Summary

You searched for: sol=9

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1

New Number: 5.58 |  AESZ: 266  |  Superseeker: -18/5 -642/5  |  Hash: 5d46913a13c5fa5fa6a547d8b5646133  

Degree: 5

\(5^{2} \theta^4-3 5 x\left(27\theta^4+108\theta^3+124\theta^2+70\theta+15\right)-2 3^{2} x^{2}\left(1377\theta^4+4536\theta^3+6507\theta^2+4455\theta+1220\right)+2 3^{5} x^{3}\left(567\theta^4+4860\theta^3+11583\theta^2+10665\theta+3445\right)+3^{8} x^{4}\left(729\theta^4+3888\theta^3+6606\theta^2+4662\theta+1184\right)+3^{15} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 171, 3087, 69579, ...
--> OEIS
Normalized instanton numbers (n0=1): -18/5, 117/10, -642/5, 1197, -76788/5, ... ; Common denominator:...

Discriminant

\((1+27z)(27z+5)^2(27z-1)^2\)

Local exponents

\(-\frac{ 5}{ 27}\)\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(0\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 267/5.59

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2

New Number: 5.68 |  AESZ: 279  |  Superseeker: -10/17 10  |  Hash: 06f80606fbeb2b0cc9559df633f1f59d  

Degree: 5

\(17^{2} \theta^4+17 x\left(286\theta^4+734\theta^3+656\theta^2+289\theta+51\right)+3^{2} x^{2}\left(4110\theta^4+22074\theta^3+37209\theta^2+26265\theta+6800\right)-3^{5} x^{3}\left(1521\theta^4+7344\theta^3+12936\theta^2+9945\theta+2822\right)+3^{8} x^{4}\left(123\theta^4+552\theta^3+879\theta^2+603\theta+152\right)-3^{12} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -3, 9, 51, -1431, ...
--> OEIS
Normalized instanton numbers (n0=1): -10/17, -19/17, 10, -369/17, -1413/17, ... ; Common denominator:...

Discriminant

\(-(729z^3-189z^2-20z-1)(-17+27z)^2\)

Local exponents

≈\(-0.044921-0.04372I\) ≈\(-0.044921+0.04372I\)\(0\) ≈\(0.349102\)\(\frac{ 17}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 280/5.69

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3

New Number: 5.71 |  AESZ: 290  |  Superseeker: 162 751026  |  Hash: 5552195a371df176b84ac2c2d791be7e  

Degree: 5

\(\theta^4+3 x\left(279\theta^4-252\theta^3-160\theta^2-34\theta-3\right)+2 3^{5} x^{2}\left(423\theta^4-468\theta^3+457\theta^2+215\theta+37\right)+2 3^{9} x^{3}\left(531\theta^4+1296\theta^3+1243\theta^2+567\theta+104\right)+3^{15} 5 x^{4}\left(51\theta^4+120\theta^3+126\theta^2+66\theta+14\right)+3^{20} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, -837, -32553, 4787019, ...
--> OEIS
Normalized instanton numbers (n0=1): 162, -8829, 751026, -163125009/2, 10343901204, ... ; Common denominator:...

Discriminant

\((27z+1)(19683z^2+1)(1+405z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 405}\)\(0-\frac{ 1}{ 243}\sqrt{ 3}I\)\(0\)\(0+\frac{ 1}{ 243}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 17/5.1

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4

New Number: 5.72 |  AESZ: 291  |  Superseeker: -28 -37768  |  Hash: cbc8242a8fecc72056e6e36b4864b868  

Degree: 5

\(\theta^4-x\left(566\theta^4+34\theta^3+62\theta^2+45\theta+9\right)+3 x^{2}\left(39370\theta^4+17302\theta^3+22493\theta^2+8369\theta+1140\right)-3^{2} x^{3}\left(1215215\theta^4+1432728\theta^3+1274122\theta^2+538245\theta+93222\right)+3^{7} 61 x^{4}\left(3029\theta^4+6544\theta^3+6135\theta^2+2863\theta+548\right)-3^{12} 61^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 189, 3375, -159651, ...
--> OEIS
Normalized instanton numbers (n0=1): -28, -809, -37768, -2185213, -143204777, ... ; Common denominator:...

