Summary

You searched for: Spectrum0=0,1,1,2

Your search produced 482 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 
 361-390  391-420  421-450  451-480  481-482 

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91

New Number: 4.56 |  AESZ: 277  |  Superseeker: 4192 2124587232  |  Hash: 9d905a8d31566f4976cbeb2d3bf0624c  

Degree: 4

\(\theta^4+2^{4} x\left(576\theta^4-1152\theta^3-724\theta^2-148\theta-13\right)-2^{17} x^{2}\left(32\theta^4+992\theta^3-166\theta^2-57\theta-6\right)-2^{26} 3 x^{3}\left(832\theta^4+768\theta^3+556\theta^2+192\theta+25\right)-2^{40} 3^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 208, 254736, 490988800, 1163138813200, ...
--> OEIS
Normalized instanton numbers (n0=1): 4192, -1708008, 2124587232, -2777042329304, 4857272052090400, ... ; Common denominator:...

Discriminant

\(-(1024z+1)(4096z-1)(1+6144z)^2\)

Local exponents

\(-\frac{ 1}{ 1024}\)\(-\frac{ 1}{ 6144}\)\(0\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to Operator 4.33, reducible to 3.35.

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92

New Number: 4.57 |  AESZ: 278  |  Superseeker: 243 513936  |  Hash: b30f6ac0da69cf91ab39089e6bf1ac8c  

Degree: 4

\(\theta^4-3 x\left(279\theta^4+882\theta^3+641\theta^2+200\theta+24\right)-2 3^{5} x^{2}\left(72\theta^4-1710\theta^3-3665\theta^2-1864\theta-296\right)+2^{2} 3^{9} x^{3}\left(909\theta^4+3888\theta^3+3082\theta^2+918\theta+92\right)+2^{4} 3^{15} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 72, 18360, 6552000, 2767980600, ...
--> OEIS
Normalized instanton numbers (n0=1): 243, -3402, 513936, 2470824, 6888345300, ... ; Common denominator:...

Discriminant

\((729z-1)(432z-1)(1+162z)^2\)

Local exponents

\(-\frac{ 1}{ 162}\)\(0\)\(\frac{ 1}{ 729}\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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93

New Number: 4.58 |  AESZ: 282  |  Superseeker: 364/5 1264916  |  Hash: 582c9abe0a0b8176a2a06ec6c223bef4  

Degree: 4

\(5^{2} \theta^4-2^{2} 5 x\left(1348\theta^4+752\theta^3+521\theta^2+145\theta+15\right)+2^{4} 3^{4} x^{2}\left(5696\theta^4-1792\theta^3-7304\theta^2-3740\theta-585\right)-2^{10} 3^{8} x^{3}\left(20\theta^4-360\theta^3-289\theta^2-90\theta-10\right)-2^{12} 3^{13} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 3564, 1081200, 418200300, ...
--> OEIS
Normalized instanton numbers (n0=1): 364/5, 43384/5, 1264916, 1297643028/5, 323354425968/5, ... ; Common denominator:...

Discriminant

\(-(62208z^2+560z-1)(-5+1296z)^2\)

Local exponents

\(-\frac{ 35}{ 7776}-\frac{ 13}{ 7776}\sqrt{ 13}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 35}{ 7776}+\frac{ 13}{ 7776}\sqrt{ 13}\)\(\frac{ 5}{ 1296}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity,corresponding to the Operator AESZ 283/4.59

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94

New Number: 4.59 |  AESZ: 283  |  Superseeker: -188 -807540  |  Hash: 987222cb05e8a3d02c76c47abefbb9f4  

Degree: 4

\(\theta^4+2^{2} x\left(20\theta^4+400\theta^3+281\theta^2+81\theta+9\right)-2^{4} 3 x^{2}\left(5696\theta^4+13184\theta^3+3928\theta^2+628\theta+39\right)+2^{10} 3^{2} 5 x^{3}\left(1348\theta^4+1944\theta^3+1415\theta^2+486\theta+63\right)-2^{12} 3^{7} 5^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -36, 7236, -2257200, 860876100, ...
--> OEIS
Normalized instanton numbers (n0=1): -188, 831, -807540, 39235244, -18812436256, ... ; Common denominator:...

