Summary

You searched for: Spectrum0=0,0,0,0

Your search produced 561 matches
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121

New Number: 4.27 |  AESZ: 189  |  Superseeker: -30 -11360  |  Hash: 2ce243b7535bf4eefb88252a3c164466  

Degree: 4

\(\theta^4-2 x\left(260\theta^4+520\theta^3+625\theta^2+365\theta+82\right)+2^{2} x^{2}\left(17412\theta^4+69648\theta^3+107199\theta^2+75102\theta+20320\right)-2^{4} x^{3}\left(33280\theta^4+199680\theta^3+476760\theta^2+531720\theta+230741\right)+2^{8} x^{4}(8\theta+13)(8\theta+15)(8\theta+17)(8\theta+19)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 164, 32886, 7144704, 1616497596, ...
--> OEIS
Normalized instanton numbers (n0=1): -30, -885/2, -11360, -365910, -13641180, ... ; Common denominator:...

Discriminant

\((256z-1)^2(4z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 13}{ 8}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 15}{ 8}\)
\(0\)\(1\)\(1\)\(\frac{ 17}{ 8}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 19}{ 8}\)

Note:

Sporadic YY-Operator

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122

New Number: 4.29 |  AESZ: 255  |  Superseeker: -20 -28820/3  |  Hash: 86173b300ea0aef95c3f2b60ce5ecf91  

Degree: 4

\(\theta^4+2^{2} x\left(256\theta^4+512\theta^3+653\theta^2+397\theta+94\right)+2^{7} x^{2}\left(3072\theta^4+12288\theta^3+22696\theta^2+20816\theta+7749\right)+2^{12} x^{3}\left(16384\theta^4+98304\theta^3+237760\theta^2+270912\theta+120731\right)+2^{22} x^{4}(4\theta+7)(4\theta+9)(8\theta+15)(8\theta+17)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -376, 117736, -34499456, 9771980456, ...
--> OEIS
Normalized instanton numbers (n0=1): -20, 295, -28820/3, 454190, -26517920, ... ; Common denominator:...

Discriminant

\((256z+1)^4\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0\)\(\infty\)
\(-\frac{ 3}{ 8}\)\(0\)\(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 8}\)\(0\)\(\frac{ 15}{ 8}\)
\(-\frac{ 5}{ 8}\)\(0\)\(\frac{ 17}{ 8}\)
\(-\frac{ 11}{ 8}\)\(0\)\(\frac{ 9}{ 4}\)

Note:

Sporadic YY-Operator.
Can be reduced to 2.70, so not primary operator.

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123

New Number: 4.2 |  AESZ: ~44  |  Superseeker: -76 -92996  |  Hash: 79f5f70bb79e740c1cd7e835ff99a64c  

Degree: 4

\(\theta^4-2^{2} x\left(272\theta^4+544\theta^3+649\theta^2+377\theta+84\right)+2^{6} 3 x^{2}\left(1544\theta^4+6176\theta^3+9307\theta^2+6262\theta+1588\right)-2^{8} x^{3}(272\theta^2+816\theta+819)(2\theta+3)^2+2^{14} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 336, 142728, 65762368, 31568339880, ...
--> OEIS
Normalized instanton numbers (n0=1): -76, -2002, -92996, -5555506, -384650592, ... ; Common denominator:...

Discriminant

\((1-544z+256z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 17}{ 16}-\frac{ 3}{ 4}\sqrt{ 2}\)\(\frac{ 17}{ 16}+\frac{ 3}{ 4}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 44=$ A \ast \gamma$

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124

New Number: 4.30 |  AESZ: 281  |  Superseeker: 5 -420  |  Hash: d24d5f19c8a8bf23ea9abd62ea9242b2  

Degree: 4

\(\theta^4+x\left(164\theta^4+328\theta^3+402\theta^2+238\theta+109/2\right)+x^{2}\left(12974\theta^4+51896\theta^3+200863/2\theta^2+97071\theta+151081/4\right)+5 x^{3}\left(102500\theta^4+615000\theta^3+1476125\theta^2+1660875\theta+728918\right)+x^{4}15625/16(10\theta+17)(10\theta+19)(10\theta+21)(10\theta+23)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -109/2, 13447/8, 58747/16, -556301557/128, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 95/4, -420, 2555, 19930, ... ; Common denominator:...

