Summary

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

Your search produced 3 matches

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1

New Number: 2.51 |  AESZ: ~88,~89  |  Superseeker: -5472 -6444589536  |  Hash: 02d09c6c320ab036e45834cf0d3951e7  

Degree: 2

\(\theta^4-2^{4} 3 x\left(1152\theta^4+2304\theta^3+2704\theta^2+1552\theta+339\right)+2^{16} 3^{2} x^{2}(6\theta+5)^2(6\theta+7)^2\)

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Coefficients of the holomorphic solution: 1, 16272, 347859216, 8115450239232, 197661638029770000, ...
--> OEIS
Normalized instanton numbers (n0=1): -5472, -4476528, -6444589536, -12228845295024, -27012506850929952, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 27648}\)\(\infty\)
\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 7}{ 6}\)

Note:

Operator equivalent to $\widehat{14}$
B-Incarnations:
Double octics: D.O.267, D.O.275

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2

New Number: 7.15 |  AESZ:  |  Superseeker: -2 -952  |  Hash: d9a911258d890c112974a4ba19e93e6d  

Degree: 7

\(\theta^4+2 x\left(138\theta^4+156\theta^3+137\theta^2+59\theta+10\right)+2^{2} x^{2}\left(4796\theta^4+15824\theta^3+16719\theta^2+7610\theta+1400\right)-2^{4} 5 x^{3}\left(5876\theta^4-28824\theta^3-58439\theta^2-39075\theta-9350\right)-2^{6} 5 x^{4}\left(184592\theta^4+414976\theta^3-60816\theta^2-180968\theta-60145\right)+2^{10} 3 x^{5}\left(240624\theta^4-905760\theta^3-1250920\theta^2-576920\theta-83925\right)+2^{18} 3^{2} x^{6}\left(13608\theta^4+48276\theta^3+66402\theta^2+41679\theta+9935\right)-2^{20} 3^{5} x^{7}(6\theta+5)^2(6\theta+7)^2\)

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Coefficients of the holomorphic solution: 1, -20, 900, -55280, 3962500, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, -343/2, -952, -45148, -17303644/25, ... ; Common denominator:...

Discriminant

\(-(-1-16z+256z^2)(32z-1)^2(108z+1)^3\)

Local exponents

\(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 1}{ 108}\)\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(1\)\(\frac{ 3}{ 2}\)\(0\)\(3\)\(1\)\(\frac{ 7}{ 6}\)
\(2\)\(2\)\(0\)\(4\)\(2\)\(\frac{ 7}{ 6}\)

Note:

This is operator "7.15" from ...

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3

New Number: 8.25 |  AESZ: 299  |  Superseeker: -54 -197216/3  |  Hash: c9e3907e21d64cf5564bf2d00992459e  

Degree: 8

\(\theta^4-2 3 x\left(144\theta^4+36\theta^3+47\theta^2+29\theta+6\right)+2^{2} 3^{2} x^{2}\left(8376\theta^4+6648\theta^3+8157\theta^2+3900\theta+724\right)-2^{4} 3^{4} x^{3}\left(42672\theta^4+68616\theta^3+81056\theta^2+44841\theta+9964\right)+2^{6} 3^{5} x^{4}\left(374028\theta^4+962040\theta^3+1262091\theta^2+794463\theta+195335\right)-2^{8} 3^{7} x^{5}\left(633840\theta^4+2243328\theta^3+3405968\theta^2+2385208\theta+629129\right)+2^{12} 3^{8} x^{6}\left(438960\theta^4+1884384\theta^3+3176664\theta^2+2380392\theta+652943\right)-2^{19} 3^{10} x^{7}\left(5760\theta^4+25128\theta^3+39548\theta^2+26606\theta+6517\right)+2^{22} 3^{11} x^{8}(6\theta+5)^2(6\theta+7)^2\)

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Coefficients of the holomorphic solution: 1, 36, 1908, 116496, 7816500, ...
--> OEIS
Normalized instanton numbers (n0=1): -54, -1530, -197216/3, -3553920, -222887448, ... ; Common denominator:...

Discriminant

\((1-144z+6912z^2)(108z-1)^2(3456z^2-252z+1)^2\)

Local exponents

\(0\)\(\frac{ 7}{ 192}-\frac{ 1}{ 576}\sqrt{ 345}\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 96}-\frac{ 1}{ 288}\sqrt{ 3}I\)\(\frac{ 1}{ 96}+\frac{ 1}{ 288}\sqrt{ 3}I\)\(\frac{ 7}{ 192}+\frac{ 1}{ 576}\sqrt{ 345}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(\frac{ 7}{ 6}\)
\(0\)\(4\)\(1\)\(2\)\(2\)\(4\)\(\frac{ 7}{ 6}\)

Note:

This is operator "8.25" from ...

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