Summary

You searched for: Spectrum0=1/2,5/2,7/2,11/2

Your search produced 6 matches

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1

New Number: 6.10 |  AESZ:  |  Superseeker: 23 16723  |  Hash: 23025d094839fb9d8e76076bd9a0bfa7  

Degree: 6

\(\theta^4-x\left(254\theta^4+508\theta^3+391\theta^2+137\theta+18\right)+x^{2}\left(4657\theta^4+18628\theta^3+27265\theta^2+17274\theta+3672\right)-2^{2} 3 x^{3}\left(2920\theta^4+17520\theta^3+36833\theta^2+31659\theta+8235\right)+2^{3} 3^{4} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{5} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{6} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, 18, 1242, 138420, 18954810, ...
--> OEIS
Normalized instanton numbers (n0=1): 23, 462, 16723, 923487, 61874817, ... ; Common denominator:...

Discriminant

\((3z-1)(3888z^3-1944z^2+243z-1)(4z-1)^2\)

Local exponents

\(0\) ≈\(0.004259\) ≈\(0.215449\)\(\frac{ 1}{ 4}\) ≈\(0.280292\)\(\frac{ 1}{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(2\)\(1\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.10" from ...

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2

New Number: 6.14 |  AESZ:  |  Superseeker: 8 9928/3  |  Hash: 44968de144621e2fa74ce3964a5435f7  

Degree: 6

\(\theta^4-2^{2} x(5\theta^2+5\theta+2)(13\theta^2+13\theta+3)+2^{5} x^{2}\left(533\theta^4+2132\theta^3+3137\theta^2+2010\theta+432\right)-2^{8} 3 x^{3}\left(652\theta^4+3912\theta^3+8229\theta^2+7083\theta+1845\right)+2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{15} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{17} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, 24, 1224, 96000, 9633960, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 471/2, 9928/3, 185385, 6071232, ... ; Common denominator:...

Discriminant

\((12z-1)(24z-1)(2304z^2-192z+1)(-1+16z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 24}-\frac{ 1}{ 48}\sqrt{ 3}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 24}+\frac{ 1}{ 48}\sqrt{ 3}\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(2\)\(1\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.14" from ...

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3

New Number: 6.39 |  AESZ:  |  Superseeker: 8 3784/3  |  Hash: 6429f42cbe18bee944ac13edab1fbbcc  

Degree: 6

\(\theta^4+2^{2} x\left(49\theta^4+98\theta^3+86\theta^2+37\theta+6\right)+2^{5} x^{2}\left(593\theta^4+2372\theta^3+3521\theta^2+2298\theta+504\right)+2^{10} 3 x^{3}\left(332\theta^4+1992\theta^3+4194\theta^2+3618\theta+945\right)+2^{14} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{18} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{21} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, -24, 648, -11520, -123480, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 39/2, 3784/3, 51036, 1659840, ... ; Common denominator:...

Discriminant

\((24z+1)(110592z^3+6912z^2+108z+1)(1+32z)^2\)

Local exponents

≈\(-0.045368\)\(-\frac{ 1}{ 24}\)\(-\frac{ 1}{ 32}\) ≈\(-0.008566-0.011222I\) ≈\(-0.008566+0.011222I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 5}{ 2}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 7}{ 2}\)
\(2\)\(2\)\(1\)\(2\)\(2\)\(0\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.39" from ...

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4

New Number: 6.5 |  AESZ:  |  Superseeker: -11 -3422/3  |  Hash: 6a4aeb5833b7673c962d5598842d3f2c  

Degree: 6

\(\theta^4-x\left(12+64\theta+125\theta^2+122\theta^3+61\theta^4\right)-2^{3} x^{2}\left(193\theta^4+772\theta^3+1033\theta^2+522\theta+72\right)+2^{9} 3 x^{3}\left(146\theta^4+876\theta^3+1838\theta^2+1572\theta+405\right)-2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{16} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{19} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, 12, 324, 5760, 215460, ...
--> OEIS
Normalized instanton numbers (n0=1): -11, 68, -3422/3, 30735, -1014993, ... ; Common denominator:...

Discriminant

\(-(24z-1)(27648z^3-1728z^2+27z+1)(-1+32z)^2\)

Local exponents

≈\(-0.016119\)\(0\)\(\frac{ 1}{ 32}\) ≈\(0.03931-0.026431I\) ≈\(0.03931+0.026431I\)\(\frac{ 1}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(2\)\(0\)\(1\)\(2\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.5" from ...

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5

New Number: 6.6 |  AESZ:  |  Superseeker: 25 17452  |  Hash: e97e9b0e87960fe4cffbb22a5e935b4a  

Degree: 6

\(\theta^4-x\left(12+100\theta+305\theta^2+410\theta^3+205\theta^4\right)-2^{5} x^{2}\left(127\theta^4+508\theta^3+742\theta^2+468\theta+99\right)-2^{2} 3 x^{3}\left(2588\theta^4+15528\theta^3+32639\theta^2+28041\theta+7290\right)-2^{6} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{7} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{7} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, 12, 972, 106200, 14027580, ...
--> OEIS
Normalized instanton numbers (n0=1): 25, 446, 17452, 958347, 65098152, ... ; Common denominator:...

Discriminant

\(-(3z+1)(3456z^3+1728z^2+216z-1)(4z+1)^2\)

Local exponents

\(-\frac{ 1}{ 3}\) ≈\(-0.252234-0.033647I\) ≈\(-0.252234+0.033647I\)\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 12}2^(\frac{ 1}{ 3})+\frac{ 1}{ 24}2^(\frac{ 2}{ 3})-\frac{ 1}{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 5}{ 2}\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 7}{ 2}\)
\(2\)\(2\)\(2\)\(1\)\(0\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.6" from ...

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6

New Number: 6.7 |  AESZ:  |  Superseeker: -9 217/3  |  Hash: 9492f991c909a6774f5546668ff53b6a  

Degree: 6

\(\theta^4-3 x\left(42\theta^4+84\theta^3+77\theta^2+35\theta+6\right)+3^{3} x^{2}\left(291\theta^4+1164\theta^3+1747\theta^2+1166\theta+264\right)-2^{2} 3^{5} x^{3}\left(360\theta^4+2160\theta^3+4553\theta^2+3939\theta+1035\right)+2^{3} 3^{8} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{11} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{14} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 378, 8820, 266490, ...
--> OEIS
Normalized instanton numbers (n0=1): -9, 18, 217/3, -9, -146079, ... ; Common denominator:...

Discriminant

\((27z-1)(34992z^3-1944z^2+27z-1)(-1+36z)^2\)

Local exponents

\(0\) ≈\(0.002095-0.023494I\) ≈\(0.002095+0.023494I\)\(\frac{ 1}{ 36}\)\(\frac{ 1}{ 27}\) ≈\(0.051365\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(2\)\(1\)\(2\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.7" from ...

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