Summary

You searched for: Spectrum0=0,1,3,4

Your search produced 381 matches
 1-30  31-60  61-90  91-120  121-150  151-180 
 181-210  211-240  241-270  271-300  301-330  331-360 
 361-381 

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91

New Number: 5.25 |  AESZ: 198  |  Superseeker: -84/11 -9052/11  |  Hash: a1f924763b047c2720d99cfca5ca63db  

Degree: 5

\(11^{2} \theta^4+7 11 x\left(130\theta^4+266\theta^3+210\theta^2+77\theta+11\right)-x^{2}\left(11198+55253\theta+103725\theta^2+89990\theta^3+32126\theta^4\right)+x^{3}\left(1716+20625\theta+63474\theta^2+74184\theta^3+28723\theta^4\right)-7 x^{4}\left(1135\theta^4+2336\theta^3+1881\theta^2+713\theta+110\right)+7^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -7, 199, -8359, 423751, ...
--> OEIS
Normalized instanton numbers (n0=1): -84/11, 639/11, -9052/11, 189021/11, -4838013/11, ... ; Common denominator:...

Discriminant

\((z^3-159z^2+84z+1)(-11+7z)^2\)

Local exponents

≈\(-0.011648\)\(0\) ≈\(0.541757\)\(\frac{ 11}{ 7}\) ≈\(158.469891\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 193/5.22

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92

New Number: 5.26 |  AESZ: 199  |  Superseeker: -2 3820/9  |  Hash: f7b5c9e3ad50b0885d03c98d07a051f1  

Degree: 5

\(\theta^4-x\left(15+88\theta+200\theta^2+224\theta^3+265\theta^4\right)+2 3 x^{2}\left(4325\theta^4+6386\theta^3+6011\theta^2+2718\theta+468\right)-2 3^{2} x^{3}\left(62015\theta^4+116478\theta^3+102361\theta^2+37422\theta+4824\right)+3^{6} 17 x^{4}\left(1465\theta^4+3092\theta^3+2686\theta^2+1140\theta+200\right)-3^{10} 17^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 15, 567, 28113, 1584279, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, 28, 3820/9, 3924, 21606, ... ; Common denominator:...

Discriminant

\(-(z-1)(81z-1)^2(51z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 1}{ 51}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(3\)\(1\)\(1\)
\(0\)\(1\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 194/5.23.

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93

New Number: 5.27 |  AESZ: 202  |  Superseeker: -113/19 -8515/19  |  Hash: 3bf3c283277de7b3808ad309fac9b7a1  

Degree: 5

\(19^{2} \theta^4+19 x\left(1370\theta^4+2620\theta^3+2089\theta^2+779\theta+114\right)+x^{2}\left(39521\theta^4-3916\theta^3-106779\theta^2-95266\theta-25384\right)-2^{3} x^{3}\left(1649\theta^4+19779\theta^3+29667\theta^2+17613\theta+3876\right)-2^{4} 5 x^{4}(\theta+1)(499\theta^3+1411\theta^2+1378\theta+456)-2^{9} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 142, -4920, 205326, ...
--> OEIS
Normalized instanton numbers (n0=1): -113/19, 2921/76, -8515/19, 146869/19, -3105422/19, ... ; Common denominator:...

Discriminant

\(-(z-1)(32z^2+71z+1)(19+20z)^2\)

Local exponents

\(-\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\)\(-\frac{ 19}{ 20}\)\(-\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\)\(0\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 203/5.28

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94

New Number: 5.28 |  AESZ: 203  |  Superseeker: -13/5 -6729/5  |  Hash: dfab012366b4bc6f7af83dc79f28b802  

Degree: 5

\(5^{2} \theta^4+5 x\theta(499\theta^3+86\theta^2+53\theta+10)+2^{4} x^{2}\left(1649\theta^4-13183\theta^3-19776\theta^2-11020\theta-2200\right)-2^{6} x^{3}\left(39521\theta^4+162000\theta^3+142095\theta^2+51540\theta+6540\right)-2^{11} 19 x^{4}\left(1370\theta^4+2860\theta^3+2449\theta^2+1019\theta+174\right)-2^{16} 19^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 88, -1728, 99576, ...
--> OEIS
Normalized instanton numbers (n0=1): -13/5, 427/5, -6729/5, 173044/5, -952275, ... ; Common denominator:...

