Summary

You searched for: sol=-9

Your search produced 5 matches

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1

New Number: 5.69 |  AESZ: 280  |  Superseeker: -117 -844872  |  Hash: 5083c4e9f432302302c564ba554e3bcd  

Degree: 5

\(\theta^4-3^{2} x\left(123\theta^4-60\theta^3-39\theta^2-9\theta-1\right)+3^{5} x^{2}\left(1521\theta^4-1260\theta^3+30\theta^2-21\theta-10\right)-3^{8} x^{3}\left(4110\theta^4-5634\theta^3-4353\theta^2-1629\theta-220\right)-3^{12} 17 x^{4}\left(286\theta^4+410\theta^3+170\theta^2-35\theta-30\right)-3^{18} 17^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -9, 81, 1017, -93231, ...
--> OEIS
Normalized instanton numbers (n0=1): -117, -28899/4, -844872, -131189436, -23932952667, ... ; Common denominator:...

Discriminant

\(-(531441z^3+14580z^2+189z-1)(-1+459z)^2\)

Local exponents

≈\(-0.015682-0.015263I\) ≈\(-0.015682+0.015263I\)\(0\)\(\frac{ 1}{ 459}\) ≈\(0.003929\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 279/5.68

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2

New Number: 11.18 |  AESZ:  |  Superseeker: -343/26 -27836/13  |  Hash: 7fd9e473da9a826dea365ad9c234d2b1  

Degree: 11

\(2^{2} 13^{2} \theta^4+2 13 x\left(2902\theta^4+6146\theta^3+4763\theta^2+1690\theta+234\right)-3 x^{2}\left(96469\theta^4+49486\theta^3-135373\theta^2-115726\theta-26754\right)+3 x^{3}\left(107658\theta^4-7866\theta^3+142429\theta^2+209352\theta+70434\right)+3^{2} x^{4}\left(27312\theta^4-323430\theta^3-1054064\theta^2-786941\theta-191951\right)-3^{4} x^{5}\left(1180\theta^4-103322\theta^3-143955\theta^2-85327\theta-20494\right)-3^{5} x^{6}\left(2379\theta^4+12696\theta^3+45266\theta^2+49297\theta+16562\right)-3^{6} x^{7}\left(929\theta^4+13156\theta^3-15355\theta^2-25877\theta-8920\right)+3^{7} x^{8}\left(1318\theta^4+2950\theta^3+2915\theta^2+772\theta-131\right)+3^{7} x^{9}\left(315\theta^4-3006\theta^3-5005\theta^2-2784\theta-504\right)-2^{2} 3^{8} x^{10}\left(42\theta^4+66\theta^3+25\theta^2-8\theta-5\right)+2^{4} 3^{10} x^{11}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -9, 333, -18639, 1264509, ...
--> OEIS
Normalized instanton numbers (n0=1): -343/26, 11207/104, -27836/13, 764852/13, -52338075/26, ... ; Common denominator:...

Discriminant

\((1+116z+75z^2+162z^3-108z^4+81z^5)(26-57z+9z^2+108z^3)^2\)

Local exponents

≈\(-0.92963\)\(0\) ≈\(0.423148-0.282683I\) ≈\(0.423148+0.282683I\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(3\)\(3\)\(1\)\(1\)
\(4\)\(0\)\(4\)\(4\)\(2\)\(1\)

Note:

This is operator "11.18" from ...

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3

New Number: 11.7 |  AESZ:  |  Superseeker: 9 2564/3  |  Hash: 3933e1482d30ea8bca1e5e5f914286e2  

Degree: 11

\(\theta^4+3 x\left(60\theta^4+12\theta^3+19\theta^2+13\theta+3\right)+3^{3} x^{2}\left(463\theta^4+304\theta^3+405\theta^2+184\theta+27\right)+3^{5} x^{3}\left(1710\theta^4+2268\theta^3+2450\theta^2+1080\theta+153\right)+3^{7} x^{4}\left(2870\theta^4+5344\theta^3+4044\theta^2-188\theta-981\right)+3^{9} x^{5}\left(560\theta^4-4552\theta^3-20650\theta^2-29130\theta-13389\right)-3^{11} x^{6}\left(5114\theta^4+37440\theta^3+101098\theta^2+119700\theta+51219\right)-3^{13} x^{7}\left(6620\theta^4+48712\theta^3+130868\theta^2+152172\theta+63981\right)-3^{16} x^{8}(\theta+1)(83\theta^3-2739\theta^2-16257\theta-20563)+3^{17} x^{9}(\theta+1)(\theta+2)(4676\theta^2+42864\theta+94887)+3^{20} x^{10}(\theta+3)(\theta+2)(\theta+1)(505\theta+2522)+2 3^{23} 7 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, -9, 135, -2115, 38799, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -72, 2564/3, -12924, 228024, ... ; Common denominator:...

Discriminant

\((18z+1)(189z^2+18z+1)(27z+1)^2(9z-1)^2(81z^2+54z+1)^2\)

Local exponents

\(-\frac{ 1}{ 3}-\frac{ 2}{ 9}\sqrt{ 2}\)\(-\frac{ 1}{ 18}\)\(-\frac{ 1}{ 21}-\frac{ 2}{ 63}\sqrt{ 3}I\)\(-\frac{ 1}{ 21}+\frac{ 2}{ 63}\sqrt{ 3}I\)\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 3}+\frac{ 2}{ 9}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(1\)\(4\)\(0\)\(1\)\(4\)

Note:

This is operator "11.7" from ...

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4

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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5

New Number: 8.59 |  AESZ:  |  Superseeker: -26/5 -234/5  |  Hash: 53885e46a1519d98ee4697de1c109214  

Degree: 8

\(5^{2} \theta^4+5 x\left(278\theta^4+772\theta^3+656\theta^2+270\theta+45\right)+x^{2}\left(19406\theta^4+145988\theta^3+259366\theta^2+172540\theta+41745\right)-3^{2} x^{3}\left(30338\theta^4+30636\theta^3-177680\theta^2-235350\theta-80565\right)-3^{2} x^{4}\left(189512\theta^4+1676428\theta^3+3050258\theta^2+2136012\theta+525339\right)+3^{4} x^{5}\left(173242\theta^4+651964\theta^3+972352\theta^2+649458\theta+161507\right)+3^{4} x^{6}\left(85922\theta^4+248940\theta^3+209506\theta^2+37044\theta-12717\right)+3^{6} x^{7}\left(1114\theta^4+2012\theta^3+1056\theta^2+50\theta-57\right)-3^{8} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -9, 123, -1719, 17739, ...
--> OEIS
Normalized instanton numbers (n0=1): -26/5, -177/10, -234/5, -1837/2, -27716/5, ... ; Common denominator:...

Discriminant

\(-(9z+1)(9z^3-1187z^2-61z-1)(-5+36z+9z^2)^2\)

Local exponents

\(-2-\frac{ 1}{ 3}\sqrt{ 41}\)\(-\frac{ 1}{ 9}\) ≈\(-0.025688-0.0135I\) ≈\(-0.025688+0.0135I\)\(0\)\(-2+\frac{ 1}{ 3}\sqrt{ 41}\) ≈\(131.940265\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

This is operator "8.59" from ...

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