Summary

You searched for: inst=1/3

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1

New Number: 6.24 |  AESZ:  |  Superseeker: 1/3 5/3  |  Hash: aebe18b25bf886c4483ce54370c0fcbe  

Degree: 6

\(3^{6} \theta^4+3^{5} x\left(7\theta^2+7\theta+2\right)-3^{4} x^{2}\left(1095\theta^4+4380\theta^3+7227\theta^2+5694\theta+1760\right)-2 3^{3} x^{3}(\theta+2)(\theta+1)(4165\theta^2+12495\theta+11148)+2^{2} 3^{2} x^{4}(47961\theta^2+191844\theta+148643)(\theta+2)^2+2^{3} 3^{2} 5 7 17 73 x^{5}(\theta+1)(\theta+2)(\theta+3)(\theta+4)-2^{5} 5^{2} 7^{2} 17^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, -2/3, 112/9, -8/27, 29500/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...

Discriminant

\(-(7z-3)(34z-3)(17z+3)(20z+3)(10z-3)(14z+3)\)

Local exponents

\(-\frac{ 3}{ 14}\)\(-\frac{ 3}{ 17}\)\(-\frac{ 3}{ 20}\)\(0\)\(\frac{ 3}{ 34}\)\(\frac{ 3}{ 10}\)\(\frac{ 3}{ 7}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(4\)
\(2\)\(2\)\(2\)\(0\)\(2\)\(2\)\(2\)\(5\)

Note:

This is operator "6.24" from ...

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2

New Number: 7.6 |  AESZ:  |  Superseeker: 1/3 5/3  |  Hash: 24ba77c97bc4b46c39a41c77cc1d1ef4  

Degree: 7

\(3^{2} \theta^4-3 x\left(112\theta^4+140\theta^3+133\theta^2+63\theta+12\right)+x^{2}\left(4393\theta^4+9340\theta^3+10903\theta^2+6360\theta+1488\right)-2 x^{3}\left(11669\theta^4+27720\theta^3+27019\theta^2+8460\theta-912\right)+2^{2} x^{4}\left(6799\theta^4-10288\theta^3-82183\theta^2-119168\theta-52672\right)+2^{3} 7 x^{5}(\theta+1)(2611\theta^3+15537\theta^2+26998\theta+14360)-2^{6} 7^{2} x^{6}(\theta+1)(\theta+2)(83\theta^2+105\theta-66)-2^{10} 7^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 4, 28, 232, 2188, ...
--> OEIS
Normalized instanton numbers (n0=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...

Discriminant

\(-(2z+1)(8z-1)(7z-1)(16z-1)(z+1)(-3+14z)^2\)

Local exponents

\(-1\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 8}\)\(\frac{ 1}{ 7}\)\(\frac{ 3}{ 14}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(2\)
\(2\)\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(3\)

Note:

This is operator "7.6" from ...

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3

New Number: 8.54 |  AESZ:  |  Superseeker: 0 1/3  |  Hash: bb80872017d0578a4ae56172666b807c  

Degree: 8

\(\theta^4+x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)-2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)+2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)+2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 24, 72, 1296, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/2, 1/3, -1, 2, ... ; Common denominator:...

Discriminant

\((4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 6}\)\(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\)\(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\)\(0\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(2\)\(0\)\(1\)\(4\)

Note:

This is operator "8.54" from ...

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4

New Number: 24.12 |  AESZ:  |  Superseeker: 1/3 1289597/39366  |  Hash: 9f410e240839dfb2c31e0d9ab21bcf92  

Degree: 24

\(3^{3} \theta^4-3^{2} x\left(21\theta^4+26\theta^3+27\theta^2+14\theta+3\right)+2^{4} 3 x^{2}\left(1375\theta^4+1228\theta^3+1487\theta^2+614\theta+93\right)+2^{7} x^{3}\left(5593\theta^4-4894\theta^3-15283\theta^2-10592\theta-3189\right)-2^{10} x^{4}\left(1755\theta^4+11130\theta^3-55892\theta^2-47479\theta-15219\right)-2^{12} x^{5}\left(35483\theta^4-933060\theta^3+194605\theta^2+201774\theta+76539\right)+2^{14} x^{6}\left(105307\theta^4-637672\theta^3-308501\theta^2-310872\theta-167723\right)-2^{17} x^{7}\left(59541\theta^4-937902\theta^3-1250911\theta^2-1406132\theta-697865\right)+2^{20} x^{8}\left(150991\theta^4+759264\theta^3+3007976\theta^2+4226730\theta+2232921\right)-2^{23} x^{9}\left(303262\theta^4+2599208\theta^3+7447674\theta^2+10796900\theta+6015357\right)+2^{26} x^{10}\left(26658\theta^4-69132\theta^3-5869072\theta^2-9790622\theta-5785043\right)+2^{29} x^{11}\left(52403\theta^4+5485920\theta^3+20238530\theta^2+32576052\theta+19443807\right)-2^{32} x^{12}\left(676638\theta^4+4352088\theta^3+7488880\theta^2+5678926\theta+1126215\right)+2^{35} x^{13}\left(144814\theta^4-1215584\theta^3-10922414\theta^2-24907140\theta-173936401\right)+2^{38} x^{14}\left(464128\theta^4+5192664\theta^3+16987014\theta^2+25566882\theta+1450055\right)-2^{41} x^{15}\left(393556\theta^4+2778212\theta^3+7715696\theta^2+9949084\theta+4920079\right)+2^{44} x^{16}\left(1992\theta^4-1014792\theta^3-4709600\theta^2-7958386\theta-4559197\right)+2^{47} x^{17}\left(171070\theta^4+1455864\theta^3+5007722\theta^2+7771956\theta+4461993\right)-2^{50} x^{18}\left(80590\theta^4+559352\theta^3+1994028\theta^2+3689138\theta+2550645\right)-2^{53} x^{19}\left(38226\theta^4+30444\theta^3+878182\theta^2+886100\theta+185855\right)+2^{56} x^{20}\left(20906\theta^4+165792\theta^3+493376\theta^2+554010\theta+178671\right)+2^{59} x^{21}\left(5072\theta^4+33772\theta^3+69936\theta^2+56704\theta+16563\right)-2^{62} x^{22}\left(1691\theta^4+12560\theta^3+32617\theta^2+37570\theta+16816\right)-2^{65} 5 x^{23}\left(59\theta^4+306\theta^3+563\theta^2+408\theta+78\right)+2^{68} 5^{2} x^{24}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 1, -135/16, 672377/11664, 759635299/995328, ...
--> OEIS
Normalized instanton numbers (n0=1): 1/3, -15611/576, 1289597/39366, 2808573854873/859963392, 25331648080663241/1259712000000, ... ; Common denominator:...

Discriminant

\(27-189z-7798361057160712945664z^22-10883579003488635453440z^23+7378697629483820646400z^24+1725349888z^6-7804157952z^7+158325538816z^8-2543946039296z^9+1788988096512z^10+35043634600476672z^16+24075962132945960960z^17+66000z^2+715904z^3-1797120z^4-145338368z^5-90736273492447068160z^18+28133646401536z^11-2906138081230848z^12+4975771152023552z^13+127578533194104832z^14-865438796362022912z^15-344309198711729160192z^19+1506436060956921430016z^20+2923808935682963931136z^21\)

No data for singularities

Note:

This is operator "24.12" from ...

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