Summary

You searched for: Spectrum0=0,0,1,1

Your search produced 31 matches
 1-30  31-31 

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1

New Number: 2.63 |  AESZ: 84  |  Superseeker: -4 -44  |  Hash: 908b978c0c447d3643c3018c40e7f5d1  

Degree: 2

\(\theta^4-2^{2} x\left(32\theta^4+64\theta^3+63\theta^2+31\theta+6\right)+2^{8} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 936, 43008, 2145960, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, -11, -44, -156, -288, ... ; Common denominator:...

Discriminant

\((64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 5}{ 4}\)

Note:

This is operator "2.63" from ...

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2

New Number: 2.66 |  AESZ:  |  Superseeker: -192 -229568  |  Hash: 0fb32be57a9fcd1b243f9e1341b39d45  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(2\theta^2+2\theta+1)+2^{4} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 60, 13860, 4084080, 1338557220, ...
--> OEIS
Normalized instanton numbers (n0=1): -192, 4182, -229568, 19136058, -2006581440, ... ; Common denominator:...

Discriminant

\((432z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(1\)\(\frac{ 11}{ 6}\)

Note:

This is operator "2.66" from ...

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3

New Number: 3.16 |  AESZ: 386  |  Superseeker: 10 18328  |  Hash: 7d032616d3bd41272e22a4d23747d7a0  

Degree: 3

\(\theta^4-2 x\left(422\theta^4+844\theta^3+751\theta^2+329\theta+57\right)+2^{2} 3^{4} x^{2}(\theta+1)^2(716\theta^2+1432\theta+579)-2^{4} 3^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 114, 22518, 5236980, 1321024950, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -872, 18328, -432528, 13706388, ... ; Common denominator:...

Discriminant

\(-(196z-1)(-1+324z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 324}\)\(\frac{ 1}{ 196}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(0\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

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4

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

Degree: 3

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

Maple   LaTex

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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5

New Number: 3.18 |  AESZ: 388  |  Superseeker: 266 11433160/3  |  Hash: 7e11db69c1b7bd8781e54a5eadb0e307  

Degree: 3

\(\theta^4-2 x\left(582\theta^4+1164\theta^3+815\theta^2+233\theta+25\right)+2^{2} x^{2}(\theta+1)^2(2316\theta^2+4632\theta+1907)-2^{4} 17^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 50, 17142, 9383540, 6301530550, ...
--> OEIS
Normalized instanton numbers (n0=1): 266, 19320, 11433160/3, 1106069392, 397606861972, ... ; Common denominator:...

Discriminant

\(-(1156z-1)(4z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 1156}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "3.18" from ...

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6

New Number: 3.19 |  AESZ: 389  |  Superseeker: 66 69048  |  Hash: c5cca5b7bfc61c4e8b38fab025244078  

Degree: 3

\(\theta^4-2 x\left(742\theta^4+1484\theta^3+1295\theta^2+553\theta+95\right)+2^{2} 5^{3} x^{2}(\theta+1)^2(1468\theta^2+2936\theta+1211)-2^{4} 5^{6} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 190, 61170, 22892500, 9212271250, ...
--> OEIS
Normalized instanton numbers (n0=1): 66, -1780, 69048, -3847892, 244783420, ... ; Common denominator:...

Discriminant

\(-(484z-1)(-1+500z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 500}\)\(\frac{ 1}{ 484}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(0\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "3.19" from ...

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7

New Number: 3.7 |  AESZ: ~73  |  Superseeker: 90 151648  |  Hash: 9f672e1168859bdcc8ddc7a201c57968  

Degree: 3

\(\theta^4-2 3^{2} x\left(6\theta^4+12\theta^3+3\theta^2-3\theta-1\right)-2^{2} 3^{6} x^{2}(\theta+1)^2(20\theta^2+40\theta+17)-2^{4} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -18, 2754, 37620, 43789410, ...
--> OEIS
Normalized instanton numbers (n0=1): 90, 2196, 151648, 14813388, 1820806056, ... ; Common denominator:...