Discriminant

\((1+82z+3125z^2)^2\)

Local exponents

\(-\frac{ 41}{ 3125}-\frac{ 38}{ 3125}I\)\(-\frac{ 41}{ 3125}+\frac{ 38}{ 3125}I\)\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 17}{ 10}\)
\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(\frac{ 19}{ 10}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 21}{ 10}\)
\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 23}{ 10}\)

Note:

Sporadic YY-Operator

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125

New Number: 4.31 |  AESZ:  |  Superseeker: -10 -340  |  Hash: dc534a2a8e7bca49a87c29d9ed4e3ae8  

Degree: 4

\(\theta^4-2 x\left(172\theta^4+344\theta^3+421\theta^2+249\theta+57\right)+2^{2} x^{2}\left(10852\theta^4+43408\theta^3+78043\theta^2+69270\theta+24987\right)-2^{4} 3 x^{3}\left(49536\theta^4+297216\theta^3+712240\theta^2+799248\theta+349521\right)+2^{14} 3^{2} x^{4}(3\theta+5)(3\theta+7)(6\theta+11)(6\theta+13)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 114, 11466, 1123804, 109952106, ...
--> OEIS
Normalized instanton numbers (n0=1): -10, -40, -340, -5820, -114610, ... ; Common denominator:...

Discriminant

\((108z-1)^2(64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 5}{ 3}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 7}{ 3}\)

Note:

This is operator "4.31" from ...

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126

New Number: 4.32 |  AESZ: 356  |  Superseeker: -14 -196  |  Hash: e73c971c3ed3a4fd581234510642c285  

Degree: 4

\(\theta^4-2 x\left(236\theta^4+472\theta^3+577\theta^2+341\theta+78\right)+2^{2} x^{2}\left(20836\theta^4+83344\theta^3+150531\theta^2+134374\theta+48664\right)-2^{6} 3 x^{3}\left(33984\theta^4+203904\theta^3+487828\theta^2+545916\theta+237757\right)+2^{10} 3^{2} x^{4}(12\theta+19)(12\theta+23)(12\theta+25)(12\theta+29)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 156, 21062, 2714208, 342489420, ...
--> OEIS
Normalized instanton numbers (n0=1): -14, -42, -196, -1218, -208446/5, ... ; Common denominator:...

Discriminant

\((128z-1)^2(108z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 19}{ 12}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 23}{ 12}\)
\(0\)\(1\)\(1\)\(\frac{ 25}{ 12}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 29}{ 12}\)

Note:

Sporadic YY-Operator.

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127

New Number: 4.33 |  AESZ: 55  |  Superseeker: 76/3 144196/3  |  Hash: 7e88cd5b7dc1c51022b66ac6f009218f  

Degree: 4

\(3^{2} \theta^4-2^{2} 3 x\left(208\theta^4+224\theta^3+163\theta^2+51\theta+6\right)+2^{9} x^{2}\left(32\theta^4-928\theta^3-1606\theta^2-837\theta-141\right)+2^{16} x^{3}\left(144\theta^4+576\theta^3+467\theta^2+144\theta+15\right)-2^{24} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 936, 108800, 16748200, ...
--> OEIS
Normalized instanton numbers (n0=1): 76/3, 3476/3, 144196/3, 3563196, 309069600, ... ; Common denominator:...