Discriminant

\(-(32z-1)(32z^2+71z+1)(5+152z)^2\)

Local exponents

\(-\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\)\(-\frac{ 5}{ 152}\)\(-\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\)\(0\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 202 /5.27

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95

New Number: 5.29 |  AESZ: 208  |  Superseeker: 274/7 281388/7  |  Hash: f1d6dfa8a5cdcc2513dfca4243565b2f  

Degree: 5

\(7^{2} \theta^4-2 7 x\left(1056\theta^4+1884\theta^3+1397\theta^2+455\theta+56\right)+2^{2} 3 x^{2}\left(22760\theta^4+13672\theta^3-22537\theta^2-18116\theta-3584\right)-2^{4} x^{3}\left(53312\theta^4-162120\theta^3-195172\theta^2-78561\theta-11130\right)-2^{6} 19 x^{4}(1189\theta^2+2533\theta+1646)(2\theta+1)^2+2^{11} 19^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1440, 196000, 32418400, ...
--> OEIS
Normalized instanton numbers (n0=1): 274/7, 6115/7, 281388/7, 2815228, 1699166270/7, ... ; Common denominator:...

Discriminant

\((4z+1)(512z^2-284z+1)(-7+76z)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 71}{ 256}-\frac{ 17}{ 256}\sqrt{ 17}\)\(\frac{ 7}{ 76}\)\(\frac{ 71}{ 256}+\frac{ 17}{ 256}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.29" from ...

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96

New Number: 5.2 |  AESZ: 19  |  Superseeker: 80/23 4655/23  |  Hash: 4532f44d62f644bf66aa7b153d4f5c5a  

Degree: 5

\(23^{2} \theta^4-23 x\left(921\theta^4+2046\theta^3+1644\theta^2+621\theta+92\right)-x^{2}\left(380851\theta^4+1328584\theta^3+1772673\theta^2+1033528\theta+221168\right)-2 x^{3}\left(475861\theta^4+1310172\theta^3+1028791\theta^2+208932\theta-27232\right)-2^{2} 17 x^{4}\left(8873\theta^4+14020\theta^3+5139\theta^2-1664\theta-976\right)+2^{3} 3 17^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 84, 2200, 71140, ...
--> OEIS
Normalized instanton numbers (n0=1): 80/23, 1157/46, 4655/23, 71184/23, 1156690/23, ... ; Common denominator:...

Discriminant

\((54z-1)(z^2-11z-1)(23+34z)^2\)

Local exponents

\(-\frac{ 23}{ 34}\)\(\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\)\(0\)\(\frac{ 1}{ 54}\)\(\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.2" from ...

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97

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

Degree: 5

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

Maple   LaTex

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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98

New Number: 5.31 |  AESZ: 212  |  Superseeker: -20/7 -104  |  Hash: f72aa947ba945355102b3fef56e0af0f  

Degree: 5

\(7^{2} \theta^4+2 7 x\left(134\theta^4+286\theta^3+234\theta^2+91\theta+14\right)-2^{2} x^{2}\left(3183\theta^4+10266\theta^3+13501\theta^2+8225\theta+1918\right)+2^{3} x^{3}\left(2588\theta^4+8400\theta^3+10256\theta^2+5649\theta+1190\right)-2^{4} 3 x^{4}\left(256\theta^4+848\theta^3+1141\theta^2+717\theta+174\right)+2^{8} 3^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 64, -1408, 37216, ...
--> OEIS
Normalized instanton numbers (n0=1): -20/7, 57/4, -104, 16385/14, -110508/7, ... ; Common denominator:...

