561\theta^4+5708802\theta^3+5082043\theta^2+2161754\theta+336752\right)+2^{3} 3^{5} x^{6}\left(3133411\theta^4+6625998\theta^3+4266961\theta^2+238710\theta-485736\right)+2^{6} 3^{6} x^{7}\left(746186\theta^4+1366021\theta^3+743388\theta^2-203279\theta-212552\right)+2^{7} 3^{7} x^{8}\left(506499\theta^4+760668\theta^3+404459\theta^2-112958\theta-117216\right)+2^{11} 3^{8} x^{9}\left(27992\theta^4+34962\theta^3+7197\theta^2-14685\theta-7604\right)+2^{14} 3^{9} x^{10}\left(1381\theta^4+1244\theta^3-2460\theta^2-4030\theta-1571\right)-2^{18} 3^{10} x^{11}(22\theta^2+98\theta+105)(\theta+1)^2-2^{22} 3^{11} x^{12}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, -6, 54, -276, -8442, ...
--> OEIS
Normalized instanton numbers (n0=1): -24/7, -24/7, 117, -564, 948/7, ... ; Common denominator:...

Discriminant

\(-(6z+1)(10368z^5-864z^4-7371z^3-1440z^2-60z-1)(7+102z+648z^2+3456z^3)^2\)

Local exponents

\(-\frac{ 1}{ 6}\) ≈\(-0.097659\) ≈\(-0.04492-0.136829I\) ≈\(-0.04492+0.136829I\)\(0\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(3\)\(3\)\(0\)\(1\)\(2\)
\(2\)\(4\)\(4\)\(4\)\(0\)\(2\)\(2\)

Note:

This is operator "12.7" from ...

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10

New Number: 12.2 |  AESZ:  |  Superseeker: 64 39744  |  Hash: b92032007ecbbf3af5801c4b1e4cf97a  

Degree: 12

\(\theta^4+2^{5} x\theta(4\theta^3-10\theta^2-6\theta-1)-2^{8} x^{2}\left(92\theta^4+248\theta^3+200\theta^2+228\theta+89\right)-2^{14} x^{3}\left(84\theta^4+336\theta^3+664\theta^2+132\theta-51\right)+2^{18} x^{4}\left(944\theta^4+1312\theta^3+8928\theta^2+7384\theta+2567\right)-2^{26} x^{5}\left(176\theta^4-1456\theta^3-3477\theta^2-3814\theta-1741\right)-2^{32} x^{6}\left(216\theta^4+1200\theta^3+576\theta^2+1314\theta+697\right)+2^{38} x^{7}\left(456\theta^4+624\theta^3-3085\theta^2-5590\theta-3089\right)-2^{43} x^{8}\left(176\theta^4-3616\theta^3-2404\theta^2-288\theta+1027\right)-2^{50} x^{9}\left(208\theta^4+1824\theta^3+2581\theta^2+1434\theta+73\right)+2^{57} x^{10}\left(122\theta^4-44\theta^3-718\theta^2-1005\theta-410\right)-2^{62} 5 x^{11}\left(4\theta^4-32\theta^3-145\theta^2-190\theta-82\right)-2^{66} 5^{2} x^{12}\left((2\theta+3)^4\right)\)

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Coefficients of the holomorphic solution: 1, 0, 1424, 13312, 4213008, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, -692, 39744, -2001358, 95440576, ... ; Common denominator:...

Discriminant

\(-(-1+64z+4096z^2)(64z-1)^2(64z+1)^2(655360z^3-4096z^2+96z+1)^2\)

Local exponents

\(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\)\(-\frac{ 1}{ 64}\) ≈\(-0.006598\)\(0\) ≈\(0.006424-0.013784I\) ≈\(0.006424+0.013784I\)\(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(0\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(3\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(2\)\(1\)\(4\)\(0\)\(4\)\(4\)\(2\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.2" from ...