Discriminant

\(-(62208z^2-560z-1)(-1+240z)^2\)

Local exponents

\(\frac{ 35}{ 7776}-\frac{ 13}{ 7776}\sqrt{ 13}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 240}\)\(\frac{ 35}{ 7776}+\frac{ 13}{ 7776}\sqrt{ 13}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to AESZ 282/4.58

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95

New Number: 4.60 |  AESZ: 288  |  Superseeker: 3616 264403872  |  Hash: 3373ebdbe30d220b5562cfd77d4e8f96  

Degree: 4

\(\theta^4-2^{4} x\left(496\theta^4+1568\theta^3+1060\theta^2+276\theta+27\right)-2^{15} 3 x^{2}\left(32\theta^4-760\theta^3-1570\theta^2-651\theta-81\right)+2^{22} 3^{2} x^{3}\left(1616\theta^4+6912\theta^3+5092\theta^2+1416\theta+135\right)+2^{34} 3^{3} x^{4}(4\theta+1)(3\theta+1)(3\theta+2)(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 432, 982800, 3259872000, 12958462717200, ...
--> OEIS
Normalized instanton numbers (n0=1): 3616, 114144, 264403872, 424149521656, 710239010095456, ... ; Common denominator:...

Discriminant

\((6912z-1)(4096z-1)(1+1536z)^2\)

Local exponents

\(-\frac{ 1}{ 1536}\)\(0\)\(\frac{ 1}{ 6912}\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 3}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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96

New Number: 4.61 |  AESZ: 289  |  Superseeker: 8224 15542388128  |  Hash: 673413653f5554d4f0cc1a8af33e8bbe  

Degree: 4

\(\theta^4-2^{4} x\left(400\theta^4+2720\theta^3+1752\theta^2+392\theta+33\right)-2^{15} x^{2}\left(4272\theta^4+6288\theta^3-3184\theta^2-1484\theta-177\right)-2^{24} 5 x^{3}\left(4688\theta^4-1536\theta^3-1384\theta^2-336\theta-27\right)+2^{36} 5^{2} x^{4}(4\theta+1)(2\theta+1)^2(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 528, 2434320, 18496262400, 174225386134800, ...
--> OEIS
Normalized instanton numbers (n0=1): 8224, 3407456, 15542388128, 54609260446560, 282477571639256928, ... ; Common denominator:...

Discriminant

\((16384z-1)(256z-1)(1+5120z)^2\)

Local exponents

\(-\frac{ 1}{ 5120}\)\(0\)\(\frac{ 1}{ 16384}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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97

New Number: 4.62 |  AESZ: 292  |  Superseeker: 4300/3 1701817028/3  |  Hash: bce26f214ee56f65c7a275cd8fdcc0c7  

Degree: 4

\(3^{2} \theta^4-2^{2} 3 x\left(4636\theta^4+7928\theta^3+5347\theta^2+1383\theta+126\right)+2^{9} x^{2}\left(59048\theta^4+50888\theta^3-26248\theta^2-16827\theta-2205\right)-2^{16} 7 x^{3}\left(9004\theta^4-2304\theta^3-2511\theta^2-504\theta-27\right)-2^{24} 7^{2} x^{4}(4\theta+1)(2\theta+1)^2(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 168, 279720, 737721600, 2391487698600, ...
--> OEIS
Normalized instanton numbers (n0=1): 4300/3, 1768292/3, 1701817028/3, 2484553593752/3, 1500880129466144, ... ; Common denominator:...