Discriminant

\((4z-1)(16z^2-44z-1)(6z-7)^2\)

Local exponents

\(\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\)\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 7}{ 6}\)\(\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point corresponding to Operator AESZ 117 /5.515.

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99

New Number: 5.32 |  AESZ: 215  |  Superseeker: 220/3 89212  |  Hash: ced61f5675491a3c4446c0e55e7bc36b  

Degree: 5

\(3^{2} \theta^4-2^{2} 3 x\left(268\theta^4+632\theta^3+463\theta^2+147\theta+18\right)-2^{7} x^{2}\left(448\theta^4-1616\theta^3-4280\theta^2-2418\theta-441\right)+2^{12} x^{3}\left(416\theta^4+2016\theta^3+756\theta^2-288\theta-135\right)+2^{19} x^{4}(8\theta^2-28\theta-33)(2\theta+1)^2-2^{24} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 2664, 470400, 102047400, ...
--> OEIS
Normalized instanton numbers (n0=1): 220/3, 3538/3, 89212, 7484350, 2459418080/3, ... ; Common denominator:...

Discriminant

\(-(16z-1)(4096z^2-384z+1)(3+64z)^2\)

Local exponents

\(-\frac{ 3}{ 64}\)\(0\)\(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.32" from ...

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100

New Number: 5.33 |  AESZ: 216  |  Superseeker: 9 14201/3  |  Hash: af7027bf24acce4fd0ed5b09e575e2a5  

Degree: 5

\(\theta^4-3 x\theta(2+11\theta+18\theta^2+27\theta^3)-2 3^{3} x^{2}\left(72\theta^4+414\theta^3+603\theta^2+330\theta+64\right)+2^{2} 3^{5} x^{3}\left(93\theta^4-720\theta^2-708\theta-184\right)+2^{3} 3^{7} x^{4}(2\theta+1)(54\theta^3+405\theta^2+544\theta+200)-2^{4} 3^{10} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 216, 7200, 567000, ...
--> OEIS
Normalized instanton numbers (n0=1): 9, 225, 14201/3, 154800, 6298596, ... ; Common denominator:...

Discriminant

\(-(27z+1)(108z-1)(36z+1)(-1+18z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 36}\)\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 18}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(\frac{ 4}{ 3}\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.33" from ...

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101

New Number: 5.34 |  AESZ: 217  |  Superseeker: 17/7 5095/21  |  Hash: e8743aeac19deca699ff90aaef6b8ea7  

Degree: 5

\(7^{2} \theta^4+7 x\theta(-14-73\theta-118\theta^2+13\theta^3)-2^{3} 3 x^{2}\left(3378\theta^4+13446\theta^3+18869\theta^2+11158\theta+2352\right)-2^{4} 3^{3} x^{3}\left(3628\theta^4+17920\theta^3+31668\theta^2+22596\theta+5383\right)-2^{8} 3^{3} x^{4}(2\theta+1)(572\theta^3+2370\theta^2+2896\theta+1095)-2^{10} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 72, 720, 37800, ...
--> OEIS
Normalized instanton numbers (n0=1): 17/7, 254/7, 5095/21, 29600/7, 491991/7, ... ; Common denominator:...

Discriminant

\(-(16z+1)(27z+1)(48z-1)(7+24z)^2\)

Local exponents

\(-\frac{ 7}{ 24}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 48}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(3\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(4\)\(2\)\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.34" from ...

