Summary

You searched for: Spectrum0=1,1,1,1

Your search produced 113 matches
 1-30  31-60  61-90  91-113 

You can download all data as plain text or as JSON

91

New Number: 8.5 |  AESZ: 173  |  Superseeker: 11 -2434/3  |  Hash: afa82ed9ee239bb5fcac960f8884db01  

Degree: 8

\(\theta^4-x(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{6} x^{2}\left(55\theta^4+112\theta^3+155\theta^2+86\theta+15\right)-2^{6} 3^{2} x^{3}\left(119\theta^4-714\theta^3-2185\theta^2-1656\theta-444\right)+2^{12} 3^{2} x^{4}\left(92\theta^4+184\theta^3+98\theta^2+6\theta+9\right)+2^{12} 3^{4} x^{5}\left(119\theta^4+1190\theta^3+671\theta^2-96\theta-140\right)+2^{18} 3^{4} x^{6}\left(55\theta^4+108\theta^3+149\theta^2+108\theta+27\right)+2^{18} 3^{6} x^{7}(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{24} 3^{8} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 420, 17472, 828324, ...
--> OEIS
Normalized instanton numbers (n0=1): 11, 229/4, -2434/3, 7512, 54801, ... ; Common denominator:...

Discriminant

\((72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2\)

Local exponents

\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 9}\)\(0-\frac{ 1}{ 24}I\)\(0\)\(0+\frac{ 1}{ 24}I\)\(\frac{ 1}{ 72}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $a \ast g$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{?})$.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

92

New Number: 8.60 |  AESZ:  |  Superseeker: 247 3584909  |  Hash: 540ab51629d98ae18b7d061824bd258b  

Degree: 8

\(\theta^4-x\left(1182\theta^4+2172\theta^3+1519\theta^2+433\theta+46\right)+x^{2}\left(70937\theta^4+62468\theta^3-34151\theta^2-26294\theta-4528\right)-2^{3} x^{3}\left(140935\theta^4-41718\theta^3-83276\theta^2-29367\theta-3376\right)+2^{4} 3 x^{4}\left(21007\theta^4-134418\theta^3-100578\theta^2-26137\theta-1974\right)+2^{6} x^{5}\left(29420\theta^4+79292\theta^3-91933\theta^2-88917\theta-22012\right)-2^{6} x^{6}\left(17519\theta^4-73056\theta^3-66923\theta^2-16512\theta+1436\right)-2^{9} 5 x^{7}\left(351\theta^4+510\theta^3+176\theta^2-79\theta-46\right)-2^{12} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 46, 15670, 8332840, 5425831846, ...
--> OEIS
Normalized instanton numbers (n0=1): 247, 38017/2, 3584909, 2039721503/2, 359173241174, ... ; Common denominator:...

Discriminant

\(-(z+1)(64z^3+600z^2+1119z-1)(1-32z+40z^2)^2\)

Local exponents

≈\(-6.805514\) ≈\(-2.570379\)\(-1\)\(0\) ≈\(0.000893\)\(\frac{ 2}{ 5}-\frac{ 3}{ 20}\sqrt{ 6}\)\(\frac{ 2}{ 5}+\frac{ 3}{ 20}\sqrt{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)\(3\)\(1\)
\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)\(4\)\(1\)

Note:

This is operator "8.60" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

93

New Number: 8.61 |  AESZ:  |  Superseeker: -32/5 -863/5  |  Hash: 9699709447380eb1373469a1cf5a9586  

Degree: 8

\(5^{2} \theta^4+5 x\left(351\theta^4+894\theta^3+752\theta^2+305\theta+50\right)+x^{2}\left(17519\theta^4+143132\theta^3+257359\theta^2+171910\theta+41600\right)-2^{3} x^{3}\left(29420\theta^4+38388\theta^3-153289\theta^2-215145\theta-74900\right)-2^{4} 3 x^{4}\left(21007\theta^4+218446\theta^3+428718\theta^2+312263\theta+79010\right)+2^{6} x^{5}\left(140935\theta^4+605458\theta^3+887488\theta^2+551709\theta+125368\right)-2^{6} x^{6}\left(70937\theta^4+221280\theta^3+204067\theta^2+54336\theta-3916\right)+2^{9} x^{7}\left(1182\theta^4+2556\theta^3+2095\theta^2+817\theta+142\right)-2^{12} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -10, 190, -4888, 151246, ...
--> OEIS
Normalized instanton numbers (n0=1): -32/5, -33/10, -863/5, 715/2, -83882/5, ... ; Common denominator:...