Discriminant

\(-(65536z^2+5584z-1)(-3+896z)^2\)

Local exponents

\(-\frac{ 349}{ 8192}-\frac{ 85}{ 8192}\sqrt{ 17}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 349}{ 8192}+\frac{ 85}{ 8192}\sqrt{ 17}\)\(\frac{ 3}{ 896}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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98

New Number: 4.63 |  AESZ: 294  |  Superseeker: -80416 -15561562691488  |  Hash: f6b5a258285779facb6702e1a2a891bb  

Degree: 4

\(\theta^4-2^{4} x\left(18800\theta^4-14624\theta^3-8184\theta^2-872\theta-33\right)+2^{18} x^{2}\left(101744\theta^4-107920\theta^3+74968\theta^2+15100\theta+1191\right)-2^{30} 17 x^{3}\left(40048\theta^4+49152\theta^3+35848\theta^2+10752\theta+1143\right)+2^{50} 17^{2} x^{4}(4\theta+1)(2\theta+1)^2(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -528, -16919280, -95988076800, 3707387171888400, ...
--> OEIS
Normalized instanton numbers (n0=1): -80416, -872844376, -15561562691488, -341695175348542432, -8482586861983707669856, ... ; Common denominator:...

Discriminant

\((1073741824z^2-22272z+1)(-1+139264z)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 139264}\)\(\frac{ 87}{ 8388608}-\frac{ 91}{ 8388608}\sqrt{ 7}I\)\(\frac{ 87}{ 8388608}+\frac{ 91}{ 8388608}\sqrt{ 7}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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99

New Number: 4.64 |  AESZ: 295  |  Superseeker: -5408 -4296119968  |  Hash: e40629f953a095a2a764c68394321139  

Degree: 4

\(\theta^4-2^{4} x\left(816\theta^4-1440\theta^3-904\theta^2-184\theta-17\right)+2^{18} x^{2}\left(80\theta^4-592\theta^3+432\theta^2+164\theta+23\right)+2^{30} x^{3}\left(80\theta^4-384\theta^3-296\theta^2-96\theta-11\right)+2^{45} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -272, 93456, 194502400, -587215823600, ...
--> OEIS
Normalized instanton numbers (n0=1): -5408, -3839480, -4296119968, -6482749129792, -11816577914904160, ... ; Common denominator:...

Discriminant

\((8388608z^2+3328z+1)(-1+8192z)^2\)

Local exponents

\(-\frac{ 13}{ 65536}-\frac{ 7}{ 65536}\sqrt{ 7}I\)\(-\frac{ 13}{ 65536}+\frac{ 7}{ 65536}\sqrt{ 7}I\)\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 8192}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(2\)\(0\)\(2\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to Operator AESZ 296/4.65

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100

New Number: 4.65 |  AESZ:  |  Superseeker: 48 -9104  |  Hash: 5ec2790b5eda514313634b7aeb0a295c  

Degree: 4

\(\theta^4-2^{4} x\left(5\theta^4+34\theta^3+25\theta^2+8\theta+1\right)+2^{11} x^{2}\left(5\theta^4+47\theta^3+90\theta^2+47\theta+8\right)+2^{16} x^{3}\left(51\theta^4+192\theta^3+155\theta^2+48\theta+5\right)+2^{23} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 144, -70400, -9858800, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, -1298, -9104, 387230, 102374160, ... ; Common denominator:...

Discriminant

\((32768z^2-208z+1)(1+64z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity,
corresponding to Operator AESZ 295/4.64

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101

New Number: 4.66 |  AESZ: 300  |  Superseeker: -1616 -283183120  |  Hash: edc54887effd2ebcaa636dcc93baf0b7  

Degree: 4

\(\theta^4+2^{4} x\left(371\theta^4+862\theta^3+591\theta^2+160\theta+15\right)+2^{11} 5 x^{2}\left(224\theta^4+2069\theta^3+3277\theta^2+1363\theta+159\right)-2^{16} 5^{2} x^{3}\left(2089\theta^4+7500\theta^3+5533\theta^2+1500\theta+135\right)+2^{23} 5^{3} x^{4}(5\theta+1)(5\theta+2)(5\theta+3)(5\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -240, 378000, -941740800, 2908743037200, ...
--> OEIS
Normalized instanton numbers (n0=1): -1616, 265534, -283183120, 351860487150, -525536710386800, ... ; Common denominator:...

Discriminant

\((6400000z^2+6576z+1)(-1+320z)^2\)

Local exponents

≈\(-0.000842\) ≈\(-0.000186\)\(0\)\(s_2\)\(s_1\)\(\frac{ 1}{ 320}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 5}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 5}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 5}\)
\(2\)\(2\)\(0\)\(2\)\(2\)\(4\)\(\frac{ 4}{ 5}\)

Note:

Sporadic Operator.

