Summary

You searched for: degz=5

Your search produced 134 matches
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91

New Number: 5.60 |  AESZ: 268  |  Superseeker: -828/5 -4270932/5  |  Hash: 638e2881183378c7a47b7508d9acc072  

Degree: 5

\(5^{2} \theta^4-2^{2} 3 5 x\left(108\theta^4+432\theta^3+661\theta^2+445\theta+105\right)-2^{4} 3^{2} x^{2}\left(44064\theta^4+145152\theta^3+239004\theta^2+186300\theta+58045\right)+2^{9} 3^{5} x^{3}\left(9072\theta^4+77760\theta^3+180954\theta^2+164970\theta+53965\right)+2^{12} 3^{8} x^{4}\left(11664\theta^4+62208\theta^3+104940\theta^2+73836\theta+18659\right)+2^{20} 3^{15} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 252, 87084, 31502448, 12121584876, ...
--> OEIS
Normalized instanton numbers (n0=1): -828/5, 25533/5, -4270932/5, 598304142/5, -24767201520, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 5}{ 432}\)\(-\frac{ 1}{ 432}\)\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(\frac{ 3}{ 2}\)\(1\)

Note:

There is a second MUM-point at infinity, correspondint to
Operator AESZ 269/5.61

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92

New Number: 5.61 |  AESZ: 269  |  Superseeker: 549216 5134247872650720  |  Hash: f6285c6dd849b8edc6913a248c74c2ac  

Degree: 5

\(\theta^4+2^{4} 3^{2} x\left(11664\theta^4-15552\theta^3-11700\theta^2-3924\theta-781\right)+2^{13} 3^{8} x^{2}\left(9072\theta^4-41472\theta^3+2106\theta^2-54\theta+1261\right)-2^{20} 3^{14} x^{3}\left(44064\theta^4+31104\theta^3+67932\theta^2+32508\theta+9661\right)-2^{30} 3^{22} 5 x^{4}\left(108\theta^4+13\theta^2+13\theta-3\right)+2^{40} 3^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 112464, 16304096016, 2572332025515264, 423329707157060783376, ...
--> OEIS
Normalized instanton numbers (n0=1): 549216, -39437661960, 5134247872650720, -893529522332436373560, 182442495912657901797814560, ... ; Common denominator:...

Discriminant

\((1+186624z)(933120z+1)^2(186624z-1)^2\)

Local exponents

\(-\frac{ 1}{ 186624}\)\(-\frac{ 1}{ 933120}\)\(0\)\(\frac{ 1}{ 186624}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(\frac{ 3}{ 2}\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 268/5.60

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93

New Number: 5.62 |  AESZ: 270  |  Superseeker: -76/5 -2100  |  Hash: 256e3b3a92e3fd332be8b01f71853ea4  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(48\theta^4+192\theta^3+251\theta^2+155\theta+35\right)-2^{4} x^{2}\left(8704\theta^4+28672\theta^3+43664\theta^2+31760\theta+9265\right)+2^{11} x^{3}\left(1792\theta^4+15360\theta^3+36248\theta^2+33240\theta+10795\right)+2^{16} x^{4}\left(2304\theta^4+12288\theta^3+20816\theta^2+14672\theta+3719\right)+2^{30} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 28, 1324, 63856, 3489004, ...
--> OEIS
Normalized instanton numbers (n0=1): -76/5, 367/5, -2100, 43436, -6582256/5, ... ; Common denominator:...

Discriminant

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

Local exponents

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

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 271/ 5.63

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94

New Number: 5.63 |  AESZ: 271  |  Superseeker: 10912 71557619232  |  Hash: c20fda7ad02ecc06f9b3f74bf4327d05  

Degree: 5

\(\theta^4+2^{4} x\left(2304\theta^4-3072\theta^3-2224\theta^2-688\theta-121\right)+2^{17} x^{2}\left(1792\theta^4-8192\theta^3+920\theta^2+344\theta+235\right)-2^{28} x^{3}\left(8704\theta^4+6144\theta^3+9872\theta^2+4368\theta+1201\right)-2^{44} 5 x^{4}\left(48\theta^4-37\theta^2-37\theta-13\right)+2^{60} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1936, 5433616, 17299986688, 58672579116304, ...
--> OEIS
Normalized instanton numbers (n0=1): 10912, -20731504, 71557619232, -326717237089712, 1743820693922321120, ... ; Common denominator:...