Discriminant

\(-(8z+1)(8z^3-1119z^2-75z-1)(5-32z+8z^2)^2\)

Local exponents

\(-\frac{ 1}{ 8}\) ≈\(-0.048631\) ≈\(-0.018367\)\(0\)\(2-\frac{ 3}{ 4}\sqrt{ 6}\)\(2+\frac{ 3}{ 4}\sqrt{ 6}\) ≈\(139.941998\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(3\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(4\)\(2\)\(1\)

Note:

This is operator "8.61" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

94

New Number: 8.62 |  AESZ:  |  Superseeker: 127 1566863/3  |  Hash: 4165325308c2b65daacebc1d19717e13  

Degree: 8

\(\theta^4+x\left(578\theta^4-572\theta^3-359\theta^2-73\theta-6\right)+3^{2} x^{2}\left(4673\theta^4+1892\theta^3+31601\theta^2+11514\theta+1728\right)-2^{3} 3^{4} x^{3}\left(9185\theta^4-134298\theta^3-35420\theta^2-22329\theta-5544\right)+2^{4} 3^{8} x^{4}\left(19051\theta^4+11846\theta^3+114678\theta^2+65939\theta+14290\right)-2^{6} 3^{12} x^{5}\left(7540\theta^4+8068\theta^3-6459\theta^2-7907\theta-2300\right)-2^{6} 3^{16} x^{6}\left(3919\theta^4+27744\theta^3+29957\theta^2+14208\theta+2556\right)+2^{9} 3^{20} 5 x^{7}\left(199\theta^4+590\theta^3+744\theta^2+449\theta+106\right)-2^{12} 3^{24} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, -810, -47784, 3354534, ...
--> OEIS
Normalized instanton numbers (n0=1): 127, -14353/2, 1566863/3, -106847355/2, 6507370854, ... ; Common denominator:...

Discriminant

\(-(81z+1)(419904z^3-22680z^2+79z-1)(-1-288z+29160z^2)^2\)

Local exponents

\(-\frac{ 1}{ 81}\)\(\frac{ 2}{ 405}-\frac{ 1}{ 1620}\sqrt{ 154}\)\(0\) ≈\(0.001382-0.006675I\) ≈\(0.001382+0.006675I\)\(\frac{ 2}{ 405}+\frac{ 1}{ 1620}\sqrt{ 154}\) ≈\(0.051248\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(1\)

Note:

This is operator "8.62" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

95

New Number: 8.63 |  AESZ:  |  Superseeker: 8/5 67  |  Hash: 2c5f91dca73abc39f5d6eb00b9c4ea16  

Degree: 8

\(5^{2} \theta^4-5 x\left(199\theta^4+206\theta^3+168\theta^2+65\theta+10\right)+x^{2}\left(3919\theta^4-12068\theta^3-29761\theta^2-21850\theta-5520\right)+2^{3} x^{3}\left(7540\theta^4+22092\theta^3+14577\theta^2+945\theta-1380\right)-2^{4} x^{4}\left(19051\theta^4+64358\theta^3+193446\theta^2+204083\theta+70234\right)+2^{6} x^{5}\left(9185\theta^4+171038\theta^3+422584\theta^2+391123\theta+124848\right)-2^{6} 3^{2} x^{6}\left(4673\theta^4+16800\theta^3+53963\theta^2+64704\theta+24596\right)-2^{9} 3^{4} x^{7}\left(578\theta^4+2884\theta^3+4825\theta^2+3383\theta+858\right)-2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 30, 488, 9934, ...
--> OEIS
Normalized instanton numbers (n0=1): 8/5, 101/10, 67, 6197/10, 32978/5, ... ; Common denominator:...

Discriminant

\(-(8z+1)(648z^3-79z^2+35z-1)(-5+32z+72z^2)^2\)

Local exponents

\(-\frac{ 2}{ 9}-\frac{ 1}{ 36}\sqrt{ 154}\)\(-\frac{ 1}{ 8}\)\(0\) ≈\(0.030113\) ≈\(0.0459-0.221678I\) ≈\(0.0459+0.221678I\)\(-\frac{ 2}{ 9}+\frac{ 1}{ 36}\sqrt{ 154}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This is operator "8.63" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

96

New Number: 8.64 |  AESZ:  |  Superseeker: 0 -32768  |  Hash: 00b5810e4a2d21fec464e4e87169df86  

Degree: 8

\(\theta^4-2^{4} x\left(32\theta^4+16\theta^3+14\theta^2+6\theta+1\right)+2^{10} x^{2}\left(86\theta^4+176\theta^3+184\theta^2+76\theta+13\right)-2^{16} x^{3}\left(61\theta^4+510\theta^3+620\theta^2+327\theta+68\right)-2^{22} x^{4}\left(110\theta^4-260\theta^3-942\theta^2-608\theta-141\right)+2^{26} x^{5}\left(708\theta^4+2160\theta^3-666\theta^2-1230\theta-397\right)+2^{32} x^{6}\left(134\theta^4-1536\theta^3-1488\theta^2-492\theta-29\right)-2^{38} 5 x^{7}\left(73\theta^4+170\theta^3+168\theta^2+83\theta+17\right)-2^{44} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 272, -15104, -2814704, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, -1116, -32768, -2011784, -92274688, ... ; Common denominator:...

