Summary

You searched for: sol=14

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1

New Number: 3.5 |  AESZ:  |  Superseeker: 26 103520/9  |  Hash: 4ed9bc316d49a71649da0a1148f7ea9d  

Degree: 3

\(\theta^4-2 x\left(102\theta^4+204\theta^3+155\theta^2+53\theta+7\right)+2^{2} x^{2}(\theta+1)^2(396\theta^2+792\theta+311)-2^{4} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, 14, 834, 78260, 8970850, ...
--> OEIS
Normalized instanton numbers (n0=1): 26, 348, 103520/9, 539764, 31290280, ... ; Common denominator:...

Discriminant

\(-(196z-1)(4z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 196}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 4}\)\(1\)
\(0\)\(1\)\(\frac{ 3}{ 4}\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 214

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2

New Number: 5.30 |  AESZ: 209  |  Superseeker: 478/17 285760/17  |  Hash: a03a0a18a8b2a4926d11e4e42b958f98  

Degree: 5

\(17^{2} \theta^4-2 17 x\left(1902\theta^4+3708\theta^3+2789\theta^2+935\theta+119\right)+2^{2} x^{2}\left(62408\theta^4+68576\theta^3-10029\theta^2-24106\theta-5661\right)-2^{2} x^{3}\left(66180\theta^4+33048\theta^3+20785\theta^2+17799\theta+4794\right)+2^{7} x^{4}(2\theta+1)(196\theta^3+498\theta^2+487\theta+169)-2^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 14, 978, 103820, 13387570, ...
--> OEIS
Normalized instanton numbers (n0=1): 478/17, 7784/17, 285760/17, 15280156/17, 1006004774/17, ... ; Common denominator:...

Discriminant

\(-(16z^3-32z^2+220z-1)(-17+32z)^2\)

Local exponents

\(0\) ≈\(0.004548\)\(\frac{ 17}{ 32}\) ≈\(0.997726-3.570079I\) ≈\(0.997726+3.570079I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.30" from ...

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3

New Number: 11.8 |  AESZ:  |  Superseeker: 6/17 688/17  |  Hash: a0a3e346d09b91b8ad96e54854c136ad  

Degree: 11

\(17^{2} \theta^4-2 3 17 x\theta^2(117\theta^2+2\theta+1)+2^{2} x^{2}\left(8475\theta^4-64176\theta^3-97010\theta^2-63580\theta-16184\right)+2^{2} x^{3}\left(717094\theta^4+1400796\theta^3+1493367\theta^2+893571\theta+254082\right)-2^{4} x^{4}\left(464294\theta^4-1133264\theta^3-1648391\theta^2-1200310\theta-375336\right)-2^{4} x^{5}\left(18282700\theta^4+46995928\theta^3+83098711\theta^2+73517673\theta+25685438\right)-2^{6} 3 x^{6}\left(2709886\theta^4+7353008\theta^3+18175093\theta^2+18787708\theta+5966228\right)+2^{6} x^{7}\left(154368940\theta^4+947965400\theta^3+2363187035\theta^2+2646307981\theta+1071488886\right)+2^{8} x^{8}(\theta+1)(119648213\theta^3+399067803\theta^2+77665606\theta-498465144)-2^{8} 3 x^{9}(\theta+1)(\theta+2)(120410834\theta^2+865960638\theta+1188072247)-2^{10} 3^{2} 107 x^{10}(\theta+3)(\theta+2)(\theta+1)(218683\theta-39394)+2^{11} 3^{3} 5 107^{2} 137 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 14, 72, 1554, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...

Discriminant

\((10z+1)(6z-1)(1096z^3+228z^2+14z-1)(2z-1)^2(1284z^2+232z-17)^2\)

Local exponents

\(-\frac{ 29}{ 321}-\frac{ 1}{ 642}\sqrt{ 8821}\) ≈\(-0.124082-0.085658I\) ≈\(-0.124082+0.085658I\)\(-\frac{ 1}{ 10}\)\(0\) ≈\(0.040135\)\(-\frac{ 29}{ 321}+\frac{ 1}{ 642}\sqrt{ 8821}\)\(\frac{ 1}{ 6}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(0\)\(2\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)\(3\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)\(4\)

Note:

This is operator "11.8" from ...

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4

New Number: 6.17 |  AESZ:  |  Superseeker: 2 224/9  |  Hash: bbcabbebf6c04783d4ec5d0a5664f174  

Degree: 6

\(\theta^4-x\left(14+73\theta+154\theta^2+162\theta^3+81\theta^4\right)+x^{2}\left(3256+11390\theta+15571\theta^2+9876\theta^3+2469\theta^4\right)-x^{3}\left(162708+457536\theta+476503\theta^2+215994\theta^3+35999\theta^4\right)+2 3 5 x^{4}\left(8837\theta^4+70696\theta^3+200535\theta^2+236572\theta+98316\right)-2^{2} 3^{2} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(151\theta^2+755\theta+850)+2^{3} 3^{3} 5^{3} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, 14, 220, 3800, 70840, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -4, 224/9, -112, 4446/5, ... ; Common denominator:...