Discriminant

\(-(64z+1)(256z-1)(-3+128z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 3}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic operator. There is a second MUM-point
hiding at infinity, corresponding to Operator 4.56

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128

New Number: 4.34 |  AESZ: 99  |  Superseeker: 647/13 942613/13  |  Hash: f6c6b846edc829f336d8e4ae1dcb5618  

Degree: 4

\(13^{2} \theta^4-13 x\left(4569\theta^4+9042\theta^3+6679\theta^2+2158\theta+260\right)+2^{4} x^{2}\left(6386\theta^4-1774\theta^3-17898\theta^2-11596\theta-2119\right)+2^{8} x^{3}\left(67\theta^4+1248\theta^3+1091\theta^2+312\theta+26\right)-2^{12} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 20, 2196, 369200, 75562900, ...
--> OEIS
Normalized instanton numbers (n0=1): 647/13, 16166/13, 942613/13, 80218296/13, 8418215008/13, ... ; Common denominator:...

Discriminant

\(-(256z^2+349z-1)(-13+16z)^2\)

Local exponents

\(-\frac{ 349}{ 512}-\frac{ 85}{ 512}\sqrt{ 17}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 349}{ 512}+\frac{ 85}{ 512}\sqrt{ 17}\)\(\frac{ 13}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator.
There is a second MUM point hidden at infinity. That is operator AESZ 207/4.38
A-Incarnation: $5 \times 5$-Pfaffian in P^5

A-Incarnation: 5 \times 5 Pfaffian in P^5

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129

New Number: 4.35 |  AESZ:  |  Superseeker: -16 -1744  |  Hash: cd392ce4c33f242f5d17e59976d0ea4f  

Degree: 4

\(\theta^4-2^{4} x\left(23\theta^4+14\theta^3+13\theta^2+6\theta+1\right)+2^{11} x^{2}\theta(21\theta^3+24\theta^2+18\theta+4)-2^{16} x^{3}(2\theta+1)(10\theta^3+7\theta^2-5\theta-4)-2^{23} x^{4}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 912, 67840, 5839120, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -106, -1744, -29526, -644016, ... ; Common denominator:...

Discriminant

\(-(16z+1)(128z-1)^3\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(\frac{ 3}{ 2}\)\(1\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Operator equivalent to 3.34, equivalent to
AESZ 107 $=d \ast d$.

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130

New Number: 4.36 |  AESZ: 109  |  Superseeker: 1434/7 18676572/7  |  Hash: bca2938ac7fa09f5bdc395cab75caf82  

Degree: 4

\(7^{2} \theta^4-2 3 7 x\left(1272\theta^4+2508\theta^3+1779\theta^2+525\theta+56\right)+2^{2} 3 x^{2}\left(43704\theta^4+38088\theta^3-25757\theta^2-20608\theta-3360\right)-2^{4} 3^{3} x^{3}\left(2736\theta^4-1512\theta^3-1672\theta^2-357\theta-14\right)-2^{6} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 15840, 8148000, 5126536800, ...
--> OEIS
Normalized instanton numbers (n0=1): 1434/7, 14718, 18676572/7, 4988009280/7, 1646787631350/7, ... ; Common denominator:...

Discriminant

\(-(432z^2+1080z-1)(-7+36z)^2\)

Local exponents

\(-\frac{ 5}{ 4}-\frac{ 13}{ 18}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 5}{ 4}+\frac{ 13}{ 18}\sqrt{ 3}\)\(\frac{ 7}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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131

New Number: 4.37 |  AESZ: 206  |  Superseeker: 4 284  |  Hash: bd5dae321e1369e7fae153775f84a351  

Degree: 4

\(\theta^4-2^{2} x\theta(\theta+1)(2\theta+1)^2-2^{5} x^{2}(2\theta+1)(2\theta+3)(11\theta^2+22\theta+12)-2^{4} 3 5^{2} x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)-2^{8} 19 x^{4}(2\theta+1)(2\theta+3)(2\theta+5)(2\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 72, 1200, 44520, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 27, 284, 4368, 80968, ... ; Common denominator:...

Discriminant

\(-(16z+1)(4864z^3+896z^2+32z-1)\)

Local exponents

≈\(-0.10185-0.013248I\) ≈\(-0.10185+0.013248I\)\(-\frac{ 1}{ 16}\)\(0\)\(s_1\)\(s_3\)\(s_2\) ≈\(0.019489\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(2\)\(2\)\(2\)\(0\)\(2\)\(2\)\(2\)\(2\)\(\frac{ 7}{ 2}\)

Note:

Sporadic Operator.

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132

New Number: 4.38 |  AESZ: 207  |  Superseeker: -70944 -3707752060576  |  Hash: eadc0882a9bf59840ef2b4a602f586e8  

Degree: 4

\(\theta^4-2^{4} x\left(1072\theta^4-17824\theta^3-10888\theta^2-1976\theta-145\right)-2^{17} x^{2}\left(51088\theta^4+116368\theta^3-45264\theta^2-14228\theta-1397\right)+2^{28} 13 x^{3}\left(73104\theta^4+1536\theta^3-488\theta^2+384\theta+97\right)-2^{44} 13^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2320, 57601296, -2373661139200, 121665506430000400, ...
--> OEIS
Normalized instanton numbers (n0=1): -70944, 107317768, -3707752060576, 66327758316665792, -1970671594871618215520, ... ; Common denominator:...

Discriminant

\(-(16777216z^2-89344z-1)(-1+53248z)^2\)

Local exponents

\(\frac{ 349}{ 131072}-\frac{ 85}{ 131072}\sqrt{ 17}\)\(0\)\(s_2\)\(s_1\)\(\frac{ 1}{ 53248}\)\(\frac{ 349}{ 131072}+\frac{ 85}{ 131072}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator.
There is a further MUM point hidden at infinity.
That operator is AESZ 99/4.34

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133

New Number: 4.39 |  AESZ: 210  |  Superseeker: -444/5 -1501908/5  |  Hash: 155d0198a5b26de08a0c2caf680f0786  

Degree: 4

\(5^{2} \theta^4+2^{2} 5 x\left(688\theta^4+1352\theta^3+981\theta^2+305\theta+35\right)+2^{4} x^{2}\left(5856\theta^4+7008\theta^3+96\theta^2-1260\theta-265\right)+2^{10} x^{3}\left(176\theta^4+120\theta^3+69\theta^2+30\theta+5\right)+2^{12} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -28, 4716, -1226800, 389349100, ...
--> OEIS
Normalized instanton numbers (n0=1): -444/5, 16653/5, -1501908/5, 199965534/5, -6573697776, ... ; Common denominator:...

Discriminant

\((256z^2+544z+1)(5+16z)^2\)

Local exponents

\(-\frac{ 17}{ 16}-\frac{ 3}{ 4}\sqrt{ 2}\)\(-\frac{ 5}{ 16}\)\(-\frac{ 17}{ 16}+\frac{ 3}{ 4}\sqrt{ 2}\)\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic operator. There is a second MUM point hidden at infinity; Operator AESZ 211/4.40

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134

New Number: 4.3 |  AESZ:  |  Superseeker: -20 5924  |  Hash: 4163e7dfeb4b46f62bda072d071020fc  

Degree: 4

\(\theta^4-2^{2} x\left(112\theta^4+224\theta^3+271\theta^2+159\theta+36\right)+2^{6} x^{2}\left(1432\theta^4+5728\theta^3+10849\theta^2+10242\theta+3888\right)-2^{8} 3^{4} x^{3}(112\theta^2+336\theta+341)(2\theta+3)^2+2^{14} 3^{8} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 144, 13320, 432320, -127603800, ...
--> OEIS
Normalized instanton numbers (n0=1): -20, 199, 5924, 82010, -1170848, ... ; Common denominator:...