Discriminant

\(-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2\)

Local exponents

≈\(-0.23168\)\(-\frac{ 1}{ 160}-\frac{ 1}{ 320}\sqrt{ 14}\)\(0\)\(-\frac{ 1}{ 160}+\frac{ 1}{ 320}\sqrt{ 14}\) ≈\(0.006465-0.004906I\) ≈\(0.006465+0.004906I\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

This is operator "8.64" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

97

New Number: 8.65 |  AESZ:  |  Superseeker: -24/5 -1608/5  |  Hash: 5e457fa5807a784e24220c973aeceba8  

Degree: 8

\(5^{2} \theta^4+2^{2} 5 x\left(73\theta^4+122\theta^3+96\theta^2+35\theta+5\right)-2^{4} x^{2}\left(134\theta^4+2072\theta^3+3924\theta^2+2660\theta+645\right)-2^{6} x^{3}\left(708\theta^4+672\theta^3-2898\theta^2-3750\theta-1285\right)+2^{10} x^{4}\left(110\theta^4+700\theta^3+498\theta^2-56\theta-105\right)+2^{12} x^{5}\left(61\theta^4-266\theta^3-544\theta^2-373\theta-88\right)-2^{14} x^{6}\left(86\theta^4+168\theta^3+172\theta^2+108\theta+31\right)+2^{16} x^{7}\left(32\theta^4+112\theta^3+158\theta^2+102\theta+25\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 92, -2704, 95596, ...
--> OEIS
Normalized instanton numbers (n0=1): -24/5, 329/10, -1608/5, 48409/10, -455264/5, ... ; Common denominator:...

Discriminant

\(-(4z-1)(256z^3-192z^2+56z+1)(-5-16z+32z^2)^2\)

Local exponents

\(\frac{ 1}{ 4}-\frac{ 1}{ 8}\sqrt{ 14}\) ≈\(-0.016861\)\(0\)\(\frac{ 1}{ 4}\) ≈\(0.38343-0.290965I\) ≈\(0.38343+0.290965I\)\(\frac{ 1}{ 4}+\frac{ 1}{ 8}\sqrt{ 14}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This is operator "8.65" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

98

New Number: 8.66 |  AESZ:  |  Superseeker: 4 12332  |  Hash: d941d8e5d41f2e7285be47b4fbc81023  

Degree: 8

\(\theta^4-2^{2} x\left(12\theta^4-24\theta^3-23\theta^2-11\theta-2\right)-2^{7} x^{2}\left(32\theta^4+392\theta^3+484\theta^2+223\theta+41\right)+2^{12} x^{3}\left(31\theta^4-30\theta^3-872\theta^2-801\theta-217\right)-2^{16} 3 x^{4}\left(140\theta^4+60\theta^3-1332\theta^2-971\theta-231\right)-2^{20} x^{5}\left(772\theta^4+7960\theta^3+7483\theta^2+1509\theta-266\right)+2^{26} x^{6}\left(46\theta^4+2766\theta^3+2333\theta^2+672\theta+19\right)-2^{30} 5 x^{7}\left(477\theta^4+930\theta^3+697\theta^2+232\theta+28\right)-2^{36} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 424, -6272, 859816, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 500, 12332, 358180, 15491360, ... ; Common denominator:...

Discriminant

\(-(64z+1)(4096z^3+6144z^2+48z-1)(1-32z+2560z^2)^2\)

Local exponents

≈\(-1.492036\) ≈\(-0.017379\)\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 160}-\frac{ 3}{ 160}I\)\(\frac{ 1}{ 160}+\frac{ 3}{ 160}I\) ≈\(0.009415\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(3\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(4\)\(2\)\(1\)

Note:

This is operator "8.66" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

99

New Number: 8.67 |  AESZ:  |  Superseeker: -49/5 -5776/5  |  Hash: 807c6166f3d1991fadc5a93fdf4671e8  