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11

New Number: 12.3 |  AESZ:  |  Superseeker: -12/5 444/5  |  Hash: 45726409a4c817f929c9e6e49b33a941  

Degree: 12

\(5^{2} \theta^4+2^{2} 5 x\left(4\theta^4+56\theta^3+53\theta^2+25\theta+5\right)-2^{4} x^{2}\left(976\theta^4+6208\theta^3+9016\theta^2+6360\theta+1985\right)+2^{8} x^{3}\left(832\theta^4-2304\theta^3-11276\theta^2-12780\theta-5495\right)+2^{13} x^{4}\left(176\theta^4+4672\theta^3+16244\theta^2+19860\theta+9145\right)-2^{16} x^{5}\left(1824\theta^4+8448\theta^3+1052\theta^2-6884\theta-5771\right)+2^{21} x^{6}\left(432\theta^4+192\theta^3-3816\theta^2-9540\theta-5869\right)+2^{24} x^{7}\left(704\theta^4+10048\theta^3+21804\theta^2+22348\theta+7847\right)-2^{29} x^{8}\left(472\theta^4+2176\theta^3+7884\theta^2+11644\theta+5965\right)+2^{32} x^{9}\left(336\theta^4+672\theta^3+1144\theta^2+2904\theta+2145\right)+2^{36} x^{10}\left(368\theta^4+1216\theta^3+1304\theta^2-240\theta-697\right)-2^{44} x^{11}(2\theta+3)(4\theta^3+28\theta^2+51\theta+28)-2^{46} x^{12}\left((2\theta+3)^4\right)\)

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Coefficients of the holomorphic solution: 1, -4, 108, -912, 21484, ...
--> OEIS
Normalized instanton numbers (n0=1): -12/5, 103/5, 444/5, 1148/5, -6704, ... ; Common denominator:...

Discriminant

\(-(-1-16z+256z^2)(16z+1)^2(16z-1)^2(8192z^3+768z^2-32z+5)^2\)

Local exponents

≈\(-0.148005\)\(-\frac{ 1}{ 16}\)\(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(0\) ≈\(0.027128-0.058206I\) ≈\(0.027128+0.058206I\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(0\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 3}{ 2}\)
\(3\)\(1\)\(1\)\(0\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 3}{ 2}\)
\(4\)\(1\)\(2\)\(0\)\(4\)\(4\)\(1\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "12.3" from ...

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12

New Number: 12.5 |  AESZ:  |  Superseeker: 4 2252/9  |  Hash: bb257a283455fdd1fa17fef9649505e3  

Degree: 12

\(\theta^4+2^{2} x\left(43\theta^4+22\theta^3+25\theta^2+14\theta+3\right)+2^{4} x^{2}\left(753\theta^4+924\theta^3+1107\theta^2+622\theta+141\right)+2^{7} x^{3}\left(3377\theta^4+7218\theta^3+9261\theta^2+5764\theta+1455\right)+2^{10} x^{4}\left(7570\theta^4+24718\theta^3+34375\theta^2+21933\theta+5310\right)+2^{12} 3^{2} x^{5}\left(901\theta^4+5118\theta^3+5777\theta^2-84\theta-1829\right)-2^{14} 3^{2} x^{6}\left(7783\theta^4+33872\theta^3+83851\theta^2+107556\theta+49489\right)-2^{17} 3^{3} x^{7}\left(4895\theta^4+28154\theta^3+69267\theta^2+83564\theta+36929\right)-2^{20} 3^{4} x^{8}\left(44\theta^4+528\theta^3+247\theta^2+240\theta+274\right)+2^{23} 3^{5} x^{9}\left(664\theta^4+4760\theta^3+13781\theta^2+17353\theta+7679\right)+2^{26} 3^{6} x^{10}(\theta+1)(109\theta^3+651\theta^2+1373\theta+933)-2^{29} 3^{7} x^{11}(\theta+1)(\theta+2)(27\theta^2+153\theta+199)-2^{33} 3^{9} x^{12}(\theta+1)(\theta+2)^2(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 180, -2736, 42948, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...

Discriminant

\(-(16z+1)(432z^2+36z+1)(24z+1)^2(288z^2+48z+1)^2(8z-1)^3\)

Local exponents

\(-\frac{ 1}{ 12}-\frac{ 1}{ 24}\sqrt{ 2}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\)\(-\frac{ 1}{ 24}\)\(-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\)\(-\frac{ 1}{ 12}+\frac{ 1}{ 24}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(2\)
\(3\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(\frac{ 3}{ 2}\)\(2\)
\(4\)\(2\)\(2\)\(1\)\(2\)\(4\)\(0\)\(2\)\(3\)

Note:

This is operator "12.5" from ...

