Summary

You searched for: Spectrum0=1/6,5/6,7/6,11/6

Your search produced 10 matches

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1

New Number: 2.12 |  AESZ: 64  |  Superseeker: 432 78259376  |  Hash: 43991f21e20c16ab91690259b788b4cd  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(10\theta^2+10\theta+3)+2^{4} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 180, 207900, 379819440, 855338063580, ...
--> OEIS
Normalized instanton numbers (n0=1): 432, 130842, 78259376, 68104755558, 73096116588720, ... ; Common denominator:...

Discriminant

\((3888z-1)(432z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3888}\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product $B\ast c$.

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2

New Number: 2.16 |  AESZ: 65  |  Superseeker: 240 19105840  |  Hash: 13ba368bcbb10731ac8727b510731ff2  

Degree: 2

\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{9} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 277200, 457416960, 904864680720, ...
--> OEIS
Normalized instanton numbers (n0=1): 240, 57102, 19105840, 14810143935, 10017820614480, ... ; Common denominator:...

Discriminant

\((3456z-1)(1728z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3456}\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*d

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3

New Number: 2.19 |  AESZ: 112  |  Superseeker: -288 -96055968  |  Hash: 9a988f0cb0ca922885043cdadf98dd79  

Degree: 2

\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(8\theta^2+8\theta+3)+2^{12} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 720, 2273040, 9605756160, 46308725583120, ...
--> OEIS
Normalized instanton numbers (n0=1): -288, 162504, -96055968, 106571782296, -135291308081760, ... ; Common denominator:...

Discriminant

\((6912z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 6912}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 6}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 7}{ 6}\)
\(0\)\(1\)\(\frac{ 11}{ 6}\)

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4

New Number: 2.23 |  AESZ: 136  |  Superseeker: 180 -21847076  |  Hash: ff626c2fb953cb886f45f717a6a98a20  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 180, 124740, 85765680, 12047014980, ...
--> OEIS
Normalized instanton numbers (n0=1): 180, -15615, -21847076, -7438074210, 255591208800, ... ; Common denominator:...

Discriminant

\(1-3888z+5038848z^2\)

Local exponents

\(0\)\(\frac{ 1}{ 2592}-\frac{ 1}{ 7776}\sqrt{ 3}I\)\(\frac{ 1}{ 2592}+\frac{ 1}{ 7776}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product $D \ast f$

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5

New Number: 2.27 |  AESZ: 140  |  Superseeker: 108 -4945756  |  Hash: 74692097f8183c067c2c4b1a5c93387b  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(17\theta^2+17\theta+6)+2^{7} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 360, 582120, 1274232960, 3204505984680, ...
--> OEIS
Normalized instanton numbers (n0=1): 108, 54135, -4945756, 7925523138, -2434666062240, ... ; Common denominator:...

Discriminant

\((3888z-1)(3456z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3888}\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product $D \ast g$

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6

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

Degree: 2

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

Maple   LaTex

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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7

New Number: 2.34 |  AESZ:  |  Superseeker: -3936 -10892932064  |  Hash: 3047f1b969ee26b92708d8eab03c0aed  

Degree: 2

\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(32\theta^2+32\theta+13)+2^{16} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 3120, 41302800, 722261379840, 14304149060881680, ...
--> OEIS
Normalized instanton numbers (n0=1): -3936, 3550992, -10892932064, 48014348072136, -264897451764337440, ... ; Common denominator:...

Discriminant

\((27648z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 27648}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 5}{ 6}\)
\(0\)\(\frac{ 3}{ 4}\)\(\frac{ 7}{ 6}\)
\(0\)\(1\)\(\frac{ 11}{ 6}\)

Note:

This is operator "2.34" from ...

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8

New Number: 2.38 |  AESZ: 61  |  Superseeker: -41184 -5124430612320  |  Hash: 191cd9ad5f43862072f3be6811803748  

Degree: 2

\(\theta^4-2^{4} 3^{2} x(6\theta+1)(6\theta+5)(72\theta^2+72\theta+31)+2^{12} 3^{8} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 22320, 2060205840, 248752033770240, 33839074380496104720, ...
--> OEIS
Normalized instanton numbers (n0=1): -41184, 251271360, -5124430612320, 160031225395327320, -6251395923736354968480, ... ; Common denominator:...

Discriminant

\((186624z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 186624}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(\frac{ 1}{ 6}\)\(\frac{ 5}{ 6}\)
\(0\)\(\frac{ 5}{ 6}\)\(\frac{ 7}{ 6}\)
\(0\)\(1\)\(\frac{ 11}{ 6}\)

Note:

This is operator "2.38" from ...

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9

New Number: 2.4 |  AESZ: 62  |  Superseeker: 372 71562236  |  Hash: 07a3fd7577f878056e765831c6820f3d  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 120, 138600, 228708480, 463140798120, ...
--> OEIS
Normalized instanton numbers (n0=1): 372, 136182, 71562236, 63364481358, 65860679690400, ... ; Common denominator:...

Discriminant

\(-(432z+1)(3456z-1)\)

Local exponents

\(-\frac{ 1}{ 432}\)\(0\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(1\)\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(2\)\(0\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*a

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10

New Number: 2.66 |  AESZ:  |  Superseeker: -192 -229568  |  Hash: 0fb32be57a9fcd1b243f9e1341b39d45  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 60, 13860, 4084080, 1338557220, ...
--> OEIS
Normalized instanton numbers (n0=1): -192, 4182, -229568, 19136058, -2006581440, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(1\)\(\frac{ 11}{ 6}\)

Note:

This is operator "2.66" from ...

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