Discriminant

\(-(59049z^3-11421z^2+200z-1)(-1+183z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 183}\) ≈\(0.009423-0.002866I\) ≈\(0.009423+0.002866I\) ≈\(0.174569\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 124/5.18

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5

New Number: 13.11 |  AESZ:  |  Superseeker: 7 -2044/9  |  Hash: d6e183df7853fe5068c8b8cdeb3f63cb  

Degree: 13

\(\theta^4-x\left(98\theta^4+164\theta^3+137\theta^2+55\theta+9\right)+x^{2}\left(3822\theta^4+11400\theta^3+14901\theta^2+8746\theta+2007\right)-x^{3}\left(64148\theta^4+196344\theta^3+271665\theta^2+199855\theta+60354\right)+x^{4}\left(802771\theta^4+2242504\theta^3+2203855\theta^2+1316868\theta+390636\right)-2 3 x^{5}\left(1040145\theta^4+2982426\theta^3+3578912\theta^2+1897395\theta+345411\right)+2 3^{2} x^{6}\left(1927994\theta^4+4917832\theta^3+7329041\theta^2+5154630\theta+1338003\right)-2 3^{5} x^{7}\left(219316\theta^4+761432\theta^3+1064075\theta^2+703129\theta+181966\right)+3^{4} x^{8}\left(754759\theta^4+7471824\theta^3+13904030\theta^2+8830464\theta+1544112\right)+3^{7} x^{9}\left(174966\theta^4+736236\theta^3+1307237\theta^2+1340471\theta+568265\right)-3^{10} x^{10}(\theta+1)(8018\theta^3+62342\theta^2+139257\theta+108861)-3^{9} x^{11}(\theta+1)(\theta+2)(28988\theta^2+81396\theta+36331)+3^{12} x^{12}(\theta+3)(\theta+2)(\theta+1)(1061\theta+5386)+2 3^{15} 17 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 135, 2115, 18063, ...
--> OEIS
Normalized instanton numbers (n0=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...

Discriminant

\((2z-1)(4131z^3-2187z^2+81z-1)(3z-1)^2(81z^2-6z+1)^2(z+1)^3\)

Local exponents

\(-1\)\(0\) ≈\(0.019487-0.01067I\) ≈\(0.019487+0.01067I\)\(\frac{ 1}{ 27}-\frac{ 2}{ 27}\sqrt{ 2}I\)\(\frac{ 1}{ 27}+\frac{ 2}{ 27}\sqrt{ 2}I\)\(\frac{ 1}{ 3}\) ≈\(0.490438\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(2\)
\(\frac{ 3}{ 2}\)\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(4\)

Note:

This is operator "13.11" from ...

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6

New Number: 8.11 |  AESZ: 162  |  Superseeker: 9 242/3  |  Hash: 542708b59b898c35f43e00120897ff8d  

Degree: 8

\(\theta^4-3 x(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+3^{3} x^{2}\left(91\theta^4+472\theta^3+659\theta^2+374\theta+81\right)+3^{6} x^{3}\left(30\theta^4-180\theta^3-551\theta^2-417\theta-111\right)-3^{8} x^{4}\left(200\theta^4+400\theta^3-514\theta^2-714\theta-237\right)+3^{11} x^{5}\left(30\theta^4+300\theta^3+169\theta^2-25\theta-35\right)+3^{13} x^{6}\left(91\theta^4-108\theta^3-211\theta^2-108\theta-15\right)-3^{16} x^{7}(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+3^{20} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 135, 1953, 5751, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -153/4, 242/3, -4923, 34245, ... ; Common denominator:...

Discriminant

\((27z^2-9z+1)(2187z^2-81z+1)(-1+243z^2)^2\)

Local exponents

\(-\frac{ 1}{ 27}\sqrt{ 3}\)\(0\)\(\frac{ 1}{ 54}-\frac{ 1}{ 162}\sqrt{ 3}I\)\(\frac{ 1}{ 54}+\frac{ 1}{ 162}\sqrt{ 3}I\)\(\frac{ 1}{ 27}\sqrt{ 3}\)\(\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\)\(\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $c \ast f$. This operator has a second MUM point at infinity with the same instanton numbers. It can be
reduced to an operator of degree 4 with a single MUM-point over
$Q(\sqrt{?})$

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7

New Number: 8.37 |  AESZ: 345  |  Superseeker: -12/11 357/11  |  Hash: 60f282ab4e1936cd96eb5ba12983db2d  

Degree: 8

\(11^{2} \theta^4+3 11 x\left(113\theta^4+184\theta^3+158\theta^2+66\theta+11\right)+2 x^{2}\left(28397\theta^4+95138\theta^3+128420\theta^2+77715\theta+17622\right)-3 x^{3}\left(3165\theta^4+180822\theta^3+560611\theta^2+539022\theta+167508\right)-3 x^{4}\left(233330\theta^4+1052614\theta^3+1424797\theta^2+774518\theta+145896\right)-3^{2} x^{5}\left(12866\theta^4-98902\theta^3-52127\theta^2+102028\theta+63723\right)+3^{2} x^{6}\left(183763\theta^4+473778\theta^3+427847\theta^2+147060\theta+11268\right)-2^{3} 3^{3} x^{7}\left(5006\theta^4+13414\theta^3+14935\theta^2+8228\theta+1869\right)+2^{6} 3^{7} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -3, 9, 141, -3879, ...
--> OEIS
Normalized instanton numbers (n0=1): -12/11, -28/11, 357/11, -1172/11, -5250/11, ... ; Common denominator:...