Degree: 8

\(5^{2} \theta^4+5 x\left(477\theta^4+978\theta^3+769\theta^2+280\theta+40\right)-2^{2} x^{2}\left(46\theta^4-2582\theta^3-5689\theta^2-4120\theta-1040\right)+2^{2} x^{3}\left(772\theta^4-4872\theta^3-11765\theta^2-7335\theta-1480\right)+2^{4} 3 x^{4}\left(140\theta^4+500\theta^3-672\theta^2-1313\theta-512\right)-2^{6} x^{5}\left(31\theta^4+154\theta^3-596\theta^2-729\theta-227\right)+2^{7} x^{6}\left(32\theta^4-264\theta^3-500\theta^2-303\theta-58\right)+2^{8} x^{7}\left(12\theta^4+72\theta^3+121\theta^2+85\theta+22\right)-2^{12} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 244, -11312, 635716, ...
--> OEIS
Normalized instanton numbers (n0=1): -49/5, 1441/20, -5776/5, 26480, -748058, ... ; Common denominator:...

Discriminant

\(-(z+1)(64z^3-48z^2-96z-1)(5-4z+8z^2)^2\)

Local exponents

\(-1\) ≈\(-0.899067\) ≈\(-0.010472\)\(0\)\(\frac{ 1}{ 4}-\frac{ 3}{ 4}I\)\(\frac{ 1}{ 4}+\frac{ 3}{ 4}I\) ≈\(1.659539\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(3\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(4\)\(2\)\(1\)

Note:

This is operator "8.67" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

100

New Number: 8.69 |  AESZ:  |  Superseeker: 4 52  |  Hash: e303d10e77a367612be2fb706f37b895  

Degree: 8

\(\theta^4-2^{2} x\left(20\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(125\theta^4+362\theta^3+471\theta^2+284\theta+66\right)-2^{7} x^{3}\left(191\theta^4+606\theta^3+855\theta^2+588\theta+154\right)+2^{10} x^{4}\left(192\theta^4+552\theta^3+562\theta^2+268\theta+49\right)-2^{13} x^{5}\left(134\theta^4+380\theta^3+373\theta^2+124\theta+3\right)+2^{16} x^{6}\left(61\theta^4+150\theta^3+173\theta^2+93\theta+19\right)-2^{19} x^{7}\left(19\theta^4+50\theta^3+56\theta^2+31\theta+7\right)+2^{23} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 128, 2816, 74896, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 15/2, 52, 1563/2, 7276, ... ; Common denominator:...

Discriminant

\((16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}\)\(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 7}I\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 7}I\)\(\frac{ 1}{ 8}\)\(\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(4\)\(2\)\(2\)\(1\)

Note:

This is operator "8.69" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

101

New Number: 8.6 |  AESZ: 113  |  Superseeker: 11 1200  |  Hash: 3754b3cce7930e99efa8acb802e524bb  

Degree: 8

\(\theta^4-x(10\theta^2+10\theta+3)(11\theta^2+11\theta+3)+x^{2}\left(1025\theta^4+3992\theta^3+5533\theta^2+3082\theta+615\right)-3^{2} x^{3}\left(110\theta^4-660\theta^3-2027\theta^2-1509\theta-369\right)+3^{2} x^{4}\left(2032\theta^4+4064\theta^3-2726\theta^2-4758\theta-1431\right)+3^{4} x^{5}\left(110\theta^4+1100\theta^3+613\theta^2-125\theta-117\right)+3^{4} x^{6}\left(1025\theta^4+108\theta^3-293\theta^2+108\theta+99\right)+3^{6} x^{7}(10\theta^2+10\theta+3)(11\theta^2+11\theta+3)+3^{8} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 285, 13671, 799389, ...
--> OEIS
Normalized instanton numbers (n0=1): 11, 66, 1200, 28201, 802124, ... ; Common denominator:...

Discriminant

\((81z^2+99z-1)(z^2+11z-1)(1+9z^2)^2\)

Local exponents

\(-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\)\(-\frac{ 11}{ 18}-\frac{ 5}{ 18}\sqrt{ 5}\)\(0-\frac{ 1}{ 3}I\)\(0\)\(0+\frac{ 1}{ 3}I\)\(-\frac{ 11}{ 18}+\frac{ 5}{ 18}\sqrt{ 5}\)\(-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $b \ast c$.This operator has a second MUM-point at infinity with the same instanton numbers.
If can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{?})$.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

102

New Number: 8.70 |  AESZ:  |  Superseeker: 32 8608  |  Hash: 664bcad4360eb63fde0fdd3018aed2f2  

Degree: 8

\(\theta^4-2^{4} x\left(19\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{9} x^{2}\left(61\theta^4+94\theta^3+89\theta^2+47\theta+10\right)-2^{14} x^{3}\left(134\theta^4+156\theta^3+37\theta^2+18\theta+6\right)+2^{19} x^{4}\left(192\theta^4+216\theta^3+58\theta^2-32\theta-17\right)-2^{24} x^{5}\left(191\theta^4+158\theta^3+183\theta^2+68\theta+6\right)+2^{29} x^{6}\left(125\theta^4+138\theta^3+135\theta^2+72\theta+16\right)-2^{35} x^{7}\left(20\theta^4+46\theta^3+47\theta^2+24\theta+5\right)+2^{41} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 848, 72448, 7745296, ...
--> OEIS
Normalized instanton numbers (n0=1): 32, 504, 8608, 475061, 28268384, ... ; Common denominator:...