Discriminant

\(-(324z-1)(1+108z)^2\)

Local exponents

\(-\frac{ 1}{ 108}\)\(0\)\(\frac{ 1}{ 324}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(0\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(2\)
\(1\)\(0\)\(2\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 73

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8

New Number: 5.56 |  AESZ: 262  |  Superseeker: -28/5 -1268/5  |  Hash: 4899f97226a5ec3b1ded2994470e9fdc  

Degree: 5

\(5^{2} \theta^4+2^{2} 5 x\left(136\theta^4+224\theta^3+197\theta^2+85\theta+15\right)+2^{4} x^{2}\left(5584\theta^4+16192\theta^3+21924\theta^2+14800\theta+3955\right)+2^{11} x^{3}\left(608\theta^4+2280\theta^3+3642\theta^2+2745\theta+780\right)+2^{14} x^{4}\left(464\theta^4+1888\theta^3+2956\theta^2+2012\theta+501\right)+2^{24} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 236, -6384, 217836, ...
--> OEIS
Normalized instanton numbers (n0=1): -28/5, 153/5, -1268/5, 18598/5, -320048/5, ... ; Common denominator:...

Discriminant

\((1+64z)(32z+5)^2(16z+1)^2\)

Local exponents

\(-\frac{ 5}{ 32}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(0\)\(1\)
\(3\)\(1\)\(1\)\(0\)\(1\)
\(4\)\(1\)\(2\)\(0\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to the Operator AESZ 263/5.57

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9

New Number: 5.57 |  AESZ: 263  |  Superseeker: 1312 58156704  |  Hash: 2157fe92de97f7b684b3cbd7b8bdf280  

Degree: 5

\(\theta^4+2^{4} x\left(464\theta^4-32\theta^3+76\theta^2+92\theta+21\right)+2^{15} x^{2}\left(608\theta^4+152\theta^3+450\theta^2+131\theta+5\right)+2^{22} x^{3}\left(5584\theta^4+6144\theta^3+6852\theta^2+2808\theta+471\right)+2^{34} 5 x^{4}\left(136\theta^4+320\theta^3+341\theta^2+181\theta+39\right)+2^{46} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -336, 198416, -142318848, 112152177936, ...
--> OEIS
Normalized instanton numbers (n0=1): 1312, -211968, 58156704, -19819112104, 7519377878624, ... ; Common denominator:...

Discriminant

\((1+256z)(1024z+1)^2(2560z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 1024}\)\(-\frac{ 1}{ 2560}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)
\(2\)\(1\)\(4\)\(0\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 262/5.56

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10

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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11

New Number: 5.59 |  AESZ: 267  |  Superseeker: 1818 467810538  |  Hash: 924287a9ba8517571071ec73d860af7e  

Degree: 5

\(\theta^4+3^{2} x\left(729\theta^4-972\theta^3-684\theta^2-198\theta-31\right)+2 3^{8} x^{2}\left(567\theta^4-2592\theta^3+405\theta^2+189\theta+70\right)-2 3^{14} x^{3}\left(1377\theta^4+972\theta^3+1161\theta^2+459\theta+113\right)-3^{22} 5 x^{4}\left(27\theta^4-38\theta^2-38\theta-12\right)+3^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 279, 124011, 64869777, 36848978379, ...
--> OEIS
Normalized instanton numbers (n0=1): 1818, -681336, 467810538, -422903176767, 446062311232740, ... ; Common denominator:...

Discriminant

\((1+729z)(3645z+1)^2(729z-1)^2\)

Local exponents

\(-\frac{ 1}{ 729}\)\(-\frac{ 1}{ 3645}\)\(0\)\(\frac{ 1}{ 729}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(0\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 266/5.58

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12

New Number: 5.67 |  AESZ: 275  |  Superseeker: 116/5 186172/5  |  Hash: f411d346afd4b8ff14b8b4c1836bae77  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(592\theta^4+1568\theta^3+1419\theta^2+635\theta+115\right)+2^{4} x^{2}\left(65536\theta^4+514048\theta^3+902816\theta^2+598400\theta+144735\right)+2^{10} x^{3}\left(106496\theta^4+122880\theta^3-594816\theta^2-794880\theta-265065\right)-2^{19} x^{4}\left(8192\theta^4+77824\theta^3+145728\theta^2+102016\theta+24527\right)-2^{26} x^{5}(8\theta+5)(8\theta+7)(8\theta+9)(8\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 92, 14124, 2572400, 510577900, ...
--> OEIS
Normalized instanton numbers (n0=1): 116/5, -5993/5, 186172/5, -8039756/5, 384321296/5, ... ; Common denominator:...