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13

New Number: 12.6 |  AESZ:  |  Superseeker: 5 953/3  |  Hash: 4ea78627bfc56ef9555d9b6b3c949e7a  

Degree: 12

\(\theta^4-x\theta(5\theta^3+46\theta^2+29\theta+6)-2 3 x^{2}\left(258\theta^4+1038\theta^3+1387\theta^2+818\theta+192\right)-2^{2} 3^{3} x^{3}\left(381\theta^4+1664\theta^3+2804\theta^2+2126\theta+624\right)-2^{4} 3^{3} x^{4}\left(1231\theta^4+5927\theta^3+11019\theta^2+9266\theta+3000\right)-2^{4} 3^{4} x^{5}\left(2621\theta^4+16730\theta^3+39069\theta^2+35141\theta+11748\right)-2^{5} 3^{5} x^{6}\left(150\theta^4+11268\theta^3+45560\theta^2+50253\theta+18756\right)+2^{6} 3^{7} x^{7}\left(1024\theta^4+800\theta^3-8483\theta^2-13641\theta-6108\right)+2^{8} 3^{7} x^{8}\left(1724\theta^4+6608\theta^3+1047\theta^2-7027\theta-4488\right)+2^{11} 3^{8} x^{9}\left(74\theta^4+1416\theta^3+1889\theta^2+687\theta-81\right)-2^{13} 3^{10} x^{10}\left(26\theta^4-16\theta^3-125\theta^2-128\theta-39\right)-2^{14} 3^{11} x^{11}(\theta+1)(16\theta^3+40\theta^2+31\theta+6)-2^{16} 3^{11} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 0, 72, 1344, 48600, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 83/2, 953/3, 5319, 97812, ... ; Common denominator:...

Discriminant

\(-(4z+1)(12z+1)(3z+1)(1728z^3+864z^2+36z-1)(-1-6z-36z^2+432z^3)^2\)

Local exponents

≈\(-0.450956\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 12}\) ≈\(-0.067934\) ≈\(-0.061146-0.08671I\) ≈\(-0.061146+0.08671I\)\(0\) ≈\(0.01889\) ≈\(0.205625\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(2\)\(2\)\(2\)\(4\)\(4\)\(0\)\(2\)\(4\)\(2\)

Note:

This is operator "12.6" from ...

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14

New Number: 12.8 |  AESZ:  |  Superseeker: 288 12718752  |  Hash: 3373bbe821cc39369e8ba8c46ec88532  

Degree: 12

\(\theta^4+2^{4} 3 x\left(112\theta^4+32\theta^3+40\theta^2+24\theta+5\right)+2^{13} x^{2}\left(1408\theta^4+1312\theta^3+1596\theta^2+784\theta+165\right)+2^{22} 3 x^{3}\left(988\theta^4+2088\theta^3+2591\theta^2+1485\theta+372\right)+2^{28} x^{4}\left(24464\theta^4+111040\theta^3+165136\theta^2+111992\theta+31983\right)+2^{38} 3^{2} x^{5}\left(288\theta^4+6544\theta^3+13980\theta^2+11216\theta+3605\right)-2^{46} x^{6}\left(14528\theta^4-36480\theta^3-205340\theta^2-205716\theta-76023\right)-2^{55} 3 x^{7}\left(4848\theta^4+13680\theta^3-20224\theta^2-34444\theta-16035\right)-2^{64} 3^{2} x^{8}\left(384\theta^4+4704\theta^3+2868\theta^2-852\theta-1307\right)+2^{74} 3 x^{9}\left(388\theta^4-1800\theta^3-3283\theta^2-2097\theta-333\right)+2^{80} 3^{2} x^{10}\left(784\theta^4+1184\theta^3+240\theta^2-592\theta-297\right)+2^{93} 3^{3} x^{11}(4\theta^2+8\theta+5)(\theta+1)^2+2^{100} 3^{2} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -240, 68880, -22281984, 7875829008, ...
--> OEIS
Normalized instanton numbers (n0=1): 288, -71872, 12718752, -4499223616, 1510063178336, ... ; Common denominator:...

