Summary

You searched for: sol=3240

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1

New Number: 5.42 |  AESZ: 231  |  Superseeker: 460/3 894404/3  |  Hash: 6f793238336123adfdcd7ee17d64e5ec  

Degree: 5

\(3^{2} \theta^4-2^{2} 3 x\left(28\theta^4+1016\theta^3+739\theta^2+231\theta+30\right)-2^{9} x^{2}\left(1168\theta^4-968\theta^3-9518\theta^2-5325\theta-1005\right)+2^{16} x^{3}\left(988\theta^4+8208\theta^3-743\theta^2-4230\theta-1245\right)+2^{24} 5 x^{4}(2\theta+1)^2(9\theta^2-279\theta-277)-2^{33} 5^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 40, 3240, 313600, 39327400, ...
--> OEIS
Normalized instanton numbers (n0=1): 460/3, -16828/3, 894404/3, -42271624/3, 2076730720/3, ... ; Common denominator:...

Discriminant

\(-(256z-1)(32768z^2-208z+1)(3+640z)^2\)

Local exponents

\(-\frac{ 3}{ 640}\)\(0\)\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.42" from ...

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2

New Number: 5.83 |  AESZ: 316  |  Superseeker: 852/11 1678156/11  |  Hash: b8201d587a016cc013e2477aadb5c1ff  

Degree: 5

\(11^{2} \theta^4-2^{2} 3 11 x\left(364\theta^4+824\theta^3+599\theta^2+187\theta+22\right)-2^{5} x^{2}\left(62164\theta^4+84496\theta^3+12499\theta^2-6402\theta-1584\right)-2^{4} 3 x^{3}\left(484016\theta^4+474144\theta^3+366952\theta^2+161832\theta+27027\right)-2^{11} 3^{2} x^{4}(964\theta^2+1360\theta+669)(2\theta+1)^2-2^{16} 3^{4} x^{5}(2\theta+1)^2(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 24, 3240, 675600, 171901800, ...
--> OEIS
Normalized instanton numbers (n0=1): 852/11, 21572/11, 1678156/11, 15912512, 22956446184/11, ... ; Common denominator:...

Discriminant

\(-(2304z^3+1664z^2+432z-1)(11+192z)^2\)

Local exponents

≈\(-0.362258-0.240689I\) ≈\(-0.362258+0.240689I\)\(-\frac{ 11}{ 192}\)\(0\) ≈\(0.002294\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.83" from ...

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3

New Number: 9.2 |  AESZ:  |  Superseeker: 9/7 49/3  |  Hash: 356d4564e48d7a04e815fa223b6ccc46  

Degree: 9

\(7^{2} \theta^4+7 x\theta(165\theta^3-102\theta^2-65\theta-14)-2^{3} x^{2}\left(920\theta^4+11726\theta^3+15277\theta^2+9478\theta+2352\right)-2^{4} 3^{2} x^{3}\left(4035\theta^4+19554\theta^3+29157\theta^2+20706\theta+5761\right)-2^{8} 3^{2} x^{4}\left(4156\theta^4+17951\theta^3+28198\theta^2+21045\theta+6096\right)-2^{11} 3^{3} x^{5}\left(1538\theta^4+6560\theta^3+10755\theta^2+8234\theta+2420\right)-2^{13} 3^{4} x^{6}\left(695\theta^4+3051\theta^3+5285\theta^2+4191\theta+1259\right)-2^{14} 3^{5} x^{7}\left(385\theta^4+1802\theta^3+3319\theta^2+2754\theta+855\right)-2^{18} 3^{6} x^{8}(\theta+1)^2(15\theta^2+48\theta+43)-2^{20} 3^{7} x^{9}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, 0, 24, 144, 3240, ...
--> OEIS
Normalized instanton numbers (n0=1): 9/7, 47/7, 49/3, 1370/7, 10063/7, ... ; Common denominator:...

Discriminant

\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(7+72z+288z^2)^2\)

Local exponents

\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 5}I\)\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 5}I\)\(-\frac{ 1}{ 12}\)\(0\)\(\frac{ 1}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(1\)\(3\)\(1\)\(0\)\(1\)\(2\)
\(2\)\(2\)\(4\)\(2\)\(4\)\(2\)\(0\)\(2\)\(2\)

Note:

This is operator "9.2" from ...

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4

New Number: 1.5 |  AESZ: 5  |  Superseeker: 60 134292  |  Hash: a6c4fb927cb2a4bb1103c1c739a252b0  

Degree: 1

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

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Coefficients of the holomorphic solution: 1, 24, 3240, 672000, 169785000, ...
--> OEIS
Normalized instanton numbers (n0=1): 60, 1869, 134292, 14016600, 1806410976, ... ; Common denominator:...

Discriminant

\(1-432z\)

Local exponents

\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(2\)\(\frac{ 2}{ 3}\)

Note:

A-incarnation: X(2,2,3) in $P^6$.

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