Discriminant

\((1-224z+20736z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 7}{ 1296}-\frac{ 1}{ 324}\sqrt{ 2}I\)\(\frac{ 7}{ 1296}+\frac{ 1}{ 324}\sqrt{ 2}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 150=$ A \ast \delta $

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135

New Number: 4.40 |  AESZ: 211  |  Superseeker: -2400 -2956977632  |  Hash: c923c78e33e72a3a2b294bf3f2749298  

Degree: 4

\(\theta^4+2^{4} x\left(704\theta^4+928\theta^3+612\theta^2+148\theta+13\right)+2^{12} x^{2}\left(5856\theta^4+4704\theta^3-1632\theta^2-972\theta-121\right)+2^{20} 5 x^{3}\left(2752\theta^4+96\theta^3-60\theta^2+24\theta+7\right)+2^{28} 5^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -208, 531216, -2168300800, 10900554288400, ...
--> OEIS
Normalized instanton numbers (n0=1): -2400, 1830480, -2956977632, 7117422755016, -21319886408804640, ... ; Common denominator:...

Discriminant

\((65536z^2+8704z+1)(1+1280z)^2\)

Local exponents

\(-\frac{ 17}{ 256}-\frac{ 3}{ 64}\sqrt{ 2}\)\(-\frac{ 1}{ 1280}\)\(-\frac{ 17}{ 256}+\frac{ 3}{ 64}\sqrt{ 2}\)\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM point hidden at infinity. That corresponds to Operator AESZ210/

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136

New Number: 4.41 |  AESZ: 220  |  Superseeker: 128 382592  |  Hash: 671a1aa788ead53985e13ad6774d0189  

Degree: 4

\(\theta^4-2^{4} x\left(20\theta^4+56\theta^3+38\theta^2+10\theta+1\right)-2^{10} x^{2}\left(84\theta^4+240\theta^3+261\theta^2+134\theta+25\right)-2^{16} x^{3}(2\theta+1)^2(23\theta^2+55\theta+39)-2^{23} x^{4}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 3600, 851200, 257328400, ...
--> OEIS
Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...

Discriminant

\(-(512z-1)(64z+1)^3\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 512}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(\frac{ 3}{ 2}\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Sporadic Operator.
Reducible to 3.32, so not a primary operator.
B-Incarnation: 81111- x 82--11

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137

New Number: 4.42 |  AESZ: 222  |  Superseeker: 69/5 29081/5  |  Hash: aad7a72e711c9c463396d319e0bf7603  

Degree: 4

\(5^{2} \theta^4-5 x\left(407\theta^4+1198\theta^3+909\theta^2+310\theta+40\right)-2^{7} x^{2}\left(2103\theta^4+6999\theta^3+8358\theta^2+4050\theta+680\right)-2^{12} x^{3}\left(1387\theta^4+3840\theta^3+3081\theta^2+960\theta+100\right)-2^{21} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 504, 36800, 3518200, ...
--> OEIS
Normalized instanton numbers (n0=1): 69/5, 1383/4, 29081/5, 346080, 72023607/5, ... ; Common denominator:...

Discriminant

\(-(8192z^2+107z-1)(5+64z)^2\)

Local exponents

\(-\frac{ 5}{ 64}\)\(-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43

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138

New Number: 4.43 |  AESZ: 225  |  Superseeker: 93984 25265152551072  |  Hash: 5993002ccf811247be9232b089dd8e3a  

Degree: 4

\(\theta^4+2^{4} x\left(22192\theta^4-17056\theta^3-9576\theta^2-1048\theta-49\right)+2^{20} x^{2}\left(33648\theta^4-44688\theta^3+16224\theta^2+1764\theta+17\right)+2^{34} 5 x^{3}\left(6512\theta^4-6144\theta^3-4440\theta^2-1536\theta-193\right)-2^{55} 5^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 784, 3226896, 20413907200, 157477179235600, ...
--> OEIS
Normalized instanton numbers (n0=1): 93984, -1084521600, 25265152551072, -787700706860008320, 28889437619654310485088, ... ; Common denominator:...