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102

New Number: 5.35 |  AESZ: 218  |  Superseeker: 138/7 42984/7  |  Hash: a76111af659715caf2c4344eedd9d678  

Degree: 5

\(7^{2} \theta^4-2 3 7 x\left(192\theta^4+396\theta^3+303\theta^2+105\theta+14\right)+2^{2} 3 x^{2}\left(1188\theta^4+11736\theta^3+20431\theta^2+12152\theta+2436\right)+2^{2} 3^{3} x^{3}\left(532\theta^4+504\theta^3-3455\theta^2-3829\theta-1036\right)-2^{4} 3^{4} x^{4}(2\theta+1)(36\theta^3+306\theta^2+421\theta+156)-2^{6} 3^{4} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 612, 48000, 4580100, ...
--> OEIS
Normalized instanton numbers (n0=1): 138/7, 1506/7, 42984/7, 235596, 78950334/7, ... ; Common denominator:...

Discriminant

\(-(1296z^3-864z^2+168z-1)(7+12z)^2\)

Local exponents

\(-\frac{ 7}{ 12}\)\(0\) ≈\(0.006145\) ≈\(0.330261-0.128447I\) ≈\(0.330261+0.128447I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.35" from ...

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103

New Number: 5.36 |  AESZ: 219  |  Superseeker: 166/5 360988/15  |  Hash: b7068bb339f61ebd7c591b7be3fe5893  

Degree: 5

\(5^{2} \theta^4-2 5 x\left(464\theta^4+1036\theta^3+763\theta^2+245\theta+30\right)-2^{2} 3^{2} x^{2}\left(7064\theta^4+22472\theta^3+26699\theta^2+13200\theta+2340\right)-2^{4} 3^{4} x^{3}\left(3440\theta^4+13320\theta^3+18784\theta^2+10665\theta+2070\right)-2^{6} 3^{8} x^{4}(19\theta^2+59\theta+45)(2\theta+1)^2-2^{8} 3^{9} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 972, 109200, 14949900, ...
--> OEIS
Normalized instanton numbers (n0=1): 166/5, 638, 360988/15, 7222128/5, 524377242/5, ... ; Common denominator:...

Discriminant

\(-(16z+1)(3888z^2+216z-1)(5+36z)^2\)

Local exponents

\(-\frac{ 5}{ 36}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 3}\)\(0\)\(-\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(4\)\(2\)\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.36" from ...

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104

New Number: 5.37 |  AESZ: 221  |  Superseeker: 492/5 872164/5  |  Hash: b7ce7a734c057660ce3d6341a7572078  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(404\theta^4+1096\theta^3+773\theta^2+225\theta+25\right)-2^{4} x^{2}\left(66896\theta^4+137408\theta^3+101096\theta^2+52800\theta+11625\right)-2^{8} 3 5 x^{3}(2\theta+1)(5672\theta^3+9500\theta^2+8422\theta+2689)-2^{15} 3^{2} x^{4}(2\theta+1)(1208\theta^3+2892\theta^2+2842\theta+969)-2^{20} 3^{3} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 20, 2988, 618320, 156299500, ...
--> OEIS
Normalized instanton numbers (n0=1): 492/5, 10376/5, 872164/5, 91316176/5, 12181916784/5, ... ; Common denominator:...

Discriminant

\(-(-1+432z)(16z+1)^2(192z+5)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 5}{ 192}\)\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 4}\)\(1\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(\frac{ 3}{ 4}\)\(3\)\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(1\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.37" from ...

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105

New Number: 5.38 |  AESZ: 223  |  Superseeker: 18 64744/3  |  Hash: e3ab25cffe4a0968b175bd9e98c96427  

Degree: 5

\(\theta^4+2 3 x\theta(48\theta^3-12\theta^2-7\theta-1)+2^{2} 3^{3} x^{2}\left(392\theta^4+488\theta^3+775\theta^2+376\theta+64\right)+2^{4} 3^{5} x^{3}\left(1184\theta^4+3288\theta^3+3512\theta^2+1635\theta+278\right)+2^{6} 3^{8} x^{4}(169\theta^2+361\theta+238)(2\theta+1)^2+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, -432, 7200, 1587600, ...
--> OEIS
Normalized instanton numbers (n0=1): 18, -873, 64744/3, -229968, -1628892, ... ; Common denominator:...