Discriminant

\(-(-1+64z)(256z+5)^2(256z-1)^2\)

Local exponents

\(-\frac{ 5}{ 256}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 8}\)
\(1\)\(0\)\(0\)\(1\)\(\frac{ 7}{ 8}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 9}{ 8}\)
\(4\)\(0\)\(1\)\(2\)\(\frac{ 11}{ 8}\)

Note:

This is operator "5.67" from ...

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13

New Number: 10.10 |  AESZ:  |  Superseeker: 28/3 83612/81  |  Hash: 8270c1ecc701d7cbd422a656c6118587  

Degree: 10

\(3^{2} \theta^4+2^{2} 3 x\left(220\theta^4+152\theta^3+207\theta^2+131\theta+31\right)+2^{4} x^{2}\left(20608\theta^4+32896\theta^3+50132\theta^2+37496\theta+11991\right)+2^{8} x^{3}\left(89936\theta^4+243168\theta^3+429080\theta^2+391080\theta+152645\right)+2^{12} x^{4}\left(242448\theta^4+966912\theta^3+2030168\theta^2+2199488\theta+1002377\right)+2^{20} x^{5}\left(26320\theta^4+142696\theta^3+359216\theta^2+454946\theta+237357\right)+2^{23} x^{6}\left(59600\theta^4+415872\theta^3+1247376\theta^2+1826640\theta+1079063\right)+2^{28} x^{7}\left(21712\theta^4+187424\theta^3+661000\theta^2+1107048\theta+733353\right)+2^{32} x^{8}\left(9744\theta^4+100992\theta^3+412312\theta^2+779936\theta+572857\right)+2^{39} x^{9}\left(304\theta^4+3696\theta^3+17208\theta^2+36300\theta+29211\right)+2^{44} x^{10}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -124/3, 1220, -872528/27, 67351172/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 28/3, -695/9, 83612/81, -4447894/243, 274874464/729, ... ; Common denominator:...

Discriminant

\((1+48z+256z^2)(32z+1)^2(16z+1)^2(32z+3)^2(64z+1)^2\)

Local exponents

\(-\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 3}{ 32}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 32}\)\(-\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)\(0\)\(\frac{ 7}{ 2}\)
\(1\)\(-2\)\(1\)\(1\)\(1\)\(3\)\(0\)\(\frac{ 7}{ 2}\)
\(2\)\(3\)\(1\)\(1\)\(2\)\(4\)\(0\)\(\frac{ 7}{ 2}\)

Note:

This is operator "10.10" from ...

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14

New Number: 10.9 |  AESZ:  |  Superseeker: 4 116  |  Hash: dbcf215f85612454543d472ffd3bffa9  

Degree: 10

\(\theta^4-2^{2} x\left(38\theta^4+70\theta^3+93\theta^2+58\theta+14\right)+2^{4} x^{2}\left(609\theta^4+2214\theta^3+4255\theta^2+4118\theta+1630\right)-2^{8} x^{3}\left(1357\theta^4+7284\theta^3+18055\theta^2+22233\theta+11143\right)+2^{10} x^{4}\left(7450\theta^4+52316\theta^3+157665\theta^2+230387\theta+134924\right)-2^{14} x^{5}\left(6580\theta^4+56446\theta^3+198857\theta^2+332342\theta+219249\right)+2^{16} x^{6}\left(15153\theta^4+151710\theta^3+606095\theta^2+1128594\theta+818733\right)-2^{20} x^{7}\left(5621\theta^4+63496\theta^3+280382\theta^2+568755\theta+444393\right)+2^{22} x^{8}\left(5152\theta^4+63904\theta^3+304853\theta^2+659693\theta+544236\right)-2^{26} 3 x^{9}\left(220\theta^4+2928\theta^3+14781\theta^2+33462\theta+28605\right)+2^{28} 3^{2} x^{10}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 56, 2192, 74112, 2319376, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 31/2, 116, 2477/2, 16876, ... ; Common denominator:...

Discriminant

\((1-48z+256z^2)(4z-1)^2(24z-1)^2(8z-1)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 8}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(0\)\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(1\)\(-2\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(3\)\(1\)\(1\)\(2\)\(4\)\(\frac{ 7}{ 2}\)

Note:

This is operator "10.9" from ...

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15

New Number: 11.11 |  AESZ:  |  Superseeker: 256/31 28062/31  |  Hash: dbd551a4eb6b44b1575c949fe3158ad8  

Degree: 11

\(31^{2} \theta^4-31 x\theta(790\theta^3+2930\theta^2+1868\theta+403)-x^{2}\left(2814085\theta^4+9964954\theta^3+13382605\theta^2+8541027\theta+2183392\right)-x^{3}\left(77649704\theta^4+350426364\theta^3+626329390\theta^2+517109481\theta+165295596\right)-x^{4}\left(1130950485\theta^4+6282081612\theta^3+13577302372\theta^2+13176194701\theta+4791500140\right)-2 x^{5}\left(5087102169\theta^4+33490353027\theta^3+83662730413\theta^2+91498335797\theta+36413643210\right)-x^{6}\left(59691820411\theta^4+451633384578\theta^3+1266886011283\theta^2+1521913712448\theta+648339514868\right)-2^{2} x^{7}\left(57682690343\theta^4+488627614012\theta^3+1504693262559\theta^2+1947925954210\theta+874695283544\right)-2^{2} x^{8}(\theta+1)(143617960931\theta^3+1184948771451\theta^2+3211500965214\theta+2815433689448)-2^{5} x^{9}(\theta+1)(\theta+2)(27089561480\theta^2+184897066731\theta+314481835312)-2^{6} 3 7 53 x^{10}(\theta+3)(\theta+2)(\theta+1)(9822371\theta+40000042)-2^{9} 3^{2} 7^{2} 53^{2} 359 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 142, 4632, 227538, ...
--> OEIS
Normalized instanton numbers (n0=1): 256/31, 1982/31, 28062/31, 591475/31, 15400630/31, ... ; Common denominator:...

Discriminant

\(-(8z+1)(359z^2+74z-1)(7z+1)^2(6z+1)^2(212z^2+225z+31)^2\)

Local exponents

\(-\frac{ 225}{ 424}-\frac{ 1}{ 424}\sqrt{ 24337}\)\(-\frac{ 37}{ 359}-\frac{ 24}{ 359}\sqrt{ 3}\)\(-\frac{ 1}{ 6}\)\(-\frac{ 225}{ 424}+\frac{ 1}{ 424}\sqrt{ 24337}\)\(-\frac{ 1}{ 7}\)\(-\frac{ 1}{ 8}\)\(0\)\(-\frac{ 37}{ 359}+\frac{ 24}{ 359}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(2\)
\(3\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(3\)
\(4\)\(2\)\(1\)\(4\)\(1\)\(2\)\(0\)\(2\)\(4\)

Note:

This is operator "11.11" from ...

