Summary

You searched for: c3=-18

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1

New Number: 4.47 |  AESZ: 239  |  Superseeker: 1584 171534960  |  Hash: 8e610c3437d7f38e552038bc55399495  

Degree: 4

\(\theta^4+2^{4} 3 x\left(9\theta^4-198\theta^3-131\theta^2-32\theta-3\right)-2^{11} 3^{2} x^{2}\left(486\theta^4+1215\theta^3+81\theta^2-27\theta-5\right)-2^{16} 3^{5} x^{3}\left(891\theta^4+972\theta^3+675\theta^2+216\theta+25\right)-2^{23} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, 144, 147600, 239904000, 479672701200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1584, -17874, 171534960, 30012731550, 105934107802896, ... ; Common denominator:...

Discriminant

\(-(432z+1)(3456z-1)(1+1728z)^2\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 1}{ 1728}\)\(0\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 3}\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(2\)\(4\)\(0\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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2

New Number: 5.3 |  AESZ: 20  |  Superseeker: 3 245/3  |  Hash: a9a698dc5c79ffda497a7897390408b0  

Degree: 5

\(\theta^4-3 x\left(48\theta^4+60\theta^3+53\theta^2+23\theta+4\right)+3^{2} x^{2}\left(873\theta^4+1980\theta^3+2319\theta^2+1344\theta+304\right)-2 3^{4} x^{3}\left(1269\theta^4+3888\theta^3+5259\theta^2+3348\theta+800\right)+2^{2} 3^{6} x^{4}\left(891\theta^4+3240\theta^3+4653\theta^2+2952\theta+688\right)-2^{3} 3^{11} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

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Coefficients of the holomorphic solution: 1, 12, 252, 6600, 198540, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 33/2, 245/3, 879, 11829, ... ; Common denominator:...

Discriminant

\(-(54z-1)(27z-1)^2(18z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 54}\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 18}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 3}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 2}{ 3}\)\(3\)\(1\)
\(0\)\(2\)\(1\)\(4\)\(\frac{ 4}{ 3}\)

Note:

A-Incarnation: (3,0),(0,3),(1,1) intersection in $P^3 \times \P^3$.

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