Discriminant

\((1+4096z)(20480z+1)^2(4096z-1)^2\)

Local exponents

\(-\frac{ 1}{ 4096}\)\(-\frac{ 1}{ 20480}\)\(0\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 4}\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(\frac{ 5}{ 4}\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 270 /5.62

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95

New Number: 5.64 |  AESZ: 272  |  Superseeker: 468/5 11885484  |  Hash: 467bb784f4bd6e978748e98f6ea4a573  

Degree: 5

\(5^{2} \theta^4-2^{2} 3 5 x\left(1332\theta^4+3528\theta^3+3289\theta^2+1525\theta+285\right)+2^{4} 3^{2} x^{2}\left(331776\theta^4+2602368\theta^3+4533336\theta^2+2996640\theta+724415\right)+2^{8} 3^{5} x^{3}\left(539136\theta^4+622080\theta^3-3024864\theta^2-4008960\theta-1315985\right)-2^{15} 3^{8} x^{4}\left(41472\theta^4+393984\theta^3+735984\theta^2+510912\theta+120811\right)-2^{20} 3^{11} x^{5}(12\theta+7)(12\theta+11)(12\theta+13)(12\theta+17)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 684, 761004, 985011120, 1373164693740, ...
--> OEIS
Normalized instanton numbers (n0=1): 468/5, -315477/5, 11885484, -14354122356/5, 808514230608, ... ; Common denominator:...

Discriminant

\(-(-1+432z)(1728z+5)^2(1728z-1)^2\)

Local exponents

\(-\frac{ 5}{ 1728}\)\(0\)\(\frac{ 1}{ 1728}\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 12}\)
\(1\)\(0\)\(-\frac{ 1}{ 6}\)\(1\)\(\frac{ 11}{ 12}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 13}{ 12}\)
\(4\)\(0\)\(\frac{ 7}{ 6}\)\(2\)\(\frac{ 17}{ 12}\)

Note:

This is operator "5.64" from ...

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96

New Number: 5.65 |  AESZ: 273  |  Superseeker: 63/5 14016/5  |  Hash: cf49bc645cb0404ce7bc9ca1d41d3152  

Degree: 5

\(5^{2} \theta^4-3 5 x\left(333\theta^4+882\theta^3+781\theta^2+340\theta+60\right)+2^{2} 3^{2} x^{2}\left(5184\theta^4+40662\theta^3+71829\theta^2+47700\theta+11540\right)+2^{2} 3^{5} x^{3}\left(8424\theta^4+9720\theta^3-46899\theta^2-63045\theta-21260\right)-2^{4} 3^{8} x^{4}\left(1296\theta^4+12312\theta^3+23094\theta^2+16263\theta+3956\right)-2^{6} 3^{11} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 2196, 161280, 13032900, ...
--> OEIS
Normalized instanton numbers (n0=1): 63/5, -747/4, 14016/5, -55584, 6071598/5, ... ; Common denominator:...

Discriminant

\(-(-1+27z)(108z+5)^2(108z-1)^2\)

Local exponents

\(-\frac{ 5}{ 108}\)\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(0\)\(\frac{ 1}{ 6}\)\(1\)\(\frac{ 5}{ 6}\)
\(3\)\(0\)\(\frac{ 5}{ 6}\)\(1\)\(\frac{ 7}{ 6}\)
\(4\)\(0\)\(1\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.65" from ...

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97

New Number: 5.66 |  AESZ: 274  |  Superseeker: 49/5 6032/15  |  Hash: 729d44a3b7b561b49603f26a25d26069  

Degree: 5

\(5^{2} \theta^4-5 x\left(757\theta^4+1298\theta^3+1049\theta^2+400\theta+60\right)+2^{2} 3^{2} x^{2}\left(5456\theta^4+17498\theta^3+22121\theta^2+11940\theta+2340\right)-2^{2} 3^{4} x^{3}\left(15128\theta^4+68040\theta^3+112171\theta^2+73845\theta+16380\right)+2^{4} 3^{8} x^{4}(2\theta+1)(216\theta^3+864\theta^2+1015\theta+356)-2^{6} 3^{10} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 324, 12000, 548100, ...
--> OEIS
Normalized instanton numbers (n0=1): 49/5, -68/5, 6032/15, 36276/5, 350082/5, ... ; Common denominator:...