Discriminant

\(-(536870912z^2-27392z-1)(1+163840z)^2\)

Local exponents

≈\(-2.5e-05\)\(-\frac{ 1}{ 163840}\)\(0\)\(s_2\)\(s_1\) ≈\(7.6e-05\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point
hiding at infinity, corresponding to Operator
AESZ 222/4.42

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139

New Number: 4.44 |  AESZ: 232  |  Superseeker: 379/5 1364199/5  |  Hash: 8d5ff690c87757ed51a092dee764eede  

Degree: 4

\(5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ...
--> OEIS
Normalized instanton numbers (n0=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...

Discriminant

\(-(27z+1)(512z-1)(-5+96z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 512}\)\(\frac{ 5}{ 96}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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140

New Number: 4.45 |  AESZ: 233  |  Superseeker: 80 104976  |  Hash: 03f67459f6d678669f766c99281b1e79  

Degree: 4

\(\theta^4-2^{4} x\left(83\theta^4+94\theta^3+71\theta^2+24\theta+3\right)+2^{11} 3 x^{2}\left(101\theta^4+191\theta^3+174\theta^2+71\theta+10\right)-2^{16} 3^{2} x^{3}\left(203\theta^4+432\theta^3+333\theta^2+102\theta+11\right)+2^{23} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 9360, 2553600, 813027600, ...
--> OEIS
Normalized instanton numbers (n0=1): 80, 2794, 104976, 5367454, 508265072, ... ; Common denominator:...

Discriminant

\((512z-1)(432z-1)(-1+192z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 512}\)\(\frac{ 1}{ 432}\)\(\frac{ 1}{ 192}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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141

New Number: 4.46 |  AESZ: 237  |  Superseeker: 208 1218192  |  Hash: 52c18dd4477f6548dd3b185e97b94c20  

Degree: 4

\(\theta^4-2^{4} x\left(46\theta^4+128\theta^3+91\theta^2+27\theta+3\right)-2^{9} 3 x^{2}\left(74\theta^4-16\theta^3-231\theta^2-127\theta-20\right)+2^{14} 3^{2} x^{3}\left(14\theta^4+216\theta^3+175\theta^2+51\theta+5\right)+2^{19} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 12240, 4972800, 2489533200, ...
--> OEIS
Normalized instanton numbers (n0=1): 208, 5874, 1218192, 220754467, 56417503216, ... ; Common denominator:...

Discriminant

\((864z-1)(64z-1)(1+96z)^2\)

Local exponents

\(-\frac{ 1}{ 96}\)\(0\)\(\frac{ 1}{ 864}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

This is operator "4.46" from ...

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142

New Number: 4.47 |  AESZ: 239  |  Superseeker: 1584 171534960  |  Hash: 8e610c3437d7f38e552038bc55399495  

Degree: 4

\(\theta^4+2^{4} 3 x\left(9\theta^4-198\theta^3-131\theta^2-32\theta-3\right)-2^{11} 3^{2} x^{2}\left(486\theta^4+1215\theta^3+81\theta^2-27\theta-5\right)-2^{16} 3^{5} x^{3}\left(891\theta^4+972\theta^3+675\theta^2+216\theta+25\right)-2^{23} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 144, 147600, 239904000, 479672701200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1584, -17874, 171534960, 30012731550, 105934107802896, ... ; Common denominator:...

