Summary

You searched for: sol=27

Your search produced 2 matches

You can download all data as plain text or as JSON

1

New Number: 5.1 |  AESZ: 17  |  Superseeker: 6/5 118/5  |  Hash: 370d10edbf5900002f79cf6163e106a5  

Degree: 5

\(5^{2} \theta^4-3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2 3 x^{2}\left(531\theta^4+828\theta^3+541\theta^2+155\theta+15\right)-2 3^{3} x^{3}\left(423\theta^4+2160\theta^3+4399\theta^2+3795\theta+1170\right)+3^{5} x^{4}\left(279\theta^4+1368\theta^3+2270\theta^2+1586\theta+402\right)-3^{10} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 3, 27, 381, 6219, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/5, 39/10, 118/5, 1443/10, 6108/5, ... ; Common denominator:...

Discriminant

\(-(27z-1)(27z^2+1)(-5+9z)^2\)

Local exponents

\(0-\frac{ 1}{ 9}\sqrt{ 3}I\)\(0\)\(0+\frac{ 1}{ 9}\sqrt{ 3}I\)\(\frac{ 1}{ 27}\)\(\frac{ 5}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 290/5.71
A-Incarnation: diagonal subfamily 1,1,1-section in $P^2 \times P^2 \times P^2$

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

2

New Number: 24.1 |  AESZ:  |  Superseeker: 3 1322/9  |  Hash: d77f5cce80101a4e8f097ff7dc1cac1f  

Degree: 24

\(\theta^4-3 x\theta(8\theta^2+5\theta+1)-3^{2} x^{2}\left(141\theta^4-76\theta^3-53\theta^2+74\theta+48\right)+3^{3} x^{3}\left(350\theta^4+268\theta^3-911\theta^2+193\theta+366\right)+2^{2} 3^{4} x^{4}\left(1536\theta^4-210\theta^3+5498\theta^2+3259\theta+432\right)-3^{6} x^{5}\left(9982\theta^4-4940\theta^3+26473\theta^2+14567\theta+72\right)-3^{7} x^{6}\left(13329\theta^4+128212\theta^3+141347\theta^2+176702\theta+93936\right)+3^{8} x^{7}\left(179988\theta^4+489272\theta^3+581261\theta^2+545387\theta+236754\right)-3^{9} x^{8}\left(473261\theta^4-322200\theta^3-1952576\theta^2-2540184\theta-1052928\right)+2 3^{11} x^{9}\left(89272\theta^4-647728\theta^3-1032101\theta^2-477573\theta+275604\right)+2 3^{12} x^{10}\left(380267\theta^4+3534580\theta^3+6813301\theta^2+7672754\theta+3370032\right)-2 3^{13} x^{11}\left(2824394\theta^4+21447564\theta^3+70086871\theta^2+111632667\theta+67101174\right)+2^{3} 3^{15} x^{12}\left(604658\theta^4+4211064\theta^3+13816867\theta^2+20606976\theta+11731242\right)-2 3^{16} x^{13}\left(2513086\theta^4-1029540\theta^3-71899267\theta^2-199754241\theta-151321716\right)-2 3^{17} x^{14}\left(4936477\theta^4+113054700\theta^3+624917375\theta^2+1236797682\theta+810302688\right)+2 3^{19} x^{15}\left(10447060\theta^4+141814160\theta^3+623159411\theta^2+1236797682\theta+658549626\right)-3^{21} x^{16}\left(15883703\theta^4+190281632\theta^3+7662783992\theta^2+1272288312\theta+742283280\right)+3^{24} x^{17}\left(2257088\theta^4+24107672\theta^3+94611213\theta^2+157783505\theta+93169704\right)-3^{25} x^{18}\left(1409659\theta^4+13667804\theta^3+60904285\theta^2+118238478\theta+79019856\right)-3^{27} x^{19}\left(372282\theta^4+2964756\theta^3+4412579\theta^2-3409349\theta-6851134\right)+2^{2} 3^{29} x^{20}\left(79892\theta^4+648390\theta^3+1698852\theta^2+1619127\theta+396380\right)-3^{31} x^{21}\left(42578\theta^4+351292\theta^3+908415\theta^2+928057\theta+321472\right)-3^{33} x^{22}\left(10861\theta^4+68980\theta^3+157607\theta^2+161390\theta+65296\right)+3^{35} 5 x^{23}\left(444\theta^4+2616\theta^3+5783\theta^2+5673\theta+2078\right)+3^{37} 5^{2} x^{24}\left((\theta+2)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 27, -36, 891, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, -24, 1322/9, -1824, 19551, ... ; Common denominator:...

Discriminant

\((9z-1)(81z^2-9z-1)(6561z^6+66339z^5-16767z^4+2106z^3-297z^2+27z-1)(9z+1)^2(32805z^5+12393z^4-324z^3+432z^2-9z-1)^2(3z-1)^3\)

No data for singularities

Note:

This is operator "24.1" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex