Summary

You searched for: Spectrum0=0,1/3,2/3,1

Your search produced 10 matches

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1

New Number: 2.28 |  AESZ: 49  |  Superseeker: 48 2864  |  Hash: 0a357a8c4fd703ab062148eadcd94daa  

Degree: 2

\(\theta^4-2^{2} 3 x(2\theta+1)^2(18\theta^2+18\theta+7)+2^{4} 3^{6} x^{2}(2\theta+1)^2(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 84, 17820, 4868400, 1499003100, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, -438, 2864, 77958, -4942032, ... ; Common denominator:...

Discriminant

\((432z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 3}\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 2}{ 3}\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $A \ast$

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2

New Number: 2.29 |  AESZ: 142  |  Superseeker: 45 27735  |  Hash: 85c2c2d8111a859d4cc03e8892c56af9  

Degree: 2

\(\theta^4-3^{2} x(3\theta+1)(3\theta+2)(18\theta^2+18\theta+7)+3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

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Coefficients of the holomorphic solution: 1, 126, 44550, 20447280, 10600093350, ...
--> OEIS
Normalized instanton numbers (n0=1): 45, -3465/4, 27735, -1156005, 55721970, ... ; Common denominator:...

Discriminant

\((729z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 729}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(\frac{ 1}{ 3}\)\(\frac{ 2}{ 3}\)
\(0\)\(\frac{ 2}{ 3}\)\(\frac{ 4}{ 3}\)
\(0\)\(1\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $A \ast$

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3

New Number: 2.30 |  AESZ: 143  |  Superseeker: -1008 -607849200  |  Hash: e9217db4c6dcfdb9588bab85e6a5f136  

Degree: 2

\(\theta^4-2^{2} 3^{2} x(6\theta+1)(6\theta+5)(18\theta^2+18\theta+7)+2^{4} 3^{8} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

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Coefficients of the holomorphic solution: 1, 1260, 6860700, 49707337680, 409490086185180, ...
--> OEIS
Normalized instanton numbers (n0=1): -1008, 499086, -607849200, 1097705372526, -2467344815777520, ... ; Common denominator:...

Discriminant

\((11664z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 11664}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(\frac{ 1}{ 3}\)\(\frac{ 5}{ 6}\)
\(0\)\(\frac{ 2}{ 3}\)\(\frac{ 7}{ 6}\)
\(0\)\(1\)\(\frac{ 11}{ 6}\)

Note:

$D\ast h^{\tilde{\;}}B\ast\kappa$

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4

New Number: 5.3 |  AESZ: 20  |  Superseeker: 3 245/3  |  Hash: a9a698dc5c79ffda497a7897390408b0  

Degree: 5

\(\theta^4-3 x\left(48\theta^4+60\theta^3+53\theta^2+23\theta+4\right)+3^{2} x^{2}\left(873\theta^4+1980\theta^3+2319\theta^2+1344\theta+304\right)-2 3^{4} x^{3}\left(1269\theta^4+3888\theta^3+5259\theta^2+3348\theta+800\right)+2^{2} 3^{6} x^{4}\left(891\theta^4+3240\theta^3+4653\theta^2+2952\theta+688\right)-2^{3} 3^{11} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

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Coefficients of the holomorphic solution: 1, 12, 252, 6600, 198540, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 33/2, 245/3, 879, 11829, ... ; Common denominator:...

Discriminant

\(-(54z-1)(27z-1)^2(18z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 54}\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 18}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 3}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 2}{ 3}\)\(3\)\(1\)
\(0\)\(2\)\(1\)\(4\)\(\frac{ 4}{ 3}\)

Note:

A-Incarnation: (3,0),(0,3),(1,1) intersection in $P^3 \times \P^3$.

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5

New Number: 11.6 |  AESZ:  |  Superseeker: 95/102 1421/102  |  Hash: e79a3108441c74cdc23a53a603a6181e  

Degree: 11

\(2^{2} 3^{2} 17^{2} \theta^4-2 3 17 x\theta(116\theta^3+1414\theta^2+911\theta+204)-x^{2}\left(2596259\theta^4+9892670\theta^3+14508941\theta^2+9947652\theta+2663424\right)-3 x^{3}\left(8561767\theta^4+41744696\theta^3+79668236\theta^2+68977704\theta+22655832\right)-2^{2} x^{4}\left(28089475\theta^4+171762758\theta^3+396877187\theta^2+402013525\theta+149622901\right)-2 x^{5}\left(127339346\theta^4+963856934\theta^3+2636877099\theta^2+3042828449\theta+1247694978\right)-x^{6}\left(283337071\theta^4+2758627602\theta^3+9101625228\theta^2+11995897911\theta+5385015134\right)-2 x^{7}\left(43252385\theta^4+777895672\theta^3+3537873325\theta^2+5604936458\theta+2806067360\right)+2^{2} 3 x^{8}(\theta+1)(7613560\theta^3+27844427\theta^2-51849552\theta-134696600)+x^{9}(\theta+1)(\theta+2)(60585089\theta^2+495871401\theta+595115780)-2^{3} 3 5^{2} x^{10}(\theta+3)(\theta+2)(\theta+1)(10279\theta-113205)-2^{4} 5^{4} 7 97 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 16, 114, 1680, ...
--> OEIS
Normalized instanton numbers (n0=1): 95/102, 58/17, 1421/102, 1451/17, 31474/51, ... ; Common denominator:...

