Summary

You searched for: inst=39

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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: 8.71 |  AESZ:  |  Superseeker: -15 14044/3  |  Hash: de469dbb89801caa07ec523e3b0e4772  

Degree: 8

\(\theta^4+3 x\left(111\theta^4+186\theta^3+169\theta^2+76\theta+14\right)+2 3^{2} x^{2}\left(2529\theta^4+6930\theta^3+9483\theta^2+6096\theta+1508\right)+2^{2} 3^{4} x^{3}\left(11367\theta^4+32886\theta^3+47658\theta^2+36099\theta+10084\right)+2^{3} 3^{6} x^{4}\left(37017\theta^4+100278\theta^3+103626\theta^2+56025\theta+11582\right)+2^{4} 3^{9} x^{5}\left(29160\theta^4+80676\theta^3+84897\theta^2+27261\theta-568\right)+2^{5} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53991\theta^2+31131\theta+6578\right)+2^{7} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1056\theta^2+585\theta+131\right)+2^{9} 3^{20} x^{8}(\theta+1)^2(6\theta+5)(6\theta+7)\)

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Coefficients of the holomorphic solution: 1, -42, 2682, -200436, 16310250, ...
--> OEIS
Normalized instanton numbers (n0=1): -15, 39, 14044/3, 213069/2, 462576, ... ; Common denominator:...

Discriminant

\((27z+1)(54z+1)(108z+1)^2(1944z^2+18z+1)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 54}\)\(-\frac{ 1}{ 108}\)\(-\frac{ 1}{ 216}-\frac{ 1}{ 216}\sqrt{ 23}I\)\(-\frac{ 1}{ 216}+\frac{ 1}{ 216}\sqrt{ 23}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(1\)\(1\)\(\frac{ 1}{ 6}\)\(1\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 5}{ 6}\)\(3\)\(3\)\(0\)\(1\)
\(2\)\(2\)\(1\)\(4\)\(4\)\(0\)\(\frac{ 7}{ 6}\)

Note:

This is operator "8.71" from ...

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