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16

New Number: 11.8 |  AESZ:  |  Superseeker: 6/17 688/17  |  Hash: a0a3e346d09b91b8ad96e54854c136ad  

Degree: 11

\(17^{2} \theta^4-2 3 17 x\theta^2(117\theta^2+2\theta+1)+2^{2} x^{2}\left(8475\theta^4-64176\theta^3-97010\theta^2-63580\theta-16184\right)+2^{2} x^{3}\left(717094\theta^4+1400796\theta^3+1493367\theta^2+893571\theta+254082\right)-2^{4} x^{4}\left(464294\theta^4-1133264\theta^3-1648391\theta^2-1200310\theta-375336\right)-2^{4} x^{5}\left(18282700\theta^4+46995928\theta^3+83098711\theta^2+73517673\theta+25685438\right)-2^{6} 3 x^{6}\left(2709886\theta^4+7353008\theta^3+18175093\theta^2+18787708\theta+5966228\right)+2^{6} x^{7}\left(154368940\theta^4+947965400\theta^3+2363187035\theta^2+2646307981\theta+1071488886\right)+2^{8} x^{8}(\theta+1)(119648213\theta^3+399067803\theta^2+77665606\theta-498465144)-2^{8} 3 x^{9}(\theta+1)(\theta+2)(120410834\theta^2+865960638\theta+1188072247)-2^{10} 3^{2} 107 x^{10}(\theta+3)(\theta+2)(\theta+1)(218683\theta-39394)+2^{11} 3^{3} 5 107^{2} 137 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 14, 72, 1554, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...

Discriminant

\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)

Local exponents

\(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) ≈\(-0.124082-0.085658I\) ≈\(-0.124082+0.085658I\)\(-\frac{ 1}{ 10}\)\(0\) ≈\(0.040135\)\(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\)\(\frac{ 1}{ 6}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(0\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)\(4\)

Note:

This is operator "11.8" from ...

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17

New Number: 11.9 |  AESZ:  |  Superseeker: 17/3 4127/9  |  Hash: fa7c260e6f07cef5d727e6af380a6373  

Degree: 11

\(3^{2} \theta^4-3 x\theta(20\theta^3+196\theta^2+125\theta+27)-x^{2}\left(19127\theta^4+69044\theta^3+89705\theta^2+54504\theta+13248\right)-2 x^{3}\left(285799\theta^4+1251420\theta^3+2142633\theta^2+1678248\theta+511560\right)-2^{2} x^{4}\left(2058125\theta^4+11190220\theta^3+23374875\theta^2+21658060\theta+7556504\right)-2^{3} x^{5}\left(8570685\theta^4+57030456\theta^3+140934413\theta^2+149627146\theta+57858760\right)-2^{6} x^{6}\left(5382486\theta^4+43183593\theta^3+124360784\theta^2+148979343\theta+62839586\right)-2^{7} x^{7}\left(7897671\theta^4+75745098\theta^3+252663545\theta^2+339244430\theta+154810568\right)-2^{10} x^{8}(\theta+1)(1454893\theta^3+15409953\theta^2+50286726\theta+48898444)-2^{11} x^{9}(\theta+1)(\theta+2)(227963\theta^2+3375435\theta+10342960)+2^{14} x^{10}(\theta+3)(\theta+2)(\theta+1)(48476\theta+271867)-2^{15} 3 5 13 23 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 92, 2328, 91212, ...
--> OEIS
Normalized instanton numbers (n0=1): 17/3, 257/6, 4127/9, 23827/3, 496999/3, ... ; Common denominator:...

Discriminant

\(-(5z+1)(13z+1)(6z+1)(368z^2+56z-1)(4z+1)^2(8z^2-26z-3)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 5}\)\(-\frac{ 7}{ 92}-\frac{ 3}{ 46}\sqrt{ 2}\)\(-\frac{ 1}{ 6}\)\(\frac{ 13}{ 8}-\frac{ 1}{ 8}\sqrt{ 193}\)\(-\frac{ 1}{ 13}\)\(0\)\(-\frac{ 7}{ 92}+\frac{ 3}{ 46}\sqrt{ 2}\)\(\frac{ 13}{ 8}+\frac{ 1}{ 8}\sqrt{ 193}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(1\)\(3\)\(1\)\(0\)\(1\)\(3\)\(3\)
\(1\)\(2\)\(2\)\(2\)\(4\)\(2\)\(0\)\(2\)\(4\)\(4\)

Note:

This is operator "11.9" from ...