Discriminant

\((36z+1)(13824z^2+36z+1)(1+108z)^2\)

Local exponents

\(-\frac{ 1}{ 36}\)\(-\frac{ 1}{ 108}\)\(-\frac{ 1}{ 768}-\frac{ 5}{ 2304}\sqrt{ 15}I\)\(-\frac{ 1}{ 768}+\frac{ 5}{ 2304}\sqrt{ 15}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(1\)\(1\)\(0\)\(\frac{ 3}{ 2}\)
\(2\)\(4\)\(2\)\(2\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.38" from ...

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106

New Number: 5.39 |  AESZ: 224  |  Superseeker: 59/5 22503/5  |  Hash: ba17e8cb074bba75e7a27206be530698  

Degree: 5

\(5^{2} \theta^4-5 x\left(1057\theta^4+1058\theta^3+819\theta^2+290\theta+40\right)+2^{5} x^{2}\left(10123\theta^4+11419\theta^3+5838\theta^2+1510\theta+180\right)-2^{8} x^{3}\left(30981\theta^4+46560\theta^3+48211\theta^2+25500\theta+5100\right)+2^{14} 11 x^{4}(2\theta+1)(234\theta^3+591\theta^2+581\theta+202)-2^{20} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 312, 19520, 1475320, ...
--> OEIS
Normalized instanton numbers (n0=1): 59/5, 186, 22503/5, 718052/5, 29091017/5, ... ; Common denominator:...

Discriminant

\(-(128z-1)(128z^2-13z+1)(-5+176z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 5}{ 176}\)\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.39" from ...

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107

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

Degree: 5

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

Maple   LaTex

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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108

New Number: 5.40 |  AESZ: 226  |  Superseeker: 62/5 4060/3  |  Hash: 92f95cd33ac4bf18c2d05ce3040c5203  

Degree: 5

\(5^{2} \theta^4-2 5 x\left(328\theta^4+692\theta^3+551\theta^2+205\theta+30\right)+2^{2} 3 x^{2}\left(5352\theta^4+25416\theta^3+38387\theta^2+23020\theta+4860\right)-2^{4} 3^{3} x^{3}\left(352\theta^4+4520\theta^3+12108\theta^2+10205\theta+2630\right)-2^{6} 3^{3} x^{4}(2\theta+1)(586\theta^3+3039\theta^2+3947\theta+1527)-2^{8} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 396, 19920, 1241100, ...
--> OEIS
Normalized instanton numbers (n0=1): 62/5, 55, 4060/3, 28790, 861786, ... ; Common denominator:...

Discriminant

\(-(16z-1)(108z-1)(12z-1)(5+12z)^2\)

Local exponents

\(-\frac{ 5}{ 12}\)\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.40" from ...

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109

New Number: 5.41 |  AESZ: 230  |  Superseeker: 291 7935104  |  Hash: ac762b013587176079179af09a110ab6  

Degree: 5

\(\theta^4+3 x\left(945\theta^4-162\theta^3-49\theta^2+32\theta+8\right)+2 3^{4} x^{2}\left(17928\theta^4+2970\theta^3+10187\theta^2+3376\theta+408\right)+2^{2} 3^{7} x^{3}\left(156285\theta^4+200016\theta^3+193630\theta^2+84378\theta+13964\right)+2^{4} 3^{10} 19 x^{4}(4743\theta^2+8199\theta+4922)(2\theta+1)^2+2^{9} 3^{15} 19^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, -648, 494400, -82643400, ...
--> OEIS
Normalized instanton numbers (n0=1): 291, -38832, 7935104, -2098976940, 651305429796, ... ; Common denominator:...