Discriminant

\((6z-1)(14z-1)(30z-1)(21z-1)(-1+5z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 30}\)\(\frac{ 1}{ 21}\)\(\frac{ 1}{ 14}\)\(\frac{ 1}{ 6}\)\(\frac{ 1}{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(0\)\(2\)\(2\)\(2\)\(2\)\(1\)\(5\)

Note:

This is operator "6.17" from ...

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5

New Number: 6.9 |  AESZ:  |  Superseeker: 31/81 29/9  |  Hash: 98af5121f39c27098356e3ade277f975  

Degree: 6

\(3^{8} \theta^4-3^{4} x\left(1234\theta^4+2168\theta^3+1975\theta^2+891\theta+162\right)-x^{2}\left(428004+1521180\theta+2033921\theta^2+1177556\theta^3+205589\theta^4\right)+x^{3}\left(2310517\theta^4+12882402\theta^3+26939429\theta^2+25052328\theta+8683524\right)-2^{2} 5^{2} x^{4}\left(51526\theta^4+332687\theta^3+804453\theta^2+849398\theta+325796\right)+2^{2} 5^{4} x^{5}(\theta+1)(1593\theta^3+8667\theta^2+15104\theta+8516)-2^{4} 5^{6} x^{6}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 2, 14, 104, 1030, ...
--> OEIS
Normalized instanton numbers (n0=1): 31/81, 40/27, 29/9, 1532/81, 6551/81, ... ; Common denominator:...

Discriminant

\(-(16z-1)(25z^3-17z^2+2z+1)(-81+50z)^2\)

Local exponents

≈\(-0.17455\)\(0\)\(\frac{ 1}{ 16}\) ≈\(0.427275-0.215865I\) ≈\(0.427275+0.215865I\)\(\frac{ 81}{ 50}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(2\)

Note:

This is operator "6.9" from ...

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6

New Number: 8.34 |  AESZ: 323  |  Superseeker: 100/3 73111/3  |  Hash: 77c03b04c3a10350b5b0ccd2d204b18f  

Degree: 8

\(3^{2} \theta^4-3 x\left(811\theta^4+1358\theta^3+1012\theta^2+333\theta+42\right)-x^{2}\left(2424+7494\theta-17551\theta^2-88948\theta^3-73291\theta^4\right)-2^{3} x^{3}\left(94934\theta^4+80991\theta^3+29036\theta^2+5175\theta+420\right)+2^{4} x^{4}\left(180401\theta^4+173998\theta^3+77713\theta^2+15788\theta+708\right)-2^{7} x^{5}\left(33304\theta^4+24919\theta^3-2720\theta^2-8451\theta-2404\right)+2^{8} x^{6}\left(8603\theta^4+1812\theta^3-4453\theta^2-3666\theta-952\right)+2^{11} 3 x^{7}\left(5\theta^4+142\theta^3+296\theta^2+225\theta+60\right)-2^{14} 3^{2} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 14, 1054, 120776, 16816846, ...
--> OEIS
Normalized instanton numbers (n0=1): 100/3, 1880/3, 73111/3, 4310384/3, 314245046/3, ... ; Common denominator:...

Discriminant

\(-(-1+241z-827z^2+104z^3+64z^4)(3-44z+48z^2)^2\)

Local exponents

\(0\)\(\frac{ 11}{ 24}-\frac{ 1}{ 24}\sqrt{ 85}\)\(\frac{ 11}{ 24}+\frac{ 1}{ 24}\sqrt{ 85}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(3\)\(1\)\(1\)
\(0\)\(4\)\(4\)\(2\)\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.33

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7

New Number: 8.36 |  AESZ: 327  |  Superseeker: 24/29 284/29  |  Hash: 586c1906112cbba9b2d54c57ce2add99  

Degree: 8

\(29^{2} \theta^4+2 29 x\theta(24\theta^3-198\theta^2-128\theta-29)-2^{2} x^{2}\left(44284\theta^4+172954\theta^3+248589\theta^2+172057\theta+47096\right)-2^{2} x^{3}\left(525708\theta^4+2414772\theta^3+4447643\theta^2+3839049\theta+1275594\right)-2^{3} x^{4}\left(1415624\theta^4+7911004\theta^3+17395449\theta^2+17396359\theta+6496262\right)-2^{4} x^{5}(\theta+1)(2152040\theta^3+12186636\theta^2+24179373\theta+16560506)-2^{5} x^{6}(\theta+1)(\theta+2)(1912256\theta^2+9108540\theta+11349571)-2^{8} 41 x^{7}(\theta+3)(\theta+2)(\theta+1)(5671\theta+16301)-2^{8} 3 19 41^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 14, 96, 1266, ...
--> OEIS
Normalized instanton numbers (n0=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...

Discriminant

\(-(6z+1)(152z^3+84z^2+14z-1)(2z+1)^2(82z+29)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 29}{ 82}\) ≈\(-0.302804-0.180271I\) ≈\(-0.302804+0.180271I\)\(-\frac{ 1}{ 6}\)\(0\) ≈\(0.052976\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)
\(1\)\(4\)\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)

Note:

This operator is reducible to operator 6.23

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