Discriminant

\(-(81z-1)(1296z^2-56z+1)(-5+36z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I\)\(\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I\)\(\frac{ 5}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.66" from ...

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98

New Number: 5.67 |  AESZ: 275  |  Superseeker: 116/5 186172/5  |  Hash: f411d346afd4b8ff14b8b4c1836bae77  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(592\theta^4+1568\theta^3+1419\theta^2+635\theta+115\right)+2^{4} x^{2}\left(65536\theta^4+514048\theta^3+902816\theta^2+598400\theta+144735\right)+2^{10} x^{3}\left(106496\theta^4+122880\theta^3-594816\theta^2-794880\theta-265065\right)-2^{19} x^{4}\left(8192\theta^4+77824\theta^3+145728\theta^2+102016\theta+24527\right)-2^{26} x^{5}(8\theta+5)(8\theta+7)(8\theta+9)(8\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 92, 14124, 2572400, 510577900, ...
--> OEIS
Normalized instanton numbers (n0=1): 116/5, -5993/5, 186172/5, -8039756/5, 384321296/5, ... ; Common denominator:...

Discriminant

\(-(-1+64z)(256z+5)^2(256z-1)^2\)

Local exponents

\(-\frac{ 5}{ 256}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 8}\)
\(1\)\(0\)\(0\)\(1\)\(\frac{ 7}{ 8}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 9}{ 8}\)
\(4\)\(0\)\(1\)\(2\)\(\frac{ 11}{ 8}\)

Note:

This is operator "5.67" from ...

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99

New Number: 5.68 |  AESZ: 279  |  Superseeker: -10/17 10  |  Hash: 06f80606fbeb2b0cc9559df633f1f59d  

Degree: 5

\(17^{2} \theta^4+17 x\left(286\theta^4+734\theta^3+656\theta^2+289\theta+51\right)+3^{2} x^{2}\left(4110\theta^4+22074\theta^3+37209\theta^2+26265\theta+6800\right)-3^{5} x^{3}\left(1521\theta^4+7344\theta^3+12936\theta^2+9945\theta+2822\right)+3^{8} x^{4}\left(123\theta^4+552\theta^3+879\theta^2+603\theta+152\right)-3^{12} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -3, 9, 51, -1431, ...
--> OEIS
Normalized instanton numbers (n0=1): -10/17, -19/17, 10, -369/17, -1413/17, ... ; Common denominator:...

Discriminant

\(-(729z^3-189z^2-20z-1)(-17+27z)^2\)

Local exponents

≈\(-0.044921-0.04372I\) ≈\(-0.044921+0.04372I\)\(0\) ≈\(0.349102\)\(\frac{ 17}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 280/5.69

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100

New Number: 5.69 |  AESZ: 280  |  Superseeker: -117 -844872  |  Hash: 5083c4e9f432302302c564ba554e3bcd  

Degree: 5

\(\theta^4-3^{2} x\left(123\theta^4-60\theta^3-39\theta^2-9\theta-1\right)+3^{5} x^{2}\left(1521\theta^4-1260\theta^3+30\theta^2-21\theta-10\right)-3^{8} x^{3}\left(4110\theta^4-5634\theta^3-4353\theta^2-1629\theta-220\right)-3^{12} 17 x^{4}\left(286\theta^4+410\theta^3+170\theta^2-35\theta-30\right)-3^{18} 17^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -9, 81, 1017, -93231, ...
--> OEIS
Normalized instanton numbers (n0=1): -117, -28899/4, -844872, -131189436, -23932952667, ... ; Common denominator:...

Discriminant

\(-(531441z^3+14580z^2+189z-1)(-1+459z)^2\)

Local exponents

≈\(-0.015682-0.015263I\) ≈\(-0.015682+0.015263I\)\(0\)\(\frac{ 1}{ 459}\) ≈\(0.003929\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 279/5.68

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101

New Number: 5.6 |  AESZ: 23  |  Superseeker: 4/3 44/3  |  Hash: 65760d446ba9c3da587ce5bd9912745e  