Discriminant

\((1+768z+65536z^2)(256z+1)^2(512z+1)^2(201326592z^3-1536z-1)^2\)

Local exponents

\(-\frac{ 3}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 256}\) ≈\(-0.002348\)\(-\frac{ 1}{ 512}\)\(-\frac{ 3}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) ≈\(-0.000695\)\(0\) ≈\(0.003043\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(1\)\(4\)\(1\)\(2\)\(4\)\(0\)\(4\)\(2\)

Note:

This is operator "12.8" from ...

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15

New Number: 12.9 |  AESZ:  |  Superseeker: 800 38825120  |  Hash: 7e2f8423069147eb36cfd1d714d1996a  

Degree: 12

\(\theta^4+2^{4} x\left(288\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{13} x^{2}\left(864\theta^4-240\theta^3+438\theta^2+96\theta-7\right)+2^{20} x^{3}\left(3856\theta^4+1152\theta^3+1036\theta^2+192\theta-53\right)+2^{30} x^{4}\left(636\theta^4-1440\theta^3-2303\theta^2-1988\theta-672\right)-2^{38} x^{5}\left(320\theta^4+7928\theta^3+14109\theta^2+11270\theta+3517\right)-2^{48} x^{6}\left(134\theta^4+1830\theta^3+3688\theta^2+3585\theta+1195\right)-2^{56} x^{7}\left(187\theta^4+356\theta^3-2355\theta^2-2866\theta-1199\right)-2^{65} x^{8}\left(91\theta^4+202\theta^3-1069\theta^2-2020\theta-948\right)-2^{74} x^{9}\left(2\theta^4-120\theta^3-211\theta^2-198\theta-69\right)+2^{84} x^{10}\left(\theta^4+44\theta^3+122\theta^2+121\theta+41\right)+2^{92} x^{11}(\theta^2+2\theta+2)(\theta+1)^2+2^{101} x^{12}(\theta+1)^2(\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ...
--> OEIS
Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...

Discriminant

\((256z-1)(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 512}\) ≈\(-0.000552\)\(0\) ≈\(0.000276-0.00519I\) ≈\(0.000276+0.00519I\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(0\)\(3\)\(3\)\(1\)\(1\)\(2\)
\(1\)\(2\)\(2\)\(4\)\(0\)\(4\)\(4\)\(2\)\(2\)\(2\)

Note:

This is operator "12.9" from ...

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16

New Number: 12.18 |  AESZ:  |  Superseeker: 128 341632  |  Hash: 476ad437981e1b49db55e9fb4d6b4187  

Degree: 12

\(\theta^4-2^{5} x\left(2\theta^4+34\theta^3+28\theta^2+11\theta+2\right)-2^{8} x^{2}\left(396\theta^4-600\theta^3-1872\theta^2-1164\theta-335\right)+2^{16} x^{3}\left(294\theta^4+840\theta^3-1067\theta^2-906\theta-348\right)+2^{18} x^{4}\left(4816\theta^4-58528\theta^3+13728\theta^2+19808\theta+11207\right)-2^{24} x^{5}\left(46768\theta^4-73472\theta^3+29032\theta^2+39984\theta+24131\right)+2^{34} x^{6}\left(6276\theta^4-48\theta^3+6201\theta^2+5739\theta+2758\right)-2^{36} x^{7}\left(104432\theta^4+52864\theta^3+81768\theta^2+43456\theta+17559\right)+2^{43} x^{8}\left(22544\theta^4-18880\theta^3-79912\theta^2-102672\theta-42103\right)+2^{50} x^{9}\left(3568\theta^4+40896\theta^3+100264\theta^2+106320\theta+41431\right)-2^{57} x^{10}\left(3344\theta^4+20032\theta^3+45368\theta^2+46032\theta+17489\right)+2^{68} x^{11}\left(48\theta^4+276\theta^3+616\theta^2+617\theta+232\right)-2^{73} x^{12}\left((2\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 64, 4496, 339968, 27330832, ...
--> OEIS
Normalized instanton numbers (n0=1): 128, -4796, 341632, -31623118, 3395329408, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "12.18" from ...

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