Discriminant

\((3z-1)(81z^3-457z^2-30z-1)(-11-21z+24z^2)^2\)

Local exponents

\(\frac{ 7}{ 16}-\frac{ 1}{ 48}\sqrt{ 1497}\) ≈\(-0.032637-0.033136I\) ≈\(-0.032637+0.033136I\)\(0\)\(\frac{ 1}{ 3}\)\(\frac{ 7}{ 16}+\frac{ 1}{ 48}\sqrt{ 1497}\) ≈\(5.707249\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(4\)\(2\)\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

This operator has a second MUM point at infinity corresponding to operator 8.38.

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8

New Number: 8.6 |  AESZ: 113  |  Superseeker: 11 1200  |  Hash: 3754b3cce7930e99efa8acb802e524bb  

Degree: 8

\(\theta^4-x(10\theta^2+10\theta+3)(11\theta^2+11\theta+3)+x^{2}\left(1025\theta^4+3992\theta^3+5533\theta^2+3082\theta+615\right)-3^{2} x^{3}\left(110\theta^4-660\theta^3-2027\theta^2-1509\theta-369\right)+3^{2} x^{4}\left(2032\theta^4+4064\theta^3-2726\theta^2-4758\theta-1431\right)+3^{4} x^{5}\left(110\theta^4+1100\theta^3+613\theta^2-125\theta-117\right)+3^{4} x^{6}\left(1025\theta^4+108\theta^3-293\theta^2+108\theta+99\right)+3^{6} x^{7}(10\theta^2+10\theta+3)(11\theta^2+11\theta+3)+3^{8} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 285, 13671, 799389, ...
--> OEIS
Normalized instanton numbers (n0=1): 11, 66, 1200, 28201, 802124, ... ; Common denominator:...

Discriminant

\((81z^2+99z-1)(z^2+11z-1)(1+9z^2)^2\)

Local exponents

\(-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\)\(-\frac{ 11}{ 18}-\frac{ 5}{ 18}\sqrt{ 5}\)\(0-\frac{ 1}{ 3}I\)\(0\)\(0+\frac{ 1}{ 3}I\)\(-\frac{ 11}{ 18}+\frac{ 5}{ 18}\sqrt{ 5}\)\(-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $b \ast c$.This operator has a second MUM-point at infinity with the same instanton numbers.
If can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{?})$.

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9

New Number: 8.8 |  AESZ: 161  |  Superseeker: 9 -1229/3  |  Hash: 641d1de9a6564241575c5db52faef694  

Degree: 8

\(\theta^4-3 x(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+3^{2} x^{2}\left(366\theta^4+1428\theta^3+1980\theta^2+1104\theta+221\right)-3^{4} x^{3}\left(33\theta^4-198\theta^3-607\theta^2-456\theta-117\right)+3^{5} x^{4}\left(726\theta^4+1452\theta^3-978\theta^2-1704\theta-515\right)+3^{7} x^{5}\left(33\theta^4+330\theta^3+185\theta^2-32\theta-37\right)+3^{8} x^{6}\left(366\theta^4+36\theta^3-108\theta^2+36\theta+35\right)+3^{10} x^{7}(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+3^{12} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 171, 3087, 11259, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -81/4, -1229/3, -4644, -26685, ... ; Common denominator:...

Discriminant

\((729z^4+2673z^3+3240z^2-99z+1)(1+27z^2)^2\)

Local exponents

≈\(-1.848362\) ≈\(-1.848362\)\(0-\frac{ 1}{ 9}\sqrt{ 3}I\)\(0\)\(0+\frac{ 1}{ 9}\sqrt{ 3}I\) ≈\(0.015028\) ≈\(0.015028\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $b \qst f$. This operator has a second MUM-point at infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{\})$

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10

New Number: 6.35 |  AESZ:  |  Superseeker: 2 224/9  |  Hash: 31d226ff68f616edaab012f85462b8e9  

Degree: 6

\(\theta^4-x\left(9+48\theta+104\theta^2+112\theta^3+41\theta^4\right)+2 x^{2}\left(167\theta^4+1358\theta^3+2593\theta^2+1990\theta+573\right)+2 x^{3}\left(1273\theta^4-822\theta^3-16239\theta^2-22188\theta-9009\right)-5 x^{4}\left(3923\theta^4+29740\theta^3+51878\theta^2+33360\theta+6534\right)-5^{2} x^{5}(\theta+1)(2929\theta^3+4467\theta^2-1969\theta-4047)+2^{2} 3^{2} 5^{4} x^{6}(\theta+2)(\theta+1)(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 105, 1425, 21465, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -4, 224/9, -112, 4446/5, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "6.35" from ...