Discriminant

\((16z-1)(32z-1)(1024z^2-192z+1)(1-32z+2048z^2)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\)\(\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 7}I\)\(\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 7}I\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

This is operator "8.70" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

103

New Number: 8.7 |  AESZ: 106  |  Superseeker: 12 356  |  Hash: fe1c90929d18b81637eaaa93366409ed  

Degree: 8

\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+2^{4} x^{2}\left(241\theta^4+940\theta^3+1303\theta^2+726\theta+145\right)-2^{7} x^{3}\left(33\theta^4-198\theta^3-607\theta^2-456\theta-117\right)+2^{10} x^{4}\left(239\theta^4+478\theta^3-322\theta^2-561\theta-169\right)+2^{12} x^{5}\left(33\theta^4+330\theta^3+185\theta^2-32\theta-37\right)+2^{14} x^{6}\left(241\theta^4+24\theta^3-71\theta^2+24\theta+23\right)+2^{17} x^{7}(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+2^{20} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 380, 16464, 845676, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, 20, 356, 34561/4, 161840, ... ; Common denominator:...

Discriminant

\((64z^2+88z-1)(16z^2+44z-1)(1+32z^2)^2\)

Local exponents

\(-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\)\(-\frac{ 11}{ 16}-\frac{ 5}{ 16}\sqrt{ 5}\)\(0-\frac{ 1}{ 8}\sqrt{ 2}I\)\(0\)\(0+\frac{ 1}{ 8}\sqrt{ 2}I\)\(-\frac{ 11}{ 16}+\frac{ 5}{ 16}\sqrt{ 5}\)\(-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $b\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{?})$.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

104

New Number: 8.80 |  AESZ:  |  Superseeker: -28/3 2764/3  |  Hash: 01b1872abfd55652952ae535920a40fe  

Degree: 8

\(3^{2} \theta^4+2^{2} 3 x\left(148\theta^4+248\theta^3+223\theta^2+99\theta+18\right)+2^{7} x^{2}\left(1124\theta^4+3080\theta^3+4211\theta^2+2709\theta+675\right)+2^{12} x^{3}\left(1684\theta^4+4872\theta^3+7059\theta^2+5373\theta+1530\right)+2^{17} x^{4}\left(1828\theta^4+4952\theta^3+5125\theta^2+2799\theta+599\right)+2^{23} x^{5}\left(720\theta^4+1992\theta^3+2102\theta^2+691\theta-13\right)+2^{29} x^{6}\left(200\theta^4+504\theta^3+669\theta^2+390\theta+83\right)+2^{35} x^{7}\left(40\theta^4+104\theta^3+118\theta^2+66\theta+15\right)+2^{43} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, 872, -37248, 1740456, ...
--> OEIS
Normalized instanton numbers (n0=1): -28/3, 49/3, 2764/3, 13414, 44384, ... ; Common denominator:...

Discriminant

\((16z+1)(32z+1)(64z+1)^2(2048z^2+32z+3)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 32}\)\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 23}I\)\(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 23}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(3\)\(0\)\(1\)
\(2\)\(2\)\(1\)\(4\)\(4\)\(0\)\(1\)

Note:

This is operator "8.80" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

105

New Number: 8.81 |  AESZ:  |  Superseeker: -64 54464  |  Hash: 3cc4cfea037192a297dc29928555ed1d  

Degree: 8

\(\theta^4+2^{4} x\left(40\theta^4+56\theta^3+46\theta^2+18\theta+3\right)+2^{10} x^{2}\left(200\theta^4+296\theta^3+357\theta^2+236\theta+58\right)+2^{16} x^{3}\left(720\theta^4+888\theta^3+446\theta^2+417\theta+126\right)+2^{22} x^{4}\left(1828\theta^4+2360\theta^3+1237\theta^2-93\theta-199\right)+2^{29} x^{5}\left(1684\theta^4+1864\theta^3+2547\theta^2+865\theta+28\right)+2^{36} x^{6}\left(1124\theta^4+1416\theta^3+1715\theta^2+969\theta+221\right)+2^{43} 3 x^{7}\left(148\theta^4+344\theta^3+367\theta^2+195\theta+42\right)+2^{53} 3^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -48, 4112, -470784, 65066256, ...
--> OEIS
Normalized instanton numbers (n0=1): -64, 2380, 54464, -1677212, -279711424, ... ; Common denominator:...