Discriminant

\((432z+1)(93312z^2+351z+1)(1+1026z)^2\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 13}{ 6912}-\frac{ 7}{ 6912}\sqrt{ 7}I\)\(-\frac{ 13}{ 6912}+\frac{ 7}{ 6912}\sqrt{ 7}I\)\(-\frac{ 1}{ 1026}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(3\)\(0\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(2\)\(4\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.41" from ...

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110

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

Degree: 5

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

Maple   LaTex

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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111

New Number: 5.43 |  AESZ: 234  |  Superseeker: 18/7 5676/7  |  Hash: 3e70b30959c0c3bd799b435b9c842186  

Degree: 5

\(7^{2} \theta^4-2 7 x\theta(192\theta^3+60\theta^2+37\theta+7)-2^{2} x^{2}\left(17608\theta^4+115144\theta^3+166715\theta^2+94556\theta+18816\right)+2^{4} 3^{2} x^{3}\left(20288\theta^4+57288\theta^3+27524\theta^2-7455\theta-5026\right)-2^{6} 3^{5} x^{4}(2\theta+1)(458\theta^3-657\theta^2-1799\theta-846)-2^{12} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 96, 1440, 90720, ...
--> OEIS
Normalized instanton numbers (n0=1): 18/7, 515/7, 5676/7, 133796/7, 2929726/7, ... ; Common denominator:...

Discriminant

\(-(64z-1)(36z+1)(4z+1)(-7+108z)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 36}\)\(0\)\(\frac{ 1}{ 64}\)\(\frac{ 7}{ 108}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.43" from ...

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112

New Number: 5.44 |  AESZ: 240  |  Superseeker: 231/13 38037/13  |  Hash: 8f46cd6968b3b676e251a9d8635637fc  

Degree: 5

\(13^{2} \theta^4-13 x\left(1449\theta^4+4050\theta^3+3143\theta^2+1118\theta+156\right)-2^{4} x^{2}\left(22760\theta^4-27112\theta^3-121046\theta^2-82316\theta-17589\right)+2^{8} x^{3}\left(3824\theta^4+39936\theta^3-34292\theta^2-63492\theta-19539\right)-2^{16} 3 x^{4}(2\theta+1)(40\theta^3+684\theta^2+1013\theta+399)-2^{20} 3^{2} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 468, 28560, 2135700, ...
--> OEIS
Normalized instanton numbers (n0=1): 231/13, 826/13, 38037/13, 786076/13, 32662752/13, ... ; Common denominator:...

Discriminant

\(-(128z-1)(128z^2-13z+1)(13+192z)^2\)

Local exponents

\(-\frac{ 13}{ 192}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.44" from ...

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113

New Number: 5.45 |  AESZ: 242  |  Superseeker: -18 1568/3  |  Hash: 562c18d54c0080ebb0bb01b14a8241ce  

Degree: 5

\(\theta^4+2 3 x\left(72\theta^4+108\theta^3+91\theta^2+37\theta+6\right)+2^{2} 3^{3} x^{2}\left(648\theta^4+1800\theta^3+2211\theta^2+1248\theta+260\right)+2^{4} 3^{5} x^{3}\left(1344\theta^4+4968\theta^3+7320\theta^2+4749\theta+1072\right)+2^{6} 3^{7} x^{4}(2\theta+1)(630\theta^3+2241\theta^2+2617\theta+971)+2^{8} 3^{10} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -36, 2484, -208080, 19221300, ...
--> OEIS
Normalized instanton numbers (n0=1): -18, 99/2, 1568/3, 22698, -165960, ... ; Common denominator:...

Discriminant

\((1+144z)(36z+1)^2(108z+1)^2\)

Local exponents

\(-\frac{ 1}{ 36}\)\(-\frac{ 1}{ 108}\)\(-\frac{ 1}{ 144}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 5}{ 6}\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 7}{ 6}\)
\(4\)\(1\)\(2\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.45" from ...