Discriminant

\(-(-1+7z+219z^2+1115z^3+1934z^4+679z^5)(z+1)^2(100z^2-197z-102)^2\)

Local exponents

\(-1\)\(\frac{ 197}{ 200}-\frac{ 1}{ 200}\sqrt{ 79609}\)\(0\)\(\frac{ 197}{ 200}+\frac{ 1}{ 200}\sqrt{ 79609}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 3}\)\(1\)\(0\)\(1\)\(1\)\(2\)
\(\frac{ 2}{ 3}\)\(3\)\(0\)\(3\)\(1\)\(3\)
\(1\)\(4\)\(0\)\(4\)\(2\)\(4\)

Note:

This is operator "11.6" from ...

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6

New Number: 6.22 |  AESZ: 376  |  Superseeker: 5/4 35/2  |  Hash: 24fee66b67ff1a8a852f7a562f7665c1  

Degree: 6

\(2^{12} \theta^4-2^{10} x\left(106\theta^4+212\theta^3+183\theta^2+77\theta+13\right)+2^{8} x^{2}\left(19\theta^4+76\theta^3-43\theta^2-238\theta-141\right)+2^{6} 3 x^{3}\left(2988\theta^4+17928\theta^3+39970\theta^2+39234\theta+14267\right)+2^{4} 3^{3} x^{4}\left(309\theta^4+2472\theta^3+7618\theta^2+10696\theta+5311\right)-2^{2} 3^{3} 5 7^{2} x^{5}(\theta+4)(\theta+1)(22\theta^2+110\theta+123)-3^{5} 5^{2} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 13/4, 489/16, 25429/64, 1591057/256, ...
--> OEIS
Normalized instanton numbers (n0=1): 5/4, 57/16, 35/2, 459/4, 3615/4, ... ; Common denominator:...

Discriminant

\(-(7z+4)(5z-4)(105z-4)(9z-4)(4+3z)^2\)

Local exponents

\(-\frac{ 4}{ 3}\)\(-\frac{ 4}{ 7}\)\(0\)\(\frac{ 4}{ 105}\)\(\frac{ 4}{ 9}\)\(\frac{ 4}{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 3}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(2\)
\(\frac{ 2}{ 3}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(4\)
\(1\)\(2\)\(0\)\(2\)\(2\)\(2\)\(5\)

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7

New Number: 6.3 |  AESZ:  |  Superseeker: 178/7 129516/7  |  Hash: ec9e21dc2ccd3b4b4156ae1438454b96  

Degree: 6

\(7^{2} \theta^4-2 7 x\left(1488\theta^4+1452\theta^3+1125\theta^2+399\theta+56\right)+2^{2} x^{2}\left(766392\theta^4+1184952\theta^3+1010797\theta^2+454076\theta+83776\right)-2^{4} x^{3}\left(12943616\theta^4+28354200\theta^3+30710572\theta^2+16054731\theta+3215254\right)+2^{6} x^{4}\left(105973188\theta^4+333359304\theta^3+436182381\theta^2+261265857\theta+57189166\right)-2^{11} 127 x^{5}(\theta+1)(390972\theta^3+1350660\theta^2+1486781\theta+460439)+2^{14} 23^{2} 127^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 864, 80800, 9624160, ...
--> OEIS
Normalized instanton numbers (n0=1): 178/7, 3375/7, 129516/7, 6515900/7, 409239710/7, ... ; Common denominator:...

Discriminant

\((1-248z+8464z^2)(508z-7)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 31}{ 2116}-\frac{ 3}{ 529}\sqrt{ 3}\)\(\frac{ 7}{ 508}\)\(\frac{ 31}{ 2116}+\frac{ 3}{ 529}\sqrt{ 3}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 3}\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(\frac{ 2}{ 3}\)\(2\)
\(0\)\(2\)\(4\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.3" from ...