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18

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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19

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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20

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

Degree: 12

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

Maple   LaTex

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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21

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

Degree: 12

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

Maple   LaTex

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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22

New Number: 6.28 |  AESZ:  |  Superseeker: 32/3 14279/9  |  Hash: 62617eacb39580484b6f6cca4374260e  

Degree: 6

\(3^{6} \theta^4-2 3^{5} x\left(93\theta^4+186\theta^3+122\theta^2+29\theta+1\right)-2^{2} 3^{4} x^{2}\left(5958\theta^4+23832\theta^3+36111\theta^2+24558\theta+6497\right)-3^{3} x^{3}\left(999379\theta^4+5996274\theta^3+13111103\theta^2+12350076\theta+4316124\right)-2^{2} 3^{2} 11 x^{4}\left(455691\theta^4+3645528\theta^3+10306397\theta^2+12061364\theta+4978244\right)-2^{2} 3^{2} 5 11^{2} 19 x^{5}(\theta+4)(\theta+1)(1431\theta^2+7155\theta+7978)-2^{6} 5^{2} 11^{3} 19^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2/3, 1732/9, 213524/27, 37218544/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 32/3, 284/3, 14279/9, 118940/3, 1226784, ... ; Common denominator:...

Discriminant

\(-(16z+3)(19z+3)(5225z^2+795z-9)(3+22z)^2\)

Local exponents

\(-\frac{ 3}{ 16}\)\(-\frac{ 159}{ 2090}-\frac{ 81}{ 2090}\sqrt{ 5}\)\(-\frac{ 3}{ 19}\)\(-\frac{ 3}{ 22}\)\(0\)\(-\frac{ 159}{ 2090}+\frac{ 81}{ 2090}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(0\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(4\)
\(2\)\(2\)\(2\)\(1\)\(0\)\(2\)\(5\)

Note:

This is operator "6.28" from ...

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23

New Number: 6.41 |  AESZ:  |  Superseeker: 161/13 26946/13  |  Hash: a18253e410f284ecdac465808ec8a6e1  

Degree: 6

\(13^{6} \theta^4-13^{5} x\left(1382\theta^4+2764\theta^3+2109\theta^2+727\theta+96\right)-13^{4} x^{2}\left(104743\theta^4+418972\theta^3+637899\theta^2+437854\theta+116928\right)-2^{2} 13^{3} x^{3}\left(746084\theta^4+4476504\theta^3+9750459\theta^2+9107109\theta+3146850\right)-2^{5} 7 13^{2} x^{4}\left(180214\theta^4+1441712\theta^3+4063657\theta^2+4720932\theta+1930533\right)-2^{9} 3 5 7^{2} 13 x^{5}(\theta+4)(\theta+1)(688\theta^2+3440\theta+3823)-2^{13} 3^{2} 5^{2} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 96/13, 49776/169, 35502696/2197, 30531314880/28561, ...
--> OEIS
Normalized instanton numbers (n0=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...

Discriminant

\(-(-169+18720z+22400z^2)(8z+13)^2(21z+13)^2\)

Local exponents

\(-\frac{ 13}{ 8}\)\(-\frac{ 117}{ 280}-\frac{ 169}{ 560}\sqrt{ 2}\)\(-\frac{ 13}{ 21}\)\(0\)\(-\frac{ 117}{ 280}+\frac{ 169}{ 560}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(0\)\(0\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(4\)
\(1\)\(2\)\(1\)\(0\)\(2\)\(5\)

Note:

This is operator "6.41" from ...

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24

New Number: 6.33 |  AESZ:  |  Superseeker: 352 26115552  |  Hash: 0677bb20f37d2fa88bafbc665d5157c1  

Degree: 6

\(\theta^4-2^{4} x\left(96\theta^4+192\theta^3+404\theta^2+308\theta+85\right)+2^{12} x^{2}\left(112\theta^4+448\theta^3+416\theta^2-64\theta-159\right)+2^{20} x^{3}\left(192\theta^4+1152\theta^3+3448\theta^2+5160\theta+3101\right)-2^{28} x^{4}\left(272\theta^4+2176\theta^3+6880\theta^2+10112\theta+5757\right)-2^{38} 3 x^{5}\left(8\theta^4+80\theta^3+315\theta^2+575\theta+407\right)+2^{48} 3^{2} x^{6}\left((\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1360, 1516304, 1522167040, 1444349938960, ...
--> OEIS
Normalized instanton numbers (n0=1): 352, 60664, 26115552, 16623590600, 13165993300256, ... ; Common denominator:...

