Summary

You searched for: inst=127212

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1

New Number: 6.30 |  AESZ:  |  Superseeker: 4 436  |  Hash: bc45bbf252bff0ad05b31f8e076f64cb  

Degree: 6

\(\theta^4+2^{2} x(\theta^2+\theta+1)(18\theta^2+18\theta+5)+2^{4} x^{2}\left(39\theta^4+156\theta^3+337\theta^2+362\theta+135\right)-2^{6} x^{3}\left(1124\theta^4+6744\theta^3+14434\theta^2+12954\theta+4329\right)-2^{8} 3 7 x^{4}\left(445\theta^4+3560\theta^3+10034\theta^2+11656\theta+4779\right)-2^{10} 3^{2} 7^{2} x^{5}(\theta+4)(\theta+1)(62\theta^2+310\theta+345)-2^{12} 3^{4} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, -20, 480, -11264, 285712, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...

Discriminant

\(-(-1+36z)(12z+1)^2(28z+1)^3\)

Local exponents

\(-\frac{ 1}{ 12}\)\(-\frac{ 1}{ 28}\)\(0\)\(\frac{ 1}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(0\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(-\frac{ 1}{ 4}\)\(0\)\(1\)\(4\)
\(1\)\(\frac{ 1}{ 4}\)\(0\)\(2\)\(5\)

Note:

This is operator "6.30" from ...

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2

New Number: 8.74 |  AESZ:  |  Superseeker: 4 436  |  Hash: a0fbd8561e58a032d489a1dabee1e026  

Degree: 8

\(\theta^4-2^{2} x\theta(22\theta^3+14\theta^2+9\theta+2)+2^{4} x^{2}\left(109\theta^4-74\theta^3-293\theta^2-258\theta-80\right)+2^{8} x^{3}\left(39\theta^4+414\theta^3+674\theta^2+504\theta+144\right)-2^{10} x^{4}\left(405\theta^4+1170\theta^3+1321\theta^2+424\theta-104\right)-2^{14} x^{5}(\theta+1)(12\theta^3+558\theta^2+1495\theta+1255)+2^{16} x^{6}(\theta+1)(\theta+2)(467\theta^2+1593\theta+1540)-2^{20} 5 x^{7}(\theta+3)(\theta+2)(\theta+1)(\theta-40)-2^{22} 5^{2} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 80, 1536, 56592, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...

Discriminant

\(-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3\)

Local exponents

\(-\frac{ 1}{ 8}\)\(0\)\(\frac{ 1}{ 56}\)\(\frac{ 1}{ 20}\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(-\frac{ 1}{ 4}\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(3\)
\(\frac{ 1}{ 4}\)\(0\)\(2\)\(4\)\(1\)\(4\)

Note:

This is operator "8.74" from ...

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