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102

New Number: 4.67 |  AESZ: 305  |  Superseeker: 1565472 28381748186959008  |  Hash: 4ce63e568901a8cef3f9c2f60b6ce2d2  

Degree: 4

\(\theta^4+2^{4} 3 x\left(81552\theta^4-94944\theta^3-53688\theta^2-6216\theta-379\right)+2^{20} 3 x^{2}\left(1091952\theta^4-2917008\theta^3+1388032\theta^2+225284\theta+19545\right)-2^{34} 3^{3} 7 x^{3}\left(207504\theta^4-221184\theta^3-157480\theta^2-52224\theta-5855\right)+2^{59} 3^{5} 7^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18192, 178183440, -132466290835200, -18938901463932265200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1565472, -155959736064, 28381748186959008, -6798945051352302862848, 1905341636283453444266170464, ... ; Common denominator:...

Discriminant

\((57982058496z^2-214272z+1)(1+2064384z)^2\)

Local exponents

\(-\frac{ 1}{ 2064384}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 31}{ 16777216}-\frac{ 145}{ 150994944}\sqrt{ 15}I\)\(\frac{ 31}{ 16777216}+\frac{ 145}{ 150994944}\sqrt{ 15}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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103

New Number: 4.68 |  AESZ: 337  |  Superseeker: 2043/5 88982631/5  |  Hash: dc26e94a7c1daba6f627be36c42019b7  

Degree: 4

\(5^{2} \theta^4-3 5 x\left(3483\theta^4+6102\theta^3+4241\theta^2+1190\theta+120\right)+2^{5} 3^{2} x^{2}\left(31428\theta^4+35559\theta^3+243\theta^2-4320\theta-740\right)-2^{8} 3^{5} x^{3}\left(7371\theta^4+4860\theta^3+2997\theta^2+1080\theta+140\right)+2^{13} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 72, 41400, 37396800, 41397463800, ...
--> OEIS
Normalized instanton numbers (n0=1): 2043/5, 279018/5, 88982631/5, 8604708876, 25774859896713/5, ... ; Common denominator:...

Discriminant

\((23328z^2-1917z+1)(-5+432z)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 71}{ 1728}-\frac{ 17}{ 1728}\sqrt{ 17}\)\(\frac{ 5}{ 432}\)\(\frac{ 71}{ 1728}+\frac{ 17}{ 1728}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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104

New Number: 4.69 |  AESZ: 350  |  Superseeker: 49 173876/9  |  Hash: e6de16eb3758d2ed5687f4b2a2abf36b  

Degree: 4

\(\theta^4-x\left(24+184\theta+545\theta^2+722\theta^3+289\theta^4\right)+2^{3} 3 x^{2}\left(214\theta^4+2734\theta^3+4861\theta^2+2640\theta+468\right)+2^{6} 3^{2} x^{3}\left(1391\theta^4+5184\theta^3+4252\theta^2+1296\theta+126\right)+2^{10} 3^{6} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1944, 232800, 34133400, ...
--> OEIS
Normalized instanton numbers (n0=1): 49, 136, 173876/9, 781152, 57087750, ... ; Common denominator:...

Discriminant

\((256z-1)(81z-1)(1+24z)^2\)

Local exponents

\(-\frac{ 1}{ 24}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 81}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 351/4.70

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105

New Number: 4.70 |  AESZ:  |  Superseeker: 177184 45194569320864  |  Hash: 56776b8a011d3f76a664ac5c7f492c1a  

Degree: 4

\(\theta^4+2^{4} x\left(22256\theta^4-38432\theta^3-23000\theta^2-3784\theta-321\right)+2^{18} 3^{3} x^{2}\left(1712\theta^4-18448\theta^3+8648\theta^2+2220\theta+279\right)-2^{30} 3^{6} x^{3}\left(4624\theta^4-2304\theta^3-1672\theta^2-576\theta-63\right)+2^{46} 3^{10} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5136, 98870544, 2900370796800, 105956691416931600, ...
--> OEIS
Normalized instanton numbers (n0=1): 177184, -1960034336, 45194569320864, -1351787074724461344, 47485667264376266736480, ... ; Common denominator:...