Discriminant

\((256z-1)^2(768z-1)^2(256z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0\)\(\frac{ 1}{ 768}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(3\)
\(0\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(3\)
\(1\)\(0\)\(-2\)\(\frac{ 1}{ 2}\)\(3\)
\(1\)\(0\)\(3\)\(1\)\(3\)

Note:

This is operator "6.33" from ...

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25

New Number: 6.34 |  AESZ:  |  Superseeker: 4/3 -124/81  |  Hash: 1153f8807d42d96ede28f7a8d06c144b  

Degree: 6

\(3^{2} \theta^4-2^{2} 3 x\left(8\theta^4+16\theta^3+27\theta^2+19\theta+5\right)-2^{4} x^{2}\left(272\theta^4+1088\theta^3+1984\theta^2+1792\theta+621\right)+2^{8} x^{3}\left(192\theta^4+1152\theta^3+3448\theta^2+5160\theta+3101\right)+2^{12} x^{4}\left(112\theta^4+896\theta^3+2432\theta^2+2560\theta+753\right)-2^{16} x^{5}\left(96\theta^4+960\theta^3+3860\theta^2+7300\theta+5389\right)+2^{24} x^{6}\left((\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 20/3, 332/3, 13360/27, 966020/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...

Discriminant

\((16z-1)^2(16z-3)^2(16z+1)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(3\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(3\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(-2\)\(3\)
\(1\)\(0\)\(1\)\(3\)\(3\)

Note:

This is operator "6.34" from ...

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26

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

Degree: 7

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

Maple   LaTex

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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27

New Number: 7.18 |  AESZ:  |  Superseeker: 352 26115552  |  Hash: df2c3b4e6a3366531b24bb05809eb1a4  

Degree: 7

\(\theta^4-2^{4} x\left(144\theta^4-192\theta^3-172\theta^2-76\theta-11\right)+2^{14} x^{2}\left(100\theta^4-320\theta^3-25\theta^2+155\theta+36\right)-2^{21} x^{3}\left(72\theta^4-1248\theta^3+628\theta^2-180\theta-97\right)-2^{30} x^{4}\left(212\theta^4+256\theta^3-14\theta^2+86\theta+15\right)+2^{36} 3 x^{5}\left(240\theta^4-320\theta^3-332\theta^2-380\theta-119\right)+2^{46} 3^{2} x^{6}\left(12\theta^4+64\theta^3+99\theta^2+67\theta+17\right)-2^{56} 3^{3} x^{7}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -176, 17168, -4715264, 653856016, ...
--> OEIS
Normalized instanton numbers (n0=1): 352, 60664, 26115552, 16623590600, 13165993300256, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 1}{ 256}\)\(0\)\(\frac{ 1}{ 768}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(0\)\(2\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(5\)\(1\)\(1\)

Note:

This is operator "7.18" from ...

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28

New Number: 7.19 |  AESZ:  |  Superseeker: 4/3 -124/81  |  Hash: f7f0f5d883101c38ed22cb74c80c8f5c  

Degree: 7

\(3^{3} \theta^4-2^{2} 3^{2} x\left(12\theta^4-16\theta^3-21\theta^2-13\theta-3\right)-2^{4} 3 x^{2}\left(240\theta^4+1280\theta^3+2068\theta^2+1636\theta+489\right)+2^{10} x^{3}\left(212\theta^4+592\theta^3+490\theta^2-34\theta-129\right)+2^{13} x^{4}\left(72\theta^4+1536\theta^3+4804\theta^2+5468\theta+2031\right)-2^{18} x^{5}\left(100\theta^4+720\theta^3+1535\theta^2+1155\theta+276\right)+2^{20} x^{6}\left(144\theta^4+768\theta^3+1268\theta^2+884\theta+229\right)-2^{28} x^{7}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 68, -496, 9796, ...
--> OEIS
Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...

