Summary

You searched for: sol=-16

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1

New Number: 3.32 |  AESZ:  |  Superseeker: 128 382592  |  Hash: 9b39b616939718654c472dbfb37cdd4e  

Degree: 3

\(\theta^4-2^{4} x(6\theta^2+6\theta-1)(2\theta+1)^2-2^{10} x^{2}(60\theta^2+120\theta+97)(\theta+1)^2-2^{21} x^{3}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, -16, 4624, 678656, 238896400, ...
--> OEIS
Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...

Discriminant

\(-(512z-1)(1+64z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 512}\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(-\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(2\)
\(\frac{ 3}{ 2}\)\(0\)\(2\)\(2\)

Note:

Operator equivalent to AESZ 220
B-Incarnation:
Double octic:D.O.244

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2

New Number: 5.90 |  AESZ: 330  |  Superseeker: 352 3284448  |  Hash: ba5b66d5fe92237e6416a117563571e9  

Degree: 5

\(\theta^4+2^{4} x\left(112\theta^4-64\theta^3-32\theta^2+1\right)+2^{14} x^{2}\left(56\theta^4-64\theta^3+3\theta^2-10\theta-4\right)+2^{20} x^{3}\left(32\theta^4-384\theta^3-436\theta^2-264\theta-55\right)-2^{29} 3 x^{4}(2\theta+1)(10\theta+7)(2\theta^2+4\theta+3)-2^{38} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, -16, 4368, -344320, 107445520, ...
--> OEIS
Normalized instanton numbers (n0=1): 352, -23368, 3284448, -578330224, 120252731680, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 768}\)\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)
\(1\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as double octic D.O.20

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3

New Number: 5.95 |  AESZ: 338  |  Superseeker: -140/3 -66092  |  Hash: eb4f6d6e59fafa4e794fb664dbdeab3f  

Degree: 5

\(3^{2} \theta^4+2^{2} 3 x\left(278\theta^4+424\theta^3+311\theta^2+99\theta+12\right)+2^{5} x^{2}\left(5210\theta^4+3944\theta^3-2635\theta^2-2433\theta-492\right)+2^{8} x^{3}\left(8190\theta^4-3528\theta^3-3991\theta^2-585\theta+114\right)-2^{11} 11 x^{4}(2\theta+1)(86\theta^3+57\theta^2-39\theta-32)+2^{15} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, -16, 1608, -243520, 44810920, ...
--> OEIS
Normalized instanton numbers (n0=1): -140/3, 1293, -66092, 5236719, -1553321056/3, ... ; Common denominator:...

Discriminant

\((2048z^3-640z^2+312z+1)(3+88z)^2\)

Local exponents

\(-\frac{ 3}{ 88}\) ≈\(-0.003184\)\(0\) ≈\(0.157842-0.358378I\) ≈\(0.157842+0.358378I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.95" from ...

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4

New Number: 14.10 |  AESZ:  |  Superseeker: 2 38  |  Hash: 364dddcd3359111a8e01be8efc1de60c  

Degree: 14

\(\theta^4+2 x\left(72\theta^4+48\theta^3+59\theta^2+35\theta+8\right)+2^{2} x^{2}\left(2277\theta^4+3252\theta^3+4573\theta^2+3266\theta+992\right)+2^{4} x^{3}\left(20907\theta^4+47634\theta^3+77375\theta^2+65724\theta+24022\right)+2^{7} x^{4}\left(62171\theta^4+199492\theta^3+375946\theta^2+371450\theta+156488\right)+2^{9} x^{5}\left(253302\theta^4+1066440\theta^3+2327568\theta^2+2630202\theta+1250623\right)+2^{10} x^{6}\left(1459436\theta^4+7698000\theta^3+19344508\theta^2+24706800\theta+13098093\right)+2^{12} x^{7}\left(3024300\theta^4+19348248\theta^3+55554208\theta^2+79484188\theta+46581901\right)+2^{15} x^{8}\left(2268548\theta^4+17191376\theta^3+55960360\theta^2+89050336\theta+57303573\right)+2^{18} x^{9}\left(1227744\theta^4+10826688\theta^3+39662704\theta^2+69775740\theta+49021017\right)+2^{20} x^{10}\left(945104\theta^4+9566080\theta^3+39177592\theta^2+75788768\theta+57836847\right)+2^{22} x^{11}\left(502368\theta^4+5772864\theta^3+26266668\theta^2+55590540\theta+45853745\right)+2^{25} x^{12}\left(87264\theta^4+1128192\theta^3+5668024\theta^2+13052400\theta+11573495\right)+2^{30} 5 x^{13}\left(444\theta^4+6408\theta^3+35315\theta^2+87905\theta+83203\right)+2^{35} 5^{2} x^{14}\left((\theta+4)^4\right)\)

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Coefficients of the holomorphic solution: 1, -16, 196, -2352, 29920, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...

Discriminant

\((4z+1)(2z+1)^2(64z^2+24z+1)^2(160z^2+32z+1)^2(8z+1)^3\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\)\(-\frac{ 1}{ 8}\)\(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(4\)
\(-2\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(4\)
\(3\)\(1\)\(2\)\(4\)\(0\)\(1\)\(4\)\(0\)\(4\)

Note:

This is operator "14.10" from ...

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