Discriminant

\(-(432z+1)(3456z-1)(1+1728z)^2\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 1}{ 1728}\)\(0\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 3}\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(2\)\(4\)\(0\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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143

New Number: 4.48 |  AESZ: 241  |  Superseeker: 320 19748928  |  Hash: b4d16d8dd1eb7839630ecf8e8d242023  

Degree: 4

\(\theta^4-2^{4} x\left(152\theta^4+160\theta^3+110\theta^2+30\theta+3\right)+2^{10} 3 x^{2}\left(428\theta^4+176\theta^3-299\theta^2-170\theta-25\right)-2^{17} 3^{2} x^{3}\left(136\theta^4-216\theta^3-180\theta^2-51\theta-5\right)-2^{24} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 26640, 21907200, 22048765200, ...
--> OEIS
Normalized instanton numbers (n0=1): 320, 61084, 19748928, 9428973876, 5618509433280, ... ; Common denominator:...

Discriminant

\(-(64z+1)(1728z-1)(-1+384z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 1728}\)\(\frac{ 1}{ 384}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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144

New Number: 4.49 |  AESZ: 254  |  Superseeker: -5408 -22147077792  |  Hash: 2539c1ff260271c9f7de53e267e2e8cf  

Degree: 4

\(\theta^4-2^{4} x\left(2608\theta^4-544\theta^3-200\theta^2+72\theta+15\right)+2^{15} 3 x^{2}\left(6128\theta^4-208\theta^3+2328\theta^2+452\theta+25\right)-2^{24} 3^{2} 5 x^{3}\left(4592\theta^4+3456\theta^3+2632\theta^2+816\theta+95\right)+2^{38} 3^{3} 5^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 314640, 627244800, 1516001533200, ...
--> OEIS
Normalized instanton numbers (n0=1): -5408, -8033784, -22147077792, -80392290665536, -341267541912723040, ... ; Common denominator:...

Discriminant

\((6912z-1)(4096z-1)(-1+15360z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 15360}\)\(\frac{ 1}{ 6912}\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(3\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(4\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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145

New Number: 4.4 |  AESZ:  |  Superseeker: -48 -32368  |  Hash: a0903e578f379289d79849a566639775  

Degree: 4

\(\theta^4-2^{4} x\left(48\theta^4+96\theta^3+115\theta^2+67\theta+15\right)+2^{9} x^{2}\left(304\theta^4+1216\theta^3+1890\theta^2+1348\theta+375\right)-2^{14} x^{3}(48\theta^2+144\theta+145)(2\theta+3)^2+2^{22} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 69840, 22068480, 7268490000, ...
--> OEIS
Normalized instanton numbers (n0=1): -48, -910, -32368, -1409193, -71439120, ... ; Common denominator:...

Discriminant

\((1-384z+4096z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\)\(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $d \ast e \tilde A \ast \epsilon$

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146

New Number: 4.50 |  AESZ: 256  |  Superseeker: -128 -800384  |  Hash: 05e172cfdecc836685981a2b01b75d1d  

Degree: 4

\(\theta^4+2^{5} x\left(24\theta^4+42\theta^3+30\theta^2+9\theta+1\right)+2^{8} x^{2}\left(164\theta^4+104\theta^3-144\theta^2-100\theta-17\right)+2^{14} x^{3}\left(28\theta^4-48\theta^3-44\theta^2-12\theta-1\right)-2^{18} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -32, 7056, -2393600, 991152400, ...
--> OEIS
Normalized instanton numbers (n0=1): -128, 6884, -800384, 143245314, -31691939200, ... ; Common denominator:...

Discriminant

\(-(4096z^2-704z-1)(1+32z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 257/4.51
B-Incarnation:
Fibre product 4*11-- x 25311,
Double octic; D.O.257

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147

New Number: 4.51 |  AESZ:  |  Superseeker: 992 63721056  |  Hash: 1d45a05c9bcf007b5042b0f7a5672551  

Degree: 4

\(\theta^4-2^{4} x\left(112\theta^4+416\theta^3+280\theta^2+72\theta+7\right)-2^{12} x^{2}\left(656\theta^4+896\theta^3-216\theta^2-160\theta-23\right)-2^{23} x^{3}\left(96\theta^4+24\theta^3+12\theta^2+6\theta+1\right)-2^{30} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 112, 93456, 124614400, 204621667600, ...
--> OEIS
Normalized instanton numbers (n0=1): 992, 98792, 63721056, 40943244128, 36122052633760, ... ; Common denominator:...