Degree: 5

\(3^{2} \theta^4-2^{2} 3 x\left(64\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+2^{7} x^{2}\left(194\theta^4+440\theta^3+527\theta^2+315\theta+75\right)-2^{12} x^{3}\left(94\theta^4+288\theta^3+397\theta^2+261\theta+66\right)+2^{17} x^{4}\left(22\theta^4+80\theta^3+117\theta^2+77\theta+19\right)-2^{23} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 104, 1664, 30376, ...
--> OEIS
Normalized instanton numbers (n0=1): 4/3, 13/3, 44/3, 278/3, 2336/3, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(1\)
\(0\)\(2\)\(1\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,corresponding to Operator AESZ 56/5.9
A-Incarnation: (2,0),(2.0),(0,2),(0,2),(1,1).intersection in $P^4 \times P^4$

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102

New Number: 5.70 |  AESZ: 287  |  Superseeker: 361/21 120472/21  |  Hash: 97932196c46a8712f6dcb11165d698be  

Degree: 5

\(3^{2} 7^{2} \theta^4-3 7 x\left(3289\theta^4+6098\theta^3+4645\theta^2+1596\theta+210\right)+2^{2} 5 x^{2}\left(7712\theta^4-46168\theta^3-106885\theta^2-67410\theta-13629\right)+2^{4} x^{3}\left(106636\theta^4+493416\theta^3+420211\theta^2+116361\theta+6090\right)-2^{8} 5 x^{4}(2\theta+1)(1916\theta^3+2622\theta^2+1077\theta+91)-2^{12} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 510, 38260, 3473470, ...
--> OEIS
Normalized instanton numbers (n0=1): 361/21, 4780/21, 120472/21, 1537864/7, 216261320/21, ... ; Common denominator:...

Discriminant

\(-(64z^3+800z^2+149z-1)(-21+80z)^2\)

Local exponents

≈\(-12.310784\) ≈\(-0.195701\)\(0\) ≈\(0.006485\)\(\frac{ 21}{ 80}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.70" from ...

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103

New Number: 5.71 |  AESZ: 290  |  Superseeker: 162 751026  |  Hash: 5552195a371df176b84ac2c2d791be7e  

Degree: 5

\(\theta^4+3 x\left(279\theta^4-252\theta^3-160\theta^2-34\theta-3\right)+2 3^{5} x^{2}\left(423\theta^4-468\theta^3+457\theta^2+215\theta+37\right)+2 3^{9} x^{3}\left(531\theta^4+1296\theta^3+1243\theta^2+567\theta+104\right)+3^{15} 5 x^{4}\left(51\theta^4+120\theta^3+126\theta^2+66\theta+14\right)+3^{20} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, -837, -32553, 4787019, ...
--> OEIS
Normalized instanton numbers (n0=1): 162, -8829, 751026, -163125009/2, 10343901204, ... ; Common denominator:...

Discriminant

\((27z+1)(19683z^2+1)(1+405z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 405}\)\(0-\frac{ 1}{ 243}\sqrt{ 3}I\)\(0\)\(0+\frac{ 1}{ 243}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 17/5.1

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104

New Number: 5.72 |  AESZ: 291  |  Superseeker: -28 -37768  |  Hash: cbc8242a8fecc72056e6e36b4864b868  

Degree: 5

\(\theta^4-x\left(566\theta^4+34\theta^3+62\theta^2+45\theta+9\right)+3 x^{2}\left(39370\theta^4+17302\theta^3+22493\theta^2+8369\theta+1140\right)-3^{2} x^{3}\left(1215215\theta^4+1432728\theta^3+1274122\theta^2+538245\theta+93222\right)+3^{7} 61 x^{4}\left(3029\theta^4+6544\theta^3+6135\theta^2+2863\theta+548\right)-3^{12} 61^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 189, 3375, -159651, ...
--> OEIS
Normalized instanton numbers (n0=1): -28, -809, -37768, -2185213, -143204777, ... ; Common denominator:...

Discriminant

\(-(59049z^3-11421z^2+200z-1)(-1+183z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 183}\) ≈\(0.009423-0.002866I\) ≈\(0.009423+0.002866I\) ≈\(0.174569\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 124/5.18

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105

New Number: 5.73 |  AESZ: 293  |  Superseeker: 20 13188  |  Hash: f19eeaee48396d15d7cf7be47d7d48a7  

Degree: 5

\(\theta^4-2^{2} x\left(54\theta^4+66\theta^3+49\theta^2+16\theta+2\right)+2^{4} x^{2}\left(417\theta^4-306\theta^3-1219\theta^2-776\theta-154\right)+2^{8} x^{3}\left(166\theta^4+1920\theta^3+1589\theta^2+432\theta+23\right)-2^{12} 7 x^{4}(2\theta+1)(38\theta^3+45\theta^2+12\theta-2)-2^{14} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 8, 528, 45440, 4763920, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 867/2, 13188, 609734, 35512476, ... ; Common denominator:...