Discriminant

\(-(16z-1)^2(16z+1)^2(16z-3)^3\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(2\)\(1\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(3\)\(1\)
\(1\)\(0\)\(1\)\(5\)\(1\)

Note:

This is operator "7.19" from ...

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29

New Number: 8.72 |  AESZ:  |  Superseeker: 32/3 14279/9  |  Hash: d1b06e21c273cae807016268cd540d98  

Degree: 8

\(3^{2} \theta^4-2 3 x\theta(85\theta^3+176\theta^2+112\theta+24)-2^{2} x^{2}\left(6581\theta^4+25808\theta^3+38672\theta^2+26184\theta+6912\right)-x^{3}\left(433513\theta^4+2497158\theta^3+5333997\theta^2+4967532\theta+1724868\right)-2 x^{4}\left(1751393\theta^4+13178758\theta^3+35803021\theta^2+40983788\theta+16698948\right)-2^{2} x^{5}(\theta+1)(3719315\theta^3+30248511\theta^2+79801768\theta+66666732)-2^{3} 3^{3} x^{6}(\theta+1)(\theta+2)(144041\theta^2+1060683\theta+1963346)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(2449\theta+10862)-2^{9} 3^{3} 7 71 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 192, 7524, 438912, ...
--> OEIS
Normalized instanton numbers (n0=1): 32/3, 284/3, 14279/9, 118940/3, 1226784, ... ; Common denominator:...

Discriminant

\(-(7z+1)(6z+1)(639z^2+87z-1)(2z+3)^2(8z+1)^2\)

Local exponents

\(-\frac{ 3}{ 2}\)\(-\frac{ 1}{ 6}\)\(-\frac{ 29}{ 426}-\frac{ 5}{ 142}\sqrt{ 5}\)\(-\frac{ 1}{ 7}\)\(-\frac{ 1}{ 8}\)\(0\)\(-\frac{ 29}{ 426}+\frac{ 5}{ 142}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(0\)\(1\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(1\)\(0\)\(2\)\(4\)

Note:

This is operator "8.72" from ...

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30

New Number: 8.73 |  AESZ:  |  Superseeker: 161/13 26946/13  |  Hash: 13db5d8c98a3d4f31589970217896191  

Degree: 8

\(13^{2} \theta^4-13 x\theta(614\theta^3+1804\theta^2+1149\theta+247)-x^{2}\left(775399\theta^4+2692636\theta^3+3693483\theta^2+2450110\theta+648960\right)-2^{2} x^{3}\left(5408420\theta^4+24616488\theta^3+45163287\theta^2+38795913\theta+12838410\right)-2^{5} x^{4}\left(9763642\theta^4+55386224\theta^3+123097843\theta^2+124066416\theta+46600563\right)-2^{9} 3 x^{5}(\theta+1)(1717504\theta^3+9940776\theta^2+20063523\theta+13933966)-2^{13} 3^{2} x^{6}(\theta+1)(\theta+2)(178975\theta^2+874119\theta+1112486)-2^{19} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(857\theta+2533)-2^{23} 3^{6} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 240, 10440, 679104, ...
--> OEIS
Normalized instanton numbers (n0=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...

Discriminant

\(-(-1+96z+896z^2)(9z+1)^2(96z+13)^2(8z+1)^2\)

Local exponents

\(-\frac{ 13}{ 96}\)\(-\frac{ 1}{ 8}\)\(-\frac{ 3}{ 56}-\frac{ 5}{ 112}\sqrt{ 2}\)\(-\frac{ 1}{ 9}\)\(0\)\(-\frac{ 3}{ 56}+\frac{ 5}{ 112}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(0\)\(0\)\(1\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)
\(4\)\(1\)\(2\)\(1\)\(0\)\(2\)\(4\)

Note:

This is operator "8.73" from ...

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