Discriminant

\(-(65536z^2+2816z-1)(1+512z)^2\)

Local exponents

\(-\frac{ 11}{ 512}-\frac{ 5}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 512}\)\(0\)\(s_2\)\(s_1\)\(-\frac{ 11}{ 512}+\frac{ 5}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point
hiding at infinity, corresponding to Operator
AESZ 256/4.50

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148

New Number: 4.52 |  AESZ: 258  |  Superseeker: 480 4215904  |  Hash: bfb9f01124fd9980817cbf1b50f789c3  

Degree: 4

\(\theta^4-2^{4} x\left(16\theta^4+224\theta^3+156\theta^2+44\theta+5\right)-2^{14} x^{2}\left(48\theta^4+48\theta^3-120\theta^2-66\theta-11\right)-2^{22} x^{3}\left(16\theta^4-192\theta^3-156\theta^2-48\theta-5\right)+2^{32} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 80, 24336, 11398400, 6632189200, ...
--> OEIS
Normalized instanton numbers (n0=1): 480, -16536, 4215904, -242723592, 151800032928, ... ; Common denominator:...

Discriminant

\((1024z-1)(256z-1)(1+512z)^2\)

Local exponents

\(-\frac{ 1}{ 512}\)\(0\)\(\frac{ 1}{ 1024}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator.

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149

New Number: 4.53 |  AESZ: 264  |  Superseeker: 37216 464865119712  |  Hash: 625990ef22ba977bc3dd247ccc791780  

Degree: 4

\(\theta^4+2^{4} x\left(3392\theta^4-9344\theta^3-5764\theta^2-1092\theta-93\right)-2^{17} 3 x^{2}\left(1952\theta^4+15200\theta^3-7758\theta^2-2593\theta-323\right)-2^{26} 3^{2} 7 x^{3}\left(11584\theta^4-6912\theta^3-5364\theta^2-1632\theta-167\right)+2^{42} 3^{3} 7^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1488, 11258640, 139962144000, 2191135140810000, ...
--> OEIS
Normalized instanton numbers (n0=1): 37216, -75619080, 464865119712, -2749454414283384, 24030314100181942560, ... ; Common denominator:...

Discriminant

\((27648z-1)(4096z-1)(1+43008z)^2\)

Local exponents

\(-\frac{ 1}{ 43008}\)\(0\)\(\frac{ 1}{ 27648}\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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150

New Number: 4.54 |  AESZ: 265  |  Superseeker: 1056 138459552  |  Hash: fad89ac60b7ab4118edfed4cf6350d0c  

Degree: 4

\(\theta^4+2^{4} 3 x\left(96\theta^4-96\theta^3-60\theta^2-12\theta-1\right)+2^{13} 3 x^{2}\left(288\theta^4-144\theta^3+526\theta^2+206\theta+27\right)+2^{20} 3^{3} x^{3}\left(288\theta^4+864\theta^3+652\theta^2+204\theta+23\right)+2^{30} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

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Coefficients of the holomorphic solution: 1, 48, -30960, -11961600, 15342742800, ...
--> OEIS
Normalized instanton numbers (n0=1): 1056, -360672, 138459552, -50965971720, 20236543243104, ... ; Common denominator:...

Discriminant

\((1769472z^2+1)(1+2304z)^2\)

Local exponents

\(-\frac{ 1}{ 2304}\)\(0-\frac{ 1}{ 2304}\sqrt{ 3}I\)\(0\)\(s_1\)\(s_2\)\(0+\frac{ 1}{ 2304}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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