Discriminant

\((128z+1)(256z+1)(64z+1)^2(24576z^2+64z+1)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 128}\)\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 768}-\frac{ 1}{ 768}\sqrt{ 23}I\)\(-\frac{ 1}{ 768}+\frac{ 1}{ 768}\sqrt{ 23}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)
\(1\)\(2\)\(2\)\(4\)\(4\)\(0\)\(1\)

Note:

This is operator "8.81" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

106

New Number: 8.84 |  AESZ:  |  Superseeker: 1/5 224/5  |  Hash: 258fab6f0a4f132fe597fc6f30e54eea  

Degree: 8

\(5^{2} \theta^4+5 x\theta^2(-1-2\theta+107\theta^2)+2^{2} x^{2}\left(2174\theta^4+5942\theta^3+8569\theta^2+5200\theta+1200\right)+2^{2} 3^{2} x^{3}\left(308\theta^4-4248\theta^3-17051\theta^2-16785\theta-5280\right)-2^{4} 3^{2} x^{4}\left(7060\theta^4+39500\theta^3+69820\theta^2+52851\theta+14688\right)-2^{6} 3^{4} x^{5}\left(881\theta^4+3974\theta^3+8648\theta^2+7983\theta+2581\right)+2^{7} 3^{4} x^{6}\left(1192\theta^4+2376\theta^3-1132\theta^2-4185\theta-1926\right)+2^{8} 3^{6} x^{7}\left(68\theta^4+568\theta^3+1095\theta^2+811\theta+210\right)-2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, -12, 144, 324, ...
--> OEIS
Normalized instanton numbers (n0=1): 1/5, -6, 224/5, -448/5, -4334/5, ... ; Common denominator:...

Discriminant

\(-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2\)

Local exponents

≈\(-0.597246\)\(\frac{ 1}{ 4}-\frac{ 1}{ 12}\sqrt{ 19}\) ≈\(-0.020821-0.049733I\) ≈\(-0.020821+0.049733I\)\(0\)\(\frac{ 1}{ 9}\)\(\frac{ 1}{ 4}+\frac{ 1}{ 12}\sqrt{ 19}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(4\)\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

This is operator "8.84" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

107

New Number: 8.85 |  AESZ:  |  Superseeker: 196 1986884/3  |  Hash: d959f61fe3ba327116d3bae5ae5a0ade  

Degree: 8

\(\theta^4+2^{2} x\left(68\theta^4-296\theta^3-201\theta^2-53\theta-6\right)-2^{7} x^{2}\left(1192\theta^4+2392\theta^3-1108\theta^2-439\theta-57\right)-2^{12} 3^{2} x^{3}\left(881\theta^4-450\theta^3+2012\theta^2+915\theta+153\right)+2^{16} 3^{2} x^{4}\left(7060\theta^4-11260\theta^3-6320\theta^2-3471\theta-783\right)+2^{20} 3^{4} x^{5}\left(308\theta^4+5480\theta^3-2459\theta^2-3341\theta-990\right)-2^{26} 3^{4} x^{6}\left(2174\theta^4+2754\theta^3+3787\theta^2+2808\theta+801\right)+2^{30} 3^{6} 5 x^{7}(107\theta^2+216\theta+108)(\theta+1)^2-2^{36} 3^{8} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 2472, 412800, 83283624, ...
--> OEIS
Normalized instanton numbers (n0=1): 196, -5988, 1986884/3, -62128884, 8854857504, ... ; Common denominator:...

Discriminant

\(-(64z+1)(331776z^3-9216z^2+368z-1)(-1-288z+23040z^2)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(\frac{ 1}{ 160}-\frac{ 1}{ 480}\sqrt{ 19}\)\(0\) ≈\(0.002907\) ≈\(0.012435-0.029703I\) ≈\(0.012435+0.029703I\)\(\frac{ 1}{ 160}+\frac{ 1}{ 480}\sqrt{ 19}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This is operator "8.85" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

108

New Number: 8.86 |  AESZ:  |  Superseeker: 226/35 3959/7  |  Hash: 815127e123ce989d9ab793a009bb2e6a  