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114

New Number: 5.46 |  AESZ: 243  |  Superseeker: -42 -41706  |  Hash: 93c30005b5a976a2b7c5206d5e679a45  

Degree: 5

\(\theta^4+x\left(295\theta^4+572\theta^3+424\theta^2+138\theta+17\right)+2 x^{2}\left(843\theta^4+744\theta^3-473\theta^2-481\theta-101\right)+2 x^{3}\left(1129\theta^4-516\theta^3-725\theta^2-159\theta+4\right)-3 x^{4}\left(173\theta^4+352\theta^3+290\theta^2+114\theta+18\right)-3^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -17, 1549, -215585, 36505501, ...
--> OEIS
Normalized instanton numbers (n0=1): -42, 875, -41706, 2954224, -257813864, ... ; Common denominator:...

Discriminant

\(-(z^3+57z^2-289z-1)(3z+1)^2\)

Local exponents

≈\(-61.684843\)\(-\frac{ 1}{ 3}\) ≈\(-0.003458\)\(0\) ≈\(4.688301\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

A-incarnation: $7 \times 7$ linear Pfaffian in $P^7$.
There is a second MUM point at infinity, associated to
the 7 fold linear section of $G(2,7)$ AESZ 27/5.7

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115

New Number: 5.47 |  AESZ: 246  |  Superseeker: -4/5 -108/5  |  Hash: f51a0c39f9179dc6a561b9afb6f9d85f  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(12\theta^4+48\theta^3+49\theta^2+25\theta+5\right)-2^{4} x^{2}\left(544\theta^4+1792\theta^3+2444\theta^2+1580\theta+405\right)+2^{9} x^{3}\left(112\theta^4+960\theta^3+2306\theta^2+2130\theta+685\right)+2^{12} x^{4}\left(144\theta^4+768\theta^3+1308\theta^2+924\theta+235\right)+2^{20} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 44, 400, 5356, ...
--> OEIS
Normalized instanton numbers (n0=1): -4/5, 22/5, -108/5, 694/5, -1040, ... ; Common denominator:...

Discriminant

\((1+16z)(16z+5)^2(16z-1)^2\)

Local exponents

\(-\frac{ 5}{ 16}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(3\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(4\)\(2\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 247/5.48

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116

New Number: 5.48 |  AESZ: 247  |  Superseeker: 608 22293216  |  Hash: 6c0503129f3500c26cf001c1908a17f7  

Degree: 5

\(\theta^4+2^{4} x\left(144\theta^4-192\theta^3-132\theta^2-36\theta-5\right)+2^{13} x^{2}\left(112\theta^4-512\theta^3+98\theta^2+50\theta+13\right)-2^{20} x^{3}\left(544\theta^4+384\theta^3+332\theta^2+108\theta+21\right)-2^{30} 5 x^{4}\left(12\theta^4-23\theta^2-23\theta-7\right)+2^{40} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 80, 11024, 1850624, 343952656, ...
--> OEIS
Normalized instanton numbers (n0=1): 608, -85544, 22293216, -7629059800, 3042437418016, ... ; Common denominator:...

Discriminant

\((1+256z)(1280z+1)^2(256z-1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 1280}\)\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(2\)\(4\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operaor AESZ 246/ 5.47

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117

New Number: 5.49 |  AESZ: 248  |  Superseeker: 7/3 148  |  Hash: 0c9ccff1cb4f5096e455a9026799ed5a  

Degree: 5

\(3^{2} \theta^4-3 x\left(106\theta^4+146\theta^3+115\theta^2+42\theta+6\right)-x^{2}\left(4511\theta^4+24314\theta^3+37829\theta^2+23598\theta+5286\right)+2^{2} x^{3}\left(10457\theta^4+32184\theta^3+24449\theta^2+3627\theta-1317\right)-2^{2} 11 x^{4}\left(1596\theta^4+2040\theta^3-101\theta^2-1085\theta-386\right)-2^{4} 11^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 54, 1028, 29110, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/3, 551/24, 148, 8241/4, 86854/3, ... ; Common denominator:...