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8

New Number: 7.9 |  AESZ:  |  Superseeker: -3 -245/3  |  Hash: 5641c09b76662b0741e41b41b0c6f105  

Degree: 7

\(\theta^4-3 x\left(96\theta^4+120\theta^3+127\theta^2+67\theta+14\right)+3^{2} x^{2}\left(3897\theta^4+9540\theta^3+13209\theta^2+9246\theta+2608\right)-2 3^{4} x^{3}\left(14445\theta^4+52002\theta^3+88179\theta^2+73278\theta+23920\right)+2^{2} 3^{6} x^{4}\left(31671\theta^4+149364\theta^3+298089\theta^2+280512\theta+100780\right)-2^{3} 3^{12} x^{5}(\theta+1)(507\theta^3+2439\theta^2+4306\theta+2704)+2^{6} 3^{14} x^{6}(\theta+1)(\theta+2)(90\theta^2+351\theta+370)-2^{7} 3^{19} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 42, 1872, 86712, 4126716, ...
--> OEIS
Normalized instanton numbers (n0=1): -3, 69/4, -245/3, 879, -11829, ... ; Common denominator:...

Discriminant

\(-(36z-1)^2(27z-1)^2(54z-1)^3\)

Local exponents

\(0\)\(\frac{ 1}{ 54}\)\(\frac{ 1}{ 36}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(0\)\(1\)\(\frac{ 1}{ 3}\)\(2\)
\(0\)\(-\frac{ 1}{ 3}\)\(3\)\(\frac{ 2}{ 3}\)\(2\)
\(0\)\(\frac{ 1}{ 3}\)\(4\)\(1\)\(3\)

Note:

This is operator "7.9" from ...

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9

New Number: 8.40 |  AESZ:  |  Superseeker: 5/4 35/2  |  Hash: d3cb0fbbc65d6c5dace733d3d1ca181b  

Degree: 8

\(2^{4} \theta^4-2^{2} x\theta(2\theta^3+82\theta^2+53\theta+12)-x^{2}\left(4895\theta^4+18410\theta^3+26199\theta^2+18308\theta+5120\right)-x^{3}\left(60679\theta^4+272424\theta^3+497452\theta^2+430092\theta+143808\right)-x^{4}\left(344527\theta^4+1870838\theta^3+4034628\theta^2+3987101\theta+1478544\right)-x^{5}(\theta+1)(1076509\theta^3+5847783\theta^2+11226106\theta+7492832)-2 x^{6}(\theta+1)(\theta+2)(944887\theta^2+4249317\theta+5045304)-2^{8} 13 x^{7}(\theta+3)(\theta+2)(\theta+1)(518\theta+1381)-2^{5} 5 13^{2} 23 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 20, 168, 2652, ...
--> OEIS
Normalized instanton numbers (n0=1): 5/4, 57/16, 35/2, 459/4, 3615/4, ... ; Common denominator:...

Discriminant

\(-(23z-1)(5z+1)(2z+1)(z+1)(13z+4)^2(4z+1)^2\)

Local exponents

\(-1\)\(-\frac{ 1}{ 2}\)\(-\frac{ 4}{ 13}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 5}\)\(0\)\(\frac{ 1}{ 23}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 3}\)\(1\)\(0\)\(1\)\(2\)
\(1\)\(1\)\(3\)\(\frac{ 2}{ 3}\)\(1\)\(0\)\(1\)\(3\)
\(2\)\(2\)\(4\)\(1\)\(2\)\(0\)\(2\)\(4\)

Note:

This is operator "8.40" from ...

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10

New Number: 8.51 |  AESZ:  |  Superseeker: 58/43 1024/43  |  Hash: 85b9064701880ae8e0518e47cff1b030  

Degree: 8

\(43^{2} \theta^4-43 x\theta(142\theta^3+890\theta^2+574\theta+129)-x^{2}\left(647269\theta^4+2441818\theta^3+3538503\theta^2+2423953\theta+650848\right)-x^{3}\left(7200000\theta^4+34423908\theta^3+65337898\theta^2+57379329\theta+19251960\right)-x^{4}\left(37610765\theta^4+220029964\theta^3+499781264\theta^2+511393545\theta+194039928\right)-2 x^{5}(\theta+1)(54978121\theta^3+324737370\theta^2+665066226\theta+466789876)-x^{6}(\theta+1)(\theta+2)(185181547\theta^2+915931425\theta+1176131796)-2^{2} 3 101 x^{7}(\theta+3)(\theta+2)(\theta+1)(138979\theta+413408)-2^{2} 3^{2} 5^{2} 7 101^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 22, 204, 3474, ...
--> OEIS
Normalized instanton numbers (n0=1): 58/43, 211/43, 1024/43, 7544/43, 64880/43, ... ; Common denominator:...

Discriminant

\(-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 43}{ 101}\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 7}\)\(0\)\(\frac{ 1}{ 25}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 3}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(2\)
\(\frac{ 2}{ 3}\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(3\)
\(1\)\(4\)\(1\)\(2\)\(0\)\(2\)\(4\)

Note:

This is operator "8.51" from ...

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