Degree: 8

\(5^{2} 7^{2} \theta^4-5 7 x\left(3223\theta^4+4862\theta^3+3866\theta^2+1435\theta+210\right)-x^{2}\left(6440-193270\theta-1217171\theta^2-2477628\theta^3-1818051\theta^4\right)-2^{4} 3 x^{3}\left(248985\theta^4+335357\theta^3+239138\theta^2+105280\theta+22400\right)+2^{6} x^{4}\left(618707\theta^4+1107118\theta^3+1179459\theta^2+710680\theta+177284\right)-2^{11} 3 x^{5}\left(12903\theta^4+34738\theta^3+48739\theta^2+33712\theta+8972\right)+2^{15} x^{6}\left(3323\theta^4+12570\theta^3+20137\theta^2+14550\theta+3916\right)-2^{20} x^{7}(\theta+1)(99+295\theta+286\theta^2+88\theta^3)+2^{25} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 146, 5280, 229986, ...
--> OEIS
Normalized instanton numbers (n0=1): 226/35, 1599/35, 3959/7, 51101/5, 8052703/35, ... ; Common denominator:...

Discriminant

\((1-77z+251z^2-352z^3+512z^4)(32z-5)^2(8z-7)^2\)

Local exponents

\(0\)\(\frac{ 5}{ 32}\)\(\frac{ 7}{ 8}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(3\)\(1\)\(1\)
\(0\)\(4\)\(4\)\(2\)\(1\)

Note:

This is operator "8.86" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

109

New Number: 8.8 |  AESZ: 161  |  Superseeker: 9 -1229/3  |  Hash: 641d1de9a6564241575c5db52faef694  

Degree: 8

\(\theta^4-3 x(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+3^{2} x^{2}\left(366\theta^4+1428\theta^3+1980\theta^2+1104\theta+221\right)-3^{4} x^{3}\left(33\theta^4-198\theta^3-607\theta^2-456\theta-117\right)+3^{5} x^{4}\left(726\theta^4+1452\theta^3-978\theta^2-1704\theta-515\right)+3^{7} x^{5}\left(33\theta^4+330\theta^3+185\theta^2-32\theta-37\right)+3^{8} x^{6}\left(366\theta^4+36\theta^3-108\theta^2+36\theta+35\right)+3^{10} x^{7}(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+3^{12} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 171, 3087, 11259, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, -81/4, -1229/3, -4644, -26685, ... ; Common denominator:...

Discriminant

\((729z^4+2673z^3+3240z^2-99z+1)(1+27z^2)^2\)

Local exponents

≈\(-1.848362\) ≈\(-1.848362\)\(0-\frac{ 1}{ 9}\sqrt{ 3}I\)\(0\)\(0+\frac{ 1}{ 9}\sqrt{ 3}I\) ≈\(0.015028\) ≈\(0.015028\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $b \qst f$. This operator has a second MUM-point at infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{\})$

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

110

New Number: 8.9 |  AESZ: 174  |  Superseeker: 16 -13  |  Hash: 3f987b46d9ebf201eeead1a885b78e66  

Degree: 8

\(\theta^4-x(11\theta^2+11\theta+3)(17\theta^2+17\theta+6)+x^{2}\left(8711\theta^4+33980\theta^3+47095\theta^2+26230\theta+5232\right)-2^{3} 3^{2} x^{3}\left(187\theta^4-1122\theta^3-3436\theta^2-2595\theta-684\right)+2^{4} 3^{2} x^{4}\left(8639\theta^4+17278\theta^3-11650\theta^2-20289\theta-6102\right)+2^{6} 3^{4} x^{5}\left(187\theta^4+1870\theta^3+1052\theta^2-163\theta-216\right)+2^{6} 3^{4} x^{6}\left(8711\theta^4+864\theta^3-2579\theta^2+864\theta+828\right)+2^{9} 3^{6} x^{7}(11\theta^2+11\theta+3)(17\theta^2+17\theta+6)+2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 798, 45864, 2994894, ...
--> OEIS
Normalized instanton numbers (n0=1): 16, 7/2, -13, 11663/2, -26414, ... ; Common denominator:...

Discriminant

\((81z^2+99z-1)(64z^2+88z-1)(1+72z^2)^2\)

Local exponents

\(-\frac{ 11}{ 16}-\frac{ 5}{ 16}\sqrt{ 5}\)\(-\frac{ 11}{ 18}-\frac{ 5}{ 18}\sqrt{ 5}\)\(0-\frac{ 1}{ 12}\sqrt{ 2}I\)\(0\)\(0+\frac{ 1}{ 12}\sqrt{ 2}I\)\(-\frac{ 11}{ 18}+\frac{ 5}{ 18}\sqrt{ 5}\)\(-\frac{ 11}{ 16}+\frac{ 5}{ 16}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $ b \ast g$. This operator has a second MUM-point at infinity with the same instanton numbers. It
can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{?})$.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

111

New Number: 9.3 |  AESZ:  |  Superseeker: 10 3394/3  |  Hash: 40e3715abcc5c4cb07e700ca79f80abf  