Discriminant

\(-(16z+1)(16z^2+44z-1)(-3+11z)^2\)

Local exponents

\(-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\)\(-\frac{ 1}{ 16}\)\(0\)\(-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\)\(\frac{ 3}{ 11}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.49" from ...

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118

New Number: 5.4 |  AESZ: 21  |  Superseeker: 8/5 152/5  |  Hash: 42a2bc0f0ee2a405ede956176c95721f  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(36\theta^4+84\theta^3+72\theta^2+30\theta+5\right)-2^{4} x^{2}\left(181\theta^4+268\theta^3+71\theta^2-70\theta-35\right)+2^{8} x^{3}(\theta+1)(37\theta^3+248\theta^2+375\theta+165)+2^{10} x^{4}\left(39\theta^4+198\theta^3+331\theta^2+232\theta+59\right)+2^{15} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 44, 688, 13036, ...
--> OEIS
Normalized instanton numbers (n0=1): 8/5, 57/10, 152/5, 253, 11552/5, ... ; Common denominator:...

Discriminant

\((4z+1)(32z-1)(4z-1)(8z+5)^2\)

Local exponents

\(-\frac{ 5}{ 8}\)\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 71/5.11

A-Incarnation: (2,0),(02),(1,1),(1,1),(1,1) intersection in $P^4 \times P^4$

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119

New Number: 5.50 |  AESZ: 249  |  Superseeker: -44/5 -596  |  Hash: 85592af20bbb190e37428e945664c2f3  

Degree: 5

\(5^{2} \theta^4+2^{2} 5 x\left(148\theta^4+392\theta^3+341\theta^2+145\theta+25\right)+2^{4} x^{2}\left(4096\theta^4+32128\theta^3+57016\theta^2+37920\theta+9175\right)-2^{8} x^{3}\left(6656\theta^4+7680\theta^3-36960\theta^2-49920\theta-16985\right)-2^{15} x^{4}\left(512\theta^4+4864\theta^3+9136\theta^2+6464\theta+1587\right)+2^{20} x^{5}(4\theta+5)^2(4\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, -20, 684, -28496, 1317100, ...
--> OEIS
Normalized instanton numbers (n0=1): -44/5, -277/5, -596, -7236, -502128/5, ... ; Common denominator:...

Discriminant

\((1+16z)(64z+1)^2(64z-5)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 5}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(\frac{ 1}{ 2}\)\(0\)\(3\)\(\frac{ 5}{ 4}\)
\(2\)\(1\)\(0\)\(4\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.50" from ...

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120

New Number: 5.51 |  AESZ: 250  |  Superseeker: 308/23 70799/23  |  Hash: 9c19794a84073d1c6dfd11c8a7c9a740  

Degree: 5

\(23^{2} \theta^4-23 x\left(3271\theta^4+5078\theta^3+3896\theta^2+1357\theta+184\right)+x^{2}\left(1357863\theta^4+999924\theta^3-787393\theta^2-850862\theta-205712\right)-2^{3} x^{3}\left(775799\theta^4-272481\theta^3-218821\theta^2+176709\theta+100234\right)-2^{4} 61 x^{4}\left(1005\theta^4-15654\theta^3-36317\theta^2-27938\theta-7304\right)-2^{9} 61^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

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Coefficients of the holomorphic solution: 1, 8, 324, 19304, 1388260, ...
--> OEIS
Normalized instanton numbers (n0=1): 308/23, 3526/23, 70799/23, 2148684/23, 81402822/23, ... ; Common denominator:...

Discriminant

\(-(512z^3+113z^2+121z-1)(-23+244z)^2\)

Local exponents

≈\(-0.114451-0.474453I\) ≈\(-0.114451+0.474453I\)\(0\) ≈\(0.008199\)\(\frac{ 23}{ 244}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.51" from ...

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