Discriminant

\(-(16z+1)(256z^2+176z-1)(-1+28z)^2\)

Local exponents

\(-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}\)\(-\frac{ 1}{ 16}\)\(0\)\(-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 28}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.73" from ...

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106

New Number: 5.74 |  AESZ: 297  |  Superseeker: 26/7 55644/7  |  Hash: cd0b6008fa6b70d89e004100b5698063  

Degree: 5

\(7^{2} \theta^4-2 7 x\theta(520\theta^3+68\theta^2+41\theta+7)-2^{2} 3 x^{2}\left(9480\theta^4+153912\theta^3+212893\theta^2+108080\theta+18816\right)+2^{4} 3^{3} 7 x^{3}\left(13424\theta^4+48792\theta^3+45656\theta^2+17979\theta+2606\right)-2^{6} 3^{7} x^{4}(2\theta+1)^2(2257\theta^2+3601\theta+1942)+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 288, 7200, 1058400, ...
--> OEIS
Normalized instanton numbers (n0=1): 26/7, 2594/7, 55644/7, 2996576/7, 135364470/7, ... ; Common denominator:...

Discriminant

\((128z-1)(432z^2-72z-1)(-7+324z)^2\)

Local exponents

\(\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 7}{ 324}\)\(\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.74" from ...

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107

New Number: 5.75 |  AESZ: 298  |  Superseeker: 205/9 97622/9  |  Hash: e52d50673ec5c795512e2bc3e1017b12  

Degree: 5

\(3^{4} \theta^4-3^{2} x\left(1993\theta^4+3218\theta^3+2437\theta^2+828\theta+108\right)+2^{5} x^{2}\left(17486\theta^4+25184\theta^3+12239\theta^2+2790\theta+297\right)-2^{8} x^{3}\left(23620\theta^4+34776\theta^3+28905\theta^2+12447\theta+2106\right)+2^{15} x^{4}(2\theta+1)(340\theta^3+618\theta^2+455\theta+129)-2^{22} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 708, 63840, 6989220, ...
--> OEIS
Normalized instanton numbers (n0=1): 205/9, 3206/9, 97622/9, 496806, 254037095/9, ... ; Common denominator:...

Discriminant

\(-(z-1)(1024z^2-192z+1)(-9+128z)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\)\(\frac{ 9}{ 128}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.75" from ...

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108

New Number: 5.76 |  AESZ: 306  |  Superseeker: 73/3 11119  |  Hash: d14307aa38b16c728ee31e5936937c44  

Degree: 5

\(3^{2} \theta^4-3 x\left(592\theta^4+1100\theta^3+829\theta^2+279\theta+36\right)+x^{2}\left(13801\theta^4+6652\theta^3-18041\theta^2-14904\theta-3312\right)-2 x^{3}\theta(8461\theta^3-29160\theta^2-28365\theta-7236)-2^{2} 3 7 x^{4}\left(513\theta^4+864\theta^3+487\theta^2+64\theta-16\right)-2^{3} 3 7^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 732, 67080, 7456140, ...
--> OEIS
Normalized instanton numbers (n0=1): 73/3, 2131/6, 11119, 518671, 29749701, ... ; Common denominator:...

Discriminant

\(-(z+1)(54z^2+189z-1)(-3+14z)^2\)

Local exponents

\(-\frac{ 7}{ 4}-\frac{ 11}{ 36}\sqrt{ 33}\)\(-1\)\(0\)\(-\frac{ 7}{ 4}+\frac{ 11}{ 36}\sqrt{ 33}\)\(\frac{ 3}{ 14}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.76" from ...

