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You searched for: sol=7452

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1

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

Degree: 12

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

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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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2

New Number: 6.35 |  AESZ:  |  Superseeker:  |  Hash: de26083962cade55a4938b4011d0008e  

Degree: 6

\(\theta^4-3 x\left(63\theta^4+234\theta^3+247\theta^2+130\theta+28\right)+2 3^{4} x^{2}\left(9\theta^4+522\theta^3+1207\theta^2+1058\theta+356\right)+2^{2} 3^{7} x^{3}\left(135\theta^4+270\theta^3-730\theta^2-1395\theta-696\right)-2^{3} 3^{10} x^{4}\left(63\theta^4+774\theta^3+1372\theta^2+817\theta+88\right)-2^{4} 3^{13} x^{5}\left(72\theta^4+72\theta^3-325\theta^2-629\theta-308\right)+2^{5} 3^{16} x^{6}(3\theta+5)(3\theta+4)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 84, 7452, 692688, 66448116, ...
--> OEIS
Normalized instanton numbers (n0=1): 21, -1617/4, 7941, -986355/4, 8179455, ... ; Common denominator:...

Discriminant

\((54z-1)(27z-1)(54z+1)^2(108z-1)^2\)

Local exponents

\(-\frac{ 1}{ 54}\)\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 54}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 4}{ 3}\)
\(1\)\(0\)\(-\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(4\)\(0\)\(\frac{ 3}{ 2}\)\(2\)\(2\)\(\frac{ 5}{ 3}\)

Note:

This is operator "6.35" from ...

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