Summary

You searched for: h3=40

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1

New Number: 2.60 |  AESZ: 18  |  Superseeker: 4 364  |  Hash: bb479f8a4185bf4a943dba2d433e13e5  

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 4, 108, 3280, 126700, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 39, 364, 6800, 662416/5, ... ; Common denominator:...

Discriminant

\(-(16z+1)(64z-1)\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

A-Incarnation: (1,1) and (2,2) intersection in $P^3 \times P^3$

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2

New Number: 5.113 |  AESZ: 403  |  Superseeker: -29/5 -1481/5  |  Hash: 492c8a69e87d470c87b9557834f0fc5b  

Degree: 5

\(5^{2} \theta^4+5 x\left(487\theta^4+878\theta^3+709\theta^2+270\theta+40\right)+2^{5} x^{2}\left(1013\theta^4+2639\theta^3+2943\theta^2+1520\theta+280\right)-2^{8} x^{3}\left(2169\theta^4+14880\theta^3+30789\theta^2+22440\theta+5240\right)-2^{12} x^{4}(2\theta+1)(518\theta^3+2397\theta^2+2940\theta+1048)-2^{16} 3 x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, -8, 216, -8000, 359800, ...
--> OEIS
Normalized instanton numbers (n0=1): -29/5, 229/5, -1481/5, 43173/5, -155267, ... ; Common denominator:...

Discriminant

\(-(27z+1)(1024z^2-64z-1)(5+16z)^2\)

Local exponents

\(-\frac{ 5}{ 16}\)\(-\frac{ 1}{ 27}\)\(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(3\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(4\)\(2\)\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.113" from ...

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3

New Number: 8.7 |  AESZ: 106  |  Superseeker: 12 356  |  Hash: fe1c90929d18b81637eaaa93366409ed  

Degree: 8

\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+2^{4} x^{2}\left(241\theta^4+940\theta^3+1303\theta^2+726\theta+145\right)-2^{7} x^{3}\left(33\theta^4-198\theta^3-607\theta^2-456\theta-117\right)+2^{10} x^{4}\left(239\theta^4+478\theta^3-322\theta^2-561\theta-169\right)+2^{12} x^{5}\left(33\theta^4+330\theta^3+185\theta^2-32\theta-37\right)+2^{14} x^{6}\left(241\theta^4+24\theta^3-71\theta^2+24\theta+23\right)+2^{17} x^{7}(3\theta^2+3\theta+1)(11\theta^2+11\theta+3)+2^{20} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 12, 380, 16464, 845676, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, 20, 356, 34561/4, 161840, ... ; Common denominator:...

Discriminant

\((64z^2+88z-1)(16z^2+44z-1)(1+32z^2)^2\)

Local exponents

\(-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\)\(-\frac{ 11}{ 16}-\frac{ 5}{ 16}\sqrt{ 5}\)\(0-\frac{ 1}{ 8}\sqrt{ 2}I\)\(0\)\(0+\frac{ 1}{ 8}\sqrt{ 2}I\)\(-\frac{ 11}{ 16}+\frac{ 5}{ 16}\sqrt{ 5}\)\(-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $b\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{?})$.

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