Summary

You searched for: h3=10

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1

New Number: 2.7 |  AESZ: 51  |  Superseeker: 92 585396  |  Hash: e09b9b149b6845daa8d5ef03df33f22d  

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 36, 7980, 2716560, 1127025900, ...
--> OEIS
Normalized instanton numbers (n0=1): 92, 5052, 585396, 99982012, 21054159152, ... ; Common denominator:...

Discriminant

\(1-704z-4096z^2\)

Local exponents

\(-\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\)\(0\)\(-\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(0\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product C*b
Related to 8.139
A-Incarnation: double cover of $B_5$.

A:Incarnation: double cover of B

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2

New Number: 4.44 |  AESZ: 232  |  Superseeker: 379/5 1364199/5  |  Hash: 8d5ff690c87757ed51a092dee764eede  

Degree: 4

\(5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

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Coefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ...
--> OEIS
Normalized instanton numbers (n0=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...

Discriminant

\(-(27z+1)(512z-1)(-5+96z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 512}\)\(\frac{ 5}{ 96}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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3

New Number: 5.37 |  AESZ: 221  |  Superseeker: 492/5 872164/5  |  Hash: b7ce7a734c057660ce3d6341a7572078  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(404\theta^4+1096\theta^3+773\theta^2+225\theta+25\right)-2^{4} x^{2}\left(66896\theta^4+137408\theta^3+101096\theta^2+52800\theta+11625\right)-2^{8} 3 5 x^{3}(2\theta+1)(5672\theta^3+9500\theta^2+8422\theta+2689)-2^{15} 3^{2} x^{4}(2\theta+1)(1208\theta^3+2892\theta^2+2842\theta+969)-2^{20} 3^{3} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 20, 2988, 618320, 156299500, ...
--> OEIS
Normalized instanton numbers (n0=1): 492/5, 10376/5, 872164/5, 91316176/5, 12181916784/5, ... ; Common denominator:...

Discriminant

\(-(-1+432z)(16z+1)^2(192z+5)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 5}{ 192}\)\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 4}\)\(1\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(\frac{ 3}{ 4}\)\(3\)\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(1\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.37" from ...

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