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109

New Number: 5.77 |  AESZ: 307  |  Superseeker: 69/11 8883/11  |  Hash: 3a2dcd4c59d8fa5b7c57250efeecba62  

Degree: 5

\(11^{2} \theta^4-3 11 x\left(361\theta^4+530\theta^3+419\theta^2+154\theta+22\right)+2^{2} x^{2}\left(47008\theta^4+45904\theta^3-3251\theta^2-17094\theta-4851\right)-2^{4} 3 x^{3}\left(31436\theta^4+86856\theta^3+160363\theta^2+122133\theta+30294\right)+2^{9} 3^{2} x^{4}(2\theta+1)(1252\theta^3+5442\theta^2+6767\theta+2625)-2^{14} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 162, 6540, 314370, ...
--> OEIS
Normalized instanton numbers (n0=1): 69/11, 620/11, 8883/11, 171916/11, 4334406/11, ... ; Common denominator:...

Discriminant

\(-(81z-1)(64z^2+1)(-11+96z)^2\)

Local exponents

\(0-\frac{ 1}{ 8}I\)\(0\)\(0+\frac{ 1}{ 8}I\)\(\frac{ 1}{ 81}\)\(\frac{ 11}{ 96}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.77" from ...

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110

New Number: 5.78 |  AESZ: 308  |  Superseeker: 248/29 38708/29  |  Hash: 94e96c5d238b2d22a633f4e05ec1ae9f  

Degree: 5

\(29^{2} \theta^4-2 29 x\left(1318\theta^4+2336\theta^3+1806\theta^2+638\theta+87\right)-2^{2} x^{2}\left(90996\theta^4+744384\theta^3+1267526\theta^2+791584\theta+168345\right)+2^{2} 5^{2} x^{3}\left(34172\theta^4+77256\theta^3-46701\theta^2-110403\theta-36540\right)+2^{4} 5^{4} x^{4}(2\theta+1)(68\theta^3+1842\theta^2+2899\theta+1215)-2^{6} 5^{7} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 210, 9780, 551250, ...
--> OEIS
Normalized instanton numbers (n0=1): 248/29, 2476/29, 38708/29, 940480/29, 27926248/29, ... ; Common denominator:...

Discriminant

\(-(2000z^3+1024z^2+84z-1)(-29+100z)^2\)

Local exponents

≈\(-0.40534\) ≈\(-0.117186\)\(0\) ≈\(0.010526\)\(\frac{ 29}{ 100}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.78" from ...

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111

New Number: 5.79 |  AESZ: 310  |  Superseeker: 181/11 47171/11  |  Hash: 2b9b103b1c8f0d3175cd1fb9ef5aacc2  

Degree: 5

\(11^{2} \theta^4-11 x\left(1673\theta^4+3046\theta^3+2337\theta^2+814\theta+110\right)+2 5 x^{2}\left(19247\theta^4+28298\theta^3+13285\theta^2+3454\theta+660\right)-2^{2} x^{3}\left(167497\theta^4+245982\theta^3+227451\theta^2+115434\theta+22968\right)+2^{3} 5^{2} x^{4}\left(4079\theta^4+10270\theta^3+11427\theta^2+6226\theta+1340\right)-2^{5} 5^{4} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

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Coefficients of the holomorphic solution: 1, 10, 450, 30772, 2551810, ...
--> OEIS
Normalized instanton numbers (n0=1): 181/11, 2018/11, 47171/11, 3261479/22, 69313270/11, ... ; Common denominator:...

Discriminant

\(-(z-1)(128z^2-142z+1)(-11+50z)^2\)

Local exponents

\(0\)\(\frac{ 71}{ 128}-\frac{ 17}{ 128}\sqrt{ 17}\)\(\frac{ 11}{ 50}\)\(1\)\(\frac{ 71}{ 128}+\frac{ 17}{ 128}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.79" from ...

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112

New Number: 5.7 |  AESZ: 27  |  Superseeker: 14/3 910/3  |  Hash: 3671a1760894e9030e36de89070612e8  

Degree: 5

\(3^{2} \theta^4-3 x\left(173\theta^4+340\theta^3+272\theta^2+102\theta+15\right)-2 x^{2}\left(1129\theta^4+5032\theta^3+7597\theta^2+4773\theta+1083\right)+2 x^{3}\left(843\theta^4+2628\theta^3+2353\theta^2+675\theta+6\right)-x^{4}\left(295\theta^4+608\theta^3+478\theta^2+174\theta+26\right)+x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 109, 3317, 121501, ...
--> OEIS
Normalized instanton numbers (n0=1): 14/3, 175/6, 910/3, 14147/3, 265496/3, ... ; Common denominator:...