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11

New Number: 24.4 |  AESZ:  |  Superseeker: 6 -32282291/54  |  Hash: b98c7f29efec34446d8add48441fa228  

Degree: 24

\(\theta^4-3 x\left(11\theta^4+34\theta^3+32\theta^2+15\theta+3\right)+3^{2} x^{2}\left(27\theta^4+733966\theta^3+171\right)+3^{3} x^{3}\left(2926\theta^4-5560\theta^3-16480\theta^2-11928\theta-3735\right)-3^{4} x^{4}\left(30606\theta^4+32760\theta^3-132070\theta^2-121130\theta-44307\right)+3^{6} x^{5}\left(15750\theta^4+248992\theta^3-218660\theta^2-267352\theta-113937\right)+3^{7} x^{6}\left(447390\theta^4-1611064\theta^3+997138\theta^2+1525654\theta+737721\right)-3^{8} x^{7}\left(4210518\theta^4-4046728\theta^3+6791528\theta^2+9988640\theta+5160861\right)+3^{9} x^{8}\left(16918876\theta^4+1291896\theta^3+31887842\theta^2+47907054\theta+27066537\right)-3^{11} x^{9}\left(5747912\theta^4-10506476\theta^3-26158764\theta^2-16601042\theta-464415\right)-3^{12} x^{10}\left(52637104\theta^4+232675688\theta^3+616661120\theta^2+721851010\theta+337522383\right)+3^{13} x^{11}\left(277041602\theta^4+1204855368\theta^3+2973647056\theta^2+35822628224\theta+1740716235\right)-3^{15} x^{12}\left(156460502\theta^4+624228888\theta^3+1065193690\theta^2+810960198\theta+193208541\right)-3^{16} x^{13}\left(238576054\theta^4+2173084944\theta^3+8426851964\theta^2+14067417072\theta+8577791883\right)+3^{17} x^{14}\left(1561753522\theta^4+11510031576\theta^3+37524000206\theta^2+58271908434\theta+34413775443\right)-3^{19} x^{15}\left(675921878\theta^4+4776222328\theta^3+14788847224\theta^2+23325064352\theta+14445727221\right)-3^{21} x^{16}\left(332578151\theta^4+2930405144\theta^3+10261391450\theta^2+15302524086\theta+8113699269\right)+3^{24} x^{17}\left(135646615\theta^4+1173472306\theta^3+4199227068\theta^2+6859331311\theta+4126872408\right)-3^{25} x^{18}\left(52966465\theta^4+612076328\theta^3+3045213907\theta^2+6814044204\theta+5181429744\right)-2^{3} 3^{27} x^{19}\left(9827313\theta^4+76454094\theta^3+203071208\theta^2+155130637\theta-15471658\right)+2^{4} 3^{29} x^{20}\left(1601399\theta^4+15660570\theta^3+55267842\theta^2+71870481\theta+28392908\right)+2^{6} 3^{31} x^{21}\left(101735\theta^4+542938\theta^3+535032\theta^2-332573\theta-382670\right)-2^{6} 3^{33} x^{22}\left(45889\theta^4+396580\theta^3+1148993\theta^2+1448570\theta+695584\right)-2^{9} 3^{35} 5 x^{23}\left(87\theta^4+138\theta^3-716\theta^2-2001\theta-1376\right)+2^{12} 3^{37} 5^{2} x^{24}\left((\theta+2)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 513/8, -5851781/8, -32364933705/1024, ...
--> OEIS
Normalized instanton numbers (n0=1): 6, -1965/16, -32282291/54, 234744298799/32768, 976987022211008331/8000000, ... ; Common denominator:...

Discriminant

\(1-33z-16326382741674649276608z^22-11143025724449214743040z^23+46109071963238129971200z^24+978441930z^6-27625208598z^7+333014236308z^8-1018225367064z^9-27973515186864z^10-3478884927060667653z^16+38310610599666661815z^17+243z^2+79002z^3-2479086z^4+11481750z^5-44877882476961328995z^18+441693798025446z^11-2245037192371314z^12-10269916833818934z^13+201685104396904086z^14-785597953501675026z^15-599513066375840399448z^19+1758473882907940341072z^20+4021696190140630274880z^21\)

No data for singularities

Note:

This is operator "24.4" from ...

