Summary

You searched for: inst=1/2

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1

New Number: 6.20 |  AESZ:  |  Superseeker: 0 -1/3  |  Hash: 5169c67af7361bf7e6467dabea9612bd  

Degree: 6

\(\theta^4+x\left(11\theta+26\theta^3+2+13\theta^4+24\theta^2\right)-x^{2}(141\theta^2+282\theta+296)(\theta+1)^2-2 x^{3}(\theta+2)(\theta+1)(407\theta^2+1221\theta+654)+2^{2} 7 x^{4}(\theta+3)(\theta+1)(389\theta^2+1556\theta+1460)-2^{3} 3 7^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+166)+2^{5} 3 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, -2, 28, -224, 2464, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...

Discriminant

\((-1+2z)(4z-1)(21z^2-9z+1)(1+14z)^2\)

Local exponents

\(-\frac{ 1}{ 14}\)\(0\)\(\frac{ 3}{ 14}-\frac{ 1}{ 42}\sqrt{ 3}I\)\(\frac{ 3}{ 14}+\frac{ 1}{ 42}\sqrt{ 3}I\)\(\frac{ 1}{ 4}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(4\)
\(1\)\(0\)\(2\)\(2\)\(2\)\(2\)\(5\)

Note:

This is operator "6.20" from ...

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2

New Number: 8.42 |  AESZ:  |  Superseeker: -4 140  |  Hash: 7bc3855c04953ca11620400320722844  

Degree: 8

\(\theta^4+2^{2} x\left(26\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(305\theta^4+662\theta^3+781\theta^2+436\theta+94\right)+2^{8} x^{3}\left(519\theta^4+1278\theta^3+1541\theta^2+933\theta+213\right)+2^{10} x^{4}\left(2266\theta^4+4988\theta^3+3535\theta^2+633\theta-162\right)+2^{14} 3 x^{5}\left(569\theta^4+1184\theta^3+740\theta^2-81\theta-128\right)+2^{18} 3 x^{6}\left(254\theta^4+354\theta^3+161\theta^2-33\theta-28\right)+2^{22} 3^{2} x^{7}\left(23\theta^4+34\theta^3+8\theta^2-9\theta-4\right)-2^{27} 3^{2} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -8, 112, -1664, 23056, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, 1/2, 140, 1025/2, -9196, ... ; Common denominator:...

Discriminant

\(-(32z+1)(1024z^3-896z^2-48z-1)(1+12z+192z^2)^2\)

Local exponents

\(-\frac{ 1}{ 32}-\frac{ 1}{ 96}\sqrt{ 39}I\)\(-\frac{ 1}{ 32}\)\(-\frac{ 1}{ 32}+\frac{ 1}{ 96}\sqrt{ 39}I\) ≈\(-0.025859-0.019623I\) ≈\(-0.025859+0.019623I\)\(0\) ≈\(0.926719\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(3\)\(1\)\(3\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(4\)\(2\)\(2\)\(0\)\(2\)\(1\)

Note:

This is operator "8.42" from ...

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3

New Number: 8.54 |  AESZ:  |  Superseeker: 0 1/3  |  Hash: bb80872017d0578a4ae56172666b807c  

Degree: 8

\(\theta^4+x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)-2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)+2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)+2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 24, 72, 1296, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, 1/3, -1, 2, ... ; Common denominator:...

Discriminant

\((4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 6}\)\(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\)\(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\)\(0\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(2\)\(0\)\(1\)\(4\)

Note:

This is operator "8.54" from ...

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4

New Number: 8.82 |  AESZ:  |  Superseeker: 0 -1/3  |  Hash: 8bab1ddc8b31cb2c21f01402f27895ce  

Degree: 8

\(\theta^4-x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)+2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)-2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 24, -72, 1296, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...

Discriminant

\((6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2\)

Local exponents

\(-\frac{ 1}{ 12}\)\(0\)\(\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\)\(\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\)\(\frac{ 1}{ 6}\)\(\frac{ 1}{ 4}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)\(3\)
\(1\)\(0\)\(2\)\(2\)\(2\)\(2\)\(4\)\(4\)

Note:

This is operator "8.82" from ...

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