Degree: 9

\(\theta^4-x\left(57\theta^4+116\theta^3+84\theta^2+26\theta+3\right)-2 x^{2}\left(894\theta^4+3208\theta^3+4571\theta^2+2771\theta+651\right)-2 x^{3}\left(7322\theta^4+56368\theta^3+124783\theta^2+101099\theta+29757\right)+2 3^{2} x^{4}\left(6967\theta^4-27080\theta^3-139991\theta^2-138507\theta-45297\right)+2 3^{4} x^{5}\left(17617\theta^4+49068\theta^3-31255\theta^2-79893\theta-34578\right)+2 3^{8} x^{6}\left(1082\theta^4+8360\theta^3+7967\theta^2+1439\theta-773\right)-2 3^{11} x^{7}\left(198\theta^4-864\theta^3-1545\theta^2-909\theta-155\right)-3^{15} x^{8}\left(69\theta^4+144\theta^3+126\theta^2+54\theta+10\right)-3^{20} x^{9}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 3, 135, 5349, 258039, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...

Discriminant

\(-(-1+81z)(-1+9z)^2(81z^2+14z+1)^3\)

Local exponents

\(-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I\)\(-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I\)\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 1}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)
\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

This is operator "9.3" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

112

New Number: 9.4 |  AESZ:  |  Superseeker: -90 -413926  |  Hash: e2329b2f9cd1e3f65d29644e6ce39d24  

Degree: 9

\(\theta^4+3^{2} x\left(69\theta^4+132\theta^3+108\theta^2+42\theta+7\right)+2 3^{5} x^{2}\left(198\theta^4+1656\theta^3+2235\theta^2+1203\theta+271\right)-2 3^{9} x^{3}\left(1082\theta^4-4032\theta^3-10621\theta^2-6257\theta-1523\right)-2 3^{12} x^{4}\left(17617\theta^4+21400\theta^3-72757\theta^2-59353\theta-17391\right)-2 3^{17} x^{5}\left(6967\theta^4+54948\theta^3-16949\theta^2-32367\theta-12734\right)+2 3^{22} x^{6}\left(7322\theta^4-27080\theta^3-389\theta^2+8651\theta+4395\right)+2 3^{29} x^{7}\left(894\theta^4+368\theta^3+311\theta^2+323\theta+137\right)+3^{36} x^{8}\left(57\theta^4+112\theta^3+78\theta^2+22\theta+2\right)-3^{43} x^{9}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -63, 4455, 34551, -114913161, ...
--> OEIS
Normalized instanton numbers (n0=1): -90, -8685/2, -413926, -38862153, -4502063682, ... ; Common denominator:...

Discriminant

\(-(-1+27z)(-1+243z)^2(59049z^2+378z+1)^3\)

Local exponents

\(-\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\)\(-\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\)\(0\)\(\frac{ 1}{ 243}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)
\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(0\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

This is operator "9.4" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

113

New Number: 8.87 |  AESZ:  |  Superseeker: 10 18994/9  |  Hash: 038b62cbc5b6e43ac232ededcc3b6a59  

Degree: 8

\(\theta^4+2 x\theta(-2-13\theta-22\theta^2+88\theta^3)+2^{2} x^{2}\left(3323\theta^4+722\theta^3+2365\theta^2+1306\theta+256\right)+2^{4} 3 x^{3}\left(12903\theta^4+16874\theta^3+21943\theta^2+11164\theta+2164\right)+2^{5} x^{4}\left(618707\theta^4+1367710\theta^3+1570347\theta^2+801712\theta+157652\right)+2^{9} 3 x^{5}\left(248985\theta^4+660583\theta^3+726977\theta^2+362865\theta+69886\right)+2^{11} x^{6}\left(1818051\theta^4+4794576\theta^3+4692593\theta^2+2080392\theta+357884\right)+2^{17} 5 7 x^{7}\left(3223\theta^4+8030\theta^3+8618\theta^2+4603\theta+1002\right)+2^{23} 5^{2} 7^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, -64, 576, 22716, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -581/4, 18994/9, -274969/8, 3458142/5, ... ; Common denominator:...

Discriminant

\((1+44z+2008z^2+39424z^3+32768z^4)(10z+1)^2(56z+1)^2\)

Local exponents

\(-\frac{ 1}{ 10}\)\(-\frac{ 1}{ 56}\)\(0\)\(s_1\)\(s_3\)\(s_2\)\(s_4\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(4\)\(4\)\(0\)\(2\)\(2\)\(2\)\(2\)\(1\)

Note:

This is operator "8.87" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  


 1-30  31-60  61-90  91-113