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12

New Number: 24.9 |  AESZ:  |  Superseeker: -28/5 -2059/5  |  Hash: df5798b125b79096c20bb76424736f4f  

Degree: 24

\(5^{2} \theta^4+5 x\left(19\theta^4-394\theta^3-422\theta^2-225\theta-45\right)-x^{2}\left(37321\theta^4-66392\theta^3-158089\theta^2-146890\theta-42015\right)+3^{2} x^{3}\left(56362\theta^4+272064\theta^3-263800\theta^2-863100\theta-344265\right)+3^{3} x^{4}\left(753758\theta^4-3721952\theta^3-1612522\theta^2+7875882\theta+3789297\right)-3^{4} x^{5}\left(8666834\theta^4+4922312\theta^3-16890032\theta^2+62390344\theta+36295089\right)+2 3^{6} x^{6}\left(729905\theta^4+30855384\theta^3-25952555\theta^2+45786327\theta+3503895\right)+3^{7} x^{7}\left(134822030\theta^4-93224048\theta^3+625210544\theta^2+316465212\theta+17277309\right)-3^{8} x^{8}\left(706556068\theta^4+1136401312\theta^3+3007159670\theta^2+4193639906\theta+1801612197\right)-3^{10} x^{9}\left(377925716\theta^4+160172796\theta^3+2877742996\theta^2+5024274\theta-495055029\right)+3^{12} x^{10}\left(2448319808\theta^4+5232688960\theta^3+15324605244\theta^2+13824742642\theta+5444471349\right)-3^{14} x^{11}\left(2193574746\theta^4+3668054544\theta^3+11367751208\theta^2+11767214572\theta+4999425971\right)-3^{16} x^{12}\left(1682795498\theta^4+11062016256\theta^3+23629355050\theta^2+26296819542\theta+11746671063\right)+3^{18} x^{13}\left(4763496210\theta^4+22286693400\theta^3+51380463088\theta^2+59266252624\theta+27350967461\right)-3^{20} x^{14}\left(3043951122\theta^4+11179411056\theta^3+23645335946\theta^2+26971875430\theta+12853203483\right)-3^{22} x^{15}\left(953791122\theta^4+11590574448\theta^3+37576565088\theta^2+50793592500\theta+25331154139\right)+3^{24} x^{16}\left(2663679451\theta^4+21556674144\theta^3+67973830382\theta^2+94609426202\theta+49302346577\right)-3^{26} x^{17}\left(1688667811\theta^4+14622262450\theta^3+50242859262\theta^2+75169980505\theta+41538667624\right)+3^{28} x^{18}\left(373177657\theta^4+4454210088\theta^3+19022887355\theta^2+32625784812\theta+19779621968\right)+2^{3} 3^{30} x^{19}\left(13128703\theta^4+20169890\theta^3-263358082\theta^2-784811675\theta-603783258\right)-2^{4} 3^{32} x^{20}\left(5205555\theta^4+36545250\theta^3+75119194\theta^2+46359749\theta-5105268\right)+2^{6} 3^{37} x^{21}\left(239743\theta^4+2547858\theta^3+7737962\theta^2+9377577\theta+3933030\right)+2^{6} 3^{37} x^{22}\left(8715\theta^4-13108\theta^3-174133\theta^2-329058\theta-187552\right)-2^{9} 3^{40} x^{23}\left(219\theta^4+1378\theta^3+3354\theta^2+3733\theta+1600\right)+2^{12} 3^{43} x^{24}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 9, 15, 45, -3159, ...
--> OEIS
Normalized instanton numbers (n0=1): -28/5, 233/10, -2059/5, 70897/10, -784822/5, ... ; Common denominator:...

Discriminant

\(25+95z+251150351349762689186880z^22-1363214712593135312598528z^23+1344540538448023869960192z^24+1064201490z^6+294855779610z^7-4635714362148z^8-22316135604084z^9+1301137527083328z^10+752301752679894551931z^16-4292367004180034217819z^17-37321z^2+507258z^3+20351466z^4-702013554z^5+8537107808017624006377z^18-10491800009300874z^11-72438828302462058z^12+1845476031027846690z^13-10613601289596047922z^14-29930976054016991298z^15+21624668188835316881976z^19-154335976146858322828080z^20+6908954524801624371053376z^21\)

No data for singularities

Note:

This is operator "24.9" from ...

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