Discriminant

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

Local exponents

≈\(-0.213297\)\(0\) ≈\(0.016211\)\(3\) ≈\(289.197085\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

A-incarnation: X(1,1,1,1,1,1,1) in G(2,7)
There is a second MUM point at infinity related to
the Pfaffian in P^7, AESZ 243/5.46

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113

New Number: 5.80 |  AESZ: 311  |  Superseeker: 25/13 875/13  |  Hash: 8219f3f4bd56f6c2b2cc3ab9093b65d1  

Degree: 5

\(13^{2} \theta^4-13 x\left(327\theta^4+1038\theta^3+857\theta^2+338\theta+52\right)-2^{4} x^{2}\left(12848\theta^4+42008\theta^3+52082\theta^2+28548\theta+5707\right)-2^{11} x^{3}\left(122\theta^4-1872\theta^3-6341\theta^2-5772\theta-1547\right)+2^{16} x^{4}(2\theta+1)(76\theta^3+426\theta^2+570\theta+227)+2^{23} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 84, 1840, 56980, ...
--> OEIS
Normalized instanton numbers (n0=1): 25/13, 1359/52, 875/13, 36572/13, 256800/13, ... ; Common denominator:...

Discriminant

\((8192z^3-896z^2-35z+1)(13+64z)^2\)

Local exponents

\(-\frac{ 13}{ 64}\) ≈\(-0.045147\)\(0\) ≈\(0.020117\) ≈\(0.134405\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.80" from ...

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114

New Number: 5.81 |  AESZ: 312  |  Superseeker: 5/7 48/7  |  Hash: 767262575f8b1458839c1e9a8beacf0a  

Degree: 5

\(7^{2} \theta^4-7 x\left(39\theta^4+234\theta^3+201\theta^2+84\theta+14\right)-2 x^{2}\left(12073\theta^4+43222\theta^3+57461\theta^2+34328\theta+7756\right)-2^{2} x^{3}\left(28923\theta^4+48426\theta^3-33393\theta^2-80976\theta-32032\right)+2^{3} 13 x^{4}\left(359\theta^4+9790\theta^3+20805\theta^2+15784\theta+4124\right)+2^{5} 3 13^{2} x^{5}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 30, 308, 5950, ...
--> OEIS
Normalized instanton numbers (n0=1): 5/7, 239/28, 48/7, 4451/14, 5888/7, ... ; Common denominator:...

Discriminant

\((16z+1)(2z-1)(27z-1)(7+26z)^2\)

Local exponents

\(-\frac{ 7}{ 26}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 7}{ 6}\)

Note:

This is operator "5.81" from ...

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115

New Number: 5.82 |  AESZ: 313  |  Superseeker: 45 43531  |  Hash: f8bfe82988e14680bdb775a3ce956216  

Degree: 5

\(\theta^4-x(\theta+1)(285\theta^3+321\theta^2+128\theta+18)-2 x^{2}\left(1640\theta^4+1322\theta^3-1337\theta^2-1178\theta-240\right)-2^{2} 3^{2} x^{3}\left(213\theta^4-256\theta^3-286\theta^2-80\theta-5\right)+2^{3} 3^{3} x^{4}(2\theta+1)(22\theta^3+37\theta^2+24\theta+6)+2^{4} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1662, 236340, 40943070, ...
--> OEIS
Normalized instanton numbers (n0=1): 45, 845, 43531, 3091112, 273471538, ... ; Common denominator:...

Discriminant

\((z-1)(48z^2+296z-1)(6z+1)^2\)

Local exponents

\(-\frac{ 37}{ 12}-\frac{ 7}{ 6}\sqrt{ 7}\)\(-\frac{ 1}{ 6}\)\(0\)\(-\frac{ 37}{ 12}+\frac{ 7}{ 6}\sqrt{ 7}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.82" from ...