Discriminant

\((65536z-1)(20736z-1)(1+221184z)^2\)

Local exponents

\(-\frac{ 1}{ 221184}\)\(0\)\(\frac{ 1}{ 65536}\)\(\frac{ 1}{ 20736}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second
MUM-point hiding at infinity, corresponding to
Operator AESZ 350/4.69

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106

New Number: 4.71 |  AESZ: 353  |  Superseeker: -4 -1580/9  |  Hash: 33845d8200fe810109063e352fbfc8b1  

Degree: 4

\(\theta^4-2^{2} x\left(52\theta^4+40\theta^3+37\theta^2+17\theta+3\right)+2^{4} x^{2}\left(960\theta^4+1536\theta^3+1512\theta^2+688\theta+123\right)-2^{8} x^{3}\left(1792\theta^4+4608\theta^3+5184\theta^2+2816\theta+597\right)+2^{14} x^{4}(4\theta+5)^2(4\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 324, 11856, 504900, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, -24, -1580/9, -1580, -17120, ... ; Common denominator:...

Discriminant

\((16z-1)(64z-1)^3\)

Local exponents

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

Note:

Sporadic Operator, reducible to 3.33, so not a primary operator.

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107

New Number: 4.72 |  AESZ: 361  |  Superseeker: 20 -119332/9  |  Hash: f55eaa640956f064f5230c04d8173d60  

Degree: 4

\(\theta^4-2^{2} x\left(80\theta^4+88\theta^3+67\theta^2+23\theta+3\right)+2^{4} 3 x^{2}\left(928\theta^4+2080\theta^3+2176\theta^2+972\theta+153\right)-2^{10} 3^{2} x^{3}\left(272\theta^4+648\theta^3+511\theta^2+162\theta+18\right)+2^{12} 3^{6} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 324, -6000, -2778300, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, -139, -119332/9, -462222, -2113440, ... ; Common denominator:...

Discriminant

\((20736z^2-224z+1)(-1+48z)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 7}{ 1296}-\frac{ 1}{ 324}\sqrt{ 2}I\)\(\frac{ 7}{ 1296}+\frac{ 1}{ 324}\sqrt{ 2}I\)\(\frac{ 1}{ 48}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(0\)\(2\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 362/4.73

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108

New Number: 4.73 |  AESZ: 362  |  Superseeker: -2656 -2493879008  |  Hash: 57a424b3b32b72260817cb8c45a8ae8f  

Degree: 4

\(\theta^4-2^{4} x\left(1088\theta^4-416\theta^3-212\theta^2-4\theta+3\right)+2^{12} 3^{3} x^{2}\left(928\theta^4-224\theta^3+448\theta^2+108\theta+9\right)-2^{20} 3^{6} x^{3}\left(320\theta^4+288\theta^3+220\theta^2+72\theta+9\right)+2^{28} 3^{10} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, -40176, -103200000, -153639990000, ...
--> OEIS
Normalized instanton numbers (n0=1): -2656, -1985680, -2493879008, -3906525894360, -6910084057179168, ... ; Common denominator:...

Discriminant

\((5308416z^2-3584z+1)(-1+6912z)^2\)

Local exponents

\(0\)\(s_2\)\(s_1\)\(\frac{ 1}{ 6912}\)\(\frac{ 7}{ 20736}-\frac{ 1}{ 5184}\sqrt{ 2}I\)\(\frac{ 7}{ 20736}+\frac{ 1}{ 5184}\sqrt{ 2}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point corresponding to Operator AESZ 361/4.72

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109

New Number: 4.74 |  AESZ: 363  |  Superseeker: -207 621972  |  Hash: 15f3be0c25c6a6ea1d78414f1cb31713  

Degree: 4

\(\theta^4+3^{2} x\left(231\theta^4+318\theta^3+231\theta^2+72\theta+8\right)+2^{3} 3^{5} x^{2}\left(774\theta^4+1854\theta^3+1869\theta^2+768\theta+100\right)+2^{6} 3^{8} x^{3}\left(951\theta^4+2304\theta^3+1740\theta^2+504\theta+50\right)+2^{10} 3^{12} x^{4}(4\theta+1)(2\theta+1)^2(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -72, 22680, -9424800, 4199995800, ...
--> OEIS
Normalized instanton numbers (n0=1): -207, 5544, 621972, -241386048, 59946723846, ... ; Common denominator:...

