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You searched for: inst=1157421/4

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1

New Number: 11.20 |  AESZ:  |  Superseeker: 21/4 1285/2  |  Hash: b07e191c8c5d8b6a2c25e842f85fcaf0  

Degree: 11

\(2^{4} \theta^4-2^{2} x\left(278\theta^4+394\theta^3+309\theta^2+112\theta+16\right)-x^{2}\left(11952+57616\theta+96951\theta^2+56722\theta^3+4615\theta^4\right)+2 x^{3}\left(129366\theta^4+473682\theta^3+531879\theta^2+282576\theta+62656\right)-x^{4}\left(1430728+5365104\theta+7153953\theta^2+3814866\theta^3+1139565\theta^4\right)-2 3 x^{5}\left(286602\theta^4-694990\theta^3-3072025\theta^2-2917584\theta-895328\right)+2^{2} x^{6}\left(1338547\theta^4+4488552\theta^3+821964\theta^2-3171240\theta-1633306\right)+2^{4} x^{7}\left(17380\theta^4-1361536\theta^3-2049918\theta^2-1043692\theta-152703\right)-2^{6} x^{8}\left(106051\theta^4+123172\theta^3+23589\theta^2-28382\theta-10873\right)+2^{10} x^{9}\left(4885\theta^4+15033\theta^3+20559\theta^2+13908\theta+3737\right)-2^{12} x^{10}\left(335\theta^4+1270\theta^3+1875\theta^2+1240\theta+307\right)+2^{17} x^{11}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 4, 116, 3856, 163636, ...
--> OEIS
Normalized instanton numbers (n0=1): 21/4, 1965/32, 1285/2, 103095/8, 1157421/4, ... ; Common denominator:...

Discriminant

\((z-1)(16z^2-16z-1)(32z^2-71z+1)(4-27z-50z^2+16z^3)^2\)

Local exponents

≈\(-0.573963\)\(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 5}\)\(0\)\(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) ≈\(0.121762\)\(1\)\(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 5}\)\(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) ≈\(3.577201\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(4\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This is operator "11.20" from ...

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2

New Number: 14.3 |  AESZ:  |  Superseeker: 21/4 1285/2  |  Hash: fed06deb794f226dc9bf5119acb5fcf2  

Degree: 14

\(2^{4} \theta^4-2^{2} x\theta(32+149\theta+234\theta^2+54\theta^3)-x^{2}\left(39143\theta^4+143570\theta^3+193959\theta^2+113504\theta+25600\right)-2 x^{3}\left(488914\theta^4+2366790\theta^3+4293033\theta^2+3346032\theta+1000416\right)-x^{4}\left(10882749\theta^4+71055186\theta^3+164405289\theta^2+154949112\theta+53930896\right)-2 x^{5}\left(27668482\theta^4+276475198\theta^3+837116993\theta^2+935359976\theta+366972272\right)+2^{2} x^{6}\left(417907\theta^4-460236984\theta^3-2273346630\theta^2-3128567370\theta-1388917916\right)+2^{4} x^{7}\left(101741100\theta^4+252571782\theta^3-1076988014\theta^2-2508674129\theta-1362925766\right)+2^{6} x^{8}\left(136151221\theta^4+982924270\theta^3+1322951772\theta^2+257785345\theta-274176968\right)+2^{8} x^{9}\left(54403942\theta^4+889245288\theta^3+2318053632\theta^2+2306501340\theta+802166039\right)-2^{10} 3 x^{10}\left(16110621\theta^4-52456644\theta^3-344061634\theta^2-516147274\theta-239510540\right)-2^{12} x^{11}(\theta+1)(75181760\theta^3+257537898\theta^2+246848548\theta+22104519)-2^{14} 3 x^{12}(\theta+1)(\theta+2)(14369939\theta^2+55966221\theta+56991175)-2^{17} 3^{3} 5 x^{13}(\theta+3)(\theta+2)(\theta+1)(45377\theta+116950)-2^{20} 3^{5} 5^{2} 59 x^{14}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 100, 2592, 112308, ...
--> OEIS
Normalized instanton numbers (n0=1): 21/4, 1965/32, 1285/2, 103095/8, 1157421/4, ... ; Common denominator:...

Discriminant

\(-(3z+1)(64z^2+24z+1)(236z^2+63z-1)(360z^3+74z^2-21z-4)^2(4z+1)^3\)

Local exponents

\(-\frac{ 1}{ 3}\)\(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 63}{ 472}-\frac{ 17}{ 472}\sqrt{ 17}\) ≈\(-0.268785\)\(-\frac{ 1}{ 4}\) ≈\(-0.174147\)\(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\)\(0\)\(-\frac{ 63}{ 472}+\frac{ 17}{ 472}\sqrt{ 17}\) ≈\(0.237376\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(0\)\(1\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(0\)\(1\)\(3\)\(3\)
\(2\)\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(0\)\(2\)\(4\)\(4\)

Note:

This is operator "14.3" from ...

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