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116

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

Degree: 5

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

Maple   LaTex

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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117

New Number: 5.84 |  AESZ: 318  |  Superseeker: 46/5 1126  |  Hash: 3fa38f629ecd5f39b585ce0c1bd88463  

Degree: 5

\(5^{2} \theta^4-5 x\left(473\theta^4+892\theta^3+696\theta^2+250\theta+35\right)+2 x^{2}\left(1973\theta^4-4636\theta^3-14417\theta^2-10895\theta-2745\right)+2 3^{2} x^{3}\left(343\theta^4+1920\theta^3+1147\theta^2-345\theta-320\right)-3^{4} x^{4}\left(83\theta^4-104\theta^3-458\theta^2-406\theta-114\right)-3^{8} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 7, 219, 9961, 546379, ...
--> OEIS
Normalized instanton numbers (n0=1): 46/5, 717/10, 1126, 51481/2, 3609772/5, ... ; Common denominator:...

Discriminant

\(-(z+1)(81z^2+92z-1)(-5+9z)^2\)

Local exponents

\(-\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\)\(-1\)\(0\)\(-\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\)\(\frac{ 5}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 319/5.85
Fibre product: 53211- x 632--1(1)

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118

New Number: 5.85 |  AESZ: 319  |  Superseeker: -26 -14942/3  |  Hash: 40a034330b9ad40ec865803f0a601932  

Degree: 5

\(\theta^4+x\left(83\theta^4+436\theta^3+352\theta^2+134\theta+21\right)-2 3^{2} x^{2}\left(343\theta^4-548\theta^3-2555\theta^2-1749\theta-405\right)-2 3^{4} x^{3}\left(1973\theta^4+12528\theta^3+11329\theta^2+3861\theta+342\right)+3^{8} 5 x^{4}\left(473\theta^4+1000\theta^3+858\theta^2+358\theta+62\right)-3^{12} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -21, 891, -48027, 2920779, ...
--> OEIS
Normalized instanton numbers (n0=1): -26, -475/2, -14942/3, -244479/2, -3574404, ... ; Common denominator:...

Discriminant

\(-(81z+1)(81z^2-92z-1)(-1+45z)^2\)

Local exponents

\(-\frac{ 1}{ 81}\)\(\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\)\(0\)\(\frac{ 1}{ 45}\)\(\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding
to Operator AESZ 318/5.84
B-Incarnation:
Fibre product 53211- x 632--1(0)

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119

New Number: 5.86 |  AESZ: 320  |  Superseeker: 741/11 138745  |  Hash: d19e7569ce62abdd5393977835e411a9  

Degree: 5

\(11^{2} \theta^4-11 x\left(4843\theta^4+8918\theta^3+6505\theta^2+2046\theta+242\right)+2^{2} x^{2}\left(312184\theta^4+343456\theta^3-23371\theta^2-73942\theta-14883\right)-2^{4} x^{3}\left(511972\theta^4+256344\theta^3+144969\theta^2+78639\theta+15642\right)+2^{11} x^{4}(2\theta+1)(1964\theta^3+3078\theta^2+1853\theta+419)-2^{18} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 22, 2850, 568300, 138119170, ...
--> OEIS
Normalized instanton numbers (n0=1): 741/11, 22232/11, 138745, 157326644/11, 19999995398/11, ... ; Common denominator:...

Discriminant

\(-(z-1)(64z^2-416z+1)(-11+128z)^2\)

Local exponents

\(0\)\(\frac{ 13}{ 4}-\frac{ 15}{ 8}\sqrt{ 3}\)\(\frac{ 11}{ 128}\)\(1\)\(\frac{ 13}{ 4}+\frac{ 15}{ 8}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.86" from ...

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120

New Number: 5.87 |  AESZ: 321  |  Superseeker: 35/9 3002/9  |  Hash: b786027c217dd5d5c5abac7b1ecc570b  

Degree: 5

\(3^{4} \theta^4-3^{2} x\left(191\theta^4+862\theta^3+683\theta^2+252\theta+36\right)-2^{5} x^{2}\left(7225\theta^4+24835\theta^3+30634\theta^2+16173\theta+3069\right)-2^{8} x^{3}\left(13251\theta^4+35856\theta^3+27641\theta^2+6966\theta+180\right)-2^{12} 5 x^{4}(2\theta+1)(314\theta^3+363\theta^2+68\theta-31)+2^{16} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 4, 132, 4000, 179620, ...
--> OEIS
Normalized instanton numbers (n0=1): 35/9, 261/4, 3002/9, 126800/9, 1727129/9, ... ; Common denominator:...

Discriminant

\((32z+1)(32z^2-71z+1)(9+80z)^2\)

Local exponents

\(-\frac{ 9}{ 80}\)\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\)\(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.87" from ...

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