Discriminant

\((746496z^2+1647z+1)(1+216z)^2\)

Local exponents

\(-\frac{ 1}{ 216}\)\(-\frac{ 61}{ 55296}-\frac{ 5}{ 55296}\sqrt{ 15}I\)\(-\frac{ 61}{ 55296}+\frac{ 5}{ 55296}\sqrt{ 15}I\)\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(2\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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110

New Number: 4.76 |  AESZ:  |  Superseeker: 6015 9668470011  |  Hash: f16cc33931b60f0c5d3a1a0239a01062  

Degree: 4

\(\theta^4-3 x\left(2871\theta^4+10926\theta^3+7069\theta^2+1606\theta+136\right)-2^{6} 3^{4} x^{2}\left(12573\theta^4+16677\theta^3-5762\theta^2-2938\theta-348\right)-2^{10} 3^{8} x^{3}\left(14085\theta^4+864\theta^3-29\theta^2+204\theta+44\right)-2^{17} 3^{12} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 408, 1616760, 10409448000, 82877787531000, ...
--> OEIS
Normalized instanton numbers (n0=1): 6015, 3451026, 9668470011, 32924097729576, 144270059475420597, ... ; Common denominator:...

Discriminant

\(-(27z+1)(13824z-1)(1+2592z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 2592}\)\(0\)\(\frac{ 1}{ 13824}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.
B-Incarnation as Diagonal.

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111

New Number: 4.77 |  AESZ:  |  Superseeker: 1 68/9  |  Hash: f9623221ffe8be4c1e31a6e6ce195a37  

Degree: 4

\(\theta^4-x\left(16+80\theta+161\theta^2+162\theta^3+81\theta^4\right)+2^{3} x^{2}\left(303\theta^4+1212\theta^3+1952\theta^2+1480\theta+440\right)-2^{6} x^{3}(124\theta^2+372\theta+263)(2\theta+3)^2+2^{9} 3 5^{2} x^{4}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 280, 5152, 98200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...

Discriminant

\((25z-1)(24z-1)(-1+16z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 25}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 2}\)
\(0\)\(2\)\(2\)\(1\)\(3\)

Note:

Sporadic Operator.
B-Incarnation: SII4411

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112

New Number: 5.100 |  AESZ: 347  |  Superseeker: 15 27140/3  |  Hash: f00de20026c099e75b447c475ab287e4  

Degree: 5

\(\theta^4-3 x\left(213\theta^4+186\theta^3+149\theta^2+56\theta+8\right)+2^{3} 3^{3} x^{2}\left(702\theta^4+1078\theta^3+949\theta^2+392\theta+60\right)-2^{6} 3^{3} x^{3}\left(9277\theta^4+18432\theta^3+16008\theta^2+6000\theta+840\right)+2^{13} 3^{4} 5 x^{4}(2\theta+1)^2(51\theta^2+69\theta+32)-2^{14} 3^{6} 5^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1944, 218400, 28488600, ...
--> OEIS
Normalized instanton numbers (n0=1): 15, 1329/4, 27140/3, 220680, 5952570, ... ; Common denominator:...

Discriminant

\(-(192z-1)(1728z^2-207z+1)(-1+120z)^2\)

Local exponents

\(0\)\(\frac{ 23}{ 384}-\frac{ 11}{ 1152}\sqrt{ 33}\)\(\frac{ 1}{ 192}\)\(\frac{ 1}{ 120}\)\(\frac{ 23}{ 384}+\frac{ 11}{ 1152}\sqrt{ 33}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.100" from ...

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113

New Number: 5.101 |  AESZ: 348  |  Superseeker: -52 -44772  |  Hash: 8759f016475d17d0fc88f4b98a374d3f  

Degree: 5

\(\theta^4+2^{2} x\left(70\theta^4+194\theta^3+145\theta^2+48\theta+6\right)-2^{4} 3 x^{2}\left(141\theta^4-858\theta^3-2111\theta^2-1192\theta-206\right)-2^{8} 3^{2} x^{3}\left(18\theta^4-324\theta^3-2364\theta^2-1953\theta-403\right)-2^{10} 3^{4} x^{4}(3\theta+1)(3\theta+2)(42\theta^2+258\theta+223)+2^{14} 3^{6} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, 2160, -309120, 54608400, ...
--> OEIS
Normalized instanton numbers (n0=1): -52, 461/2, -44772, 3546761/2, -178670332, ... ; Common denominator:...

Discriminant

\((746496z^3+17280z^2+352z+1)(-1+36z)^2\)

Local exponents

≈\(-0.009925-0.017537I\) ≈\(-0.009925+0.017537I\) ≈\(-0.003299\)\(0\)\(\frac{ 1}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(1\)\(0\)\(3\)\(\frac{ 4}{ 3}\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.101" from ...

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114

New Number: 5.102 |  AESZ: 352  |  Superseeker: 1 -12  |  Hash: fc8b141522720827b1dd2cd28a232c1b  

Degree: 5

\(\theta^4-x\left(70\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+3 x^{2}\left(675\theta^4+1602\theta^3+1933\theta^2+1130\theta+258\right)-2^{2} 3^{3} x^{3}\left(271\theta^4+888\theta^3+1259\theta^2+831\theta+207\right)+2^{2} 3^{5} x^{4}\left(212\theta^4+808\theta^3+1189\theta^2+773\theta+186\right)-2^{4} 3^{7} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 492, 3510, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -7/8, -12, -131/4, 90, ... ; Common denominator:...

Discriminant

\(-(16z-1)(432z^2-36z+1)(-1+9z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\)\(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.102" from ...

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115

New Number: 5.103 |  AESZ: 354  |  Superseeker: 25 17175  |  Hash: 0d4263e8c85dceb5c51f8614f7c1bc79  

Degree: 5

\(\theta^4-5 x\left(170\theta^4+160\theta^3+125\theta^2+45\theta+6\right)+3 5^{3} x^{2}\left(725\theta^4+1220\theta^3+1105\theta^2+460\theta+68\right)-3^{2} 5^{5} x^{3}\left(1421\theta^4+3186\theta^3+3053\theta^2+1272\theta+188\right)+2^{2} 3^{3} 5^{7} x^{4}(3\theta+1)(3\theta+2)(34\theta^2+61\theta+36)-2^{2} 3^{4} 5^{9} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 3150, 462000, 78828750, ...
--> OEIS
Normalized instanton numbers (n0=1): 25, 2175/4, 17175, 351250, 23000351/5, ... ; Common denominator:...

Discriminant

\(-(2278125z^3-84375z^2+550z-1)(-1+150z)^2\)

Local exponents

\(0\) ≈\(0.003863-0.000232I\) ≈\(0.003863+0.000232I\)\(\frac{ 1}{ 150}\) ≈\(0.029311\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.103" from ...

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116

New Number: 5.104 |  AESZ: 357  |  Superseeker: 7/13 21/13  |  Hash: afee0651c9b3b8e98079f5c2d5bfa8a5  

Degree: 5

\(13^{2} \theta^4-13 x\left(441\theta^4+690\theta^3+631\theta^2+286\theta+52\right)+2^{4} x^{2}\left(5121\theta^4+15576\theta^3+21215\theta^2+13702\theta+3445\right)-2^{10} x^{3}\left(640\theta^4+2847\theta^3+5078\theta^2+4056\theta+1196\right)+2^{14} x^{4}\left(125\theta^4+562\theta^3+905\theta^2+624\theta+157\right)-2^{21} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 20, 112, 916, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/13, -10/13, 21/13, 296/13, 608/13, ... ; Common denominator:...

Discriminant

\(-(16z-1)(128z^2-13z+1)(-13+32z)^2\)

Local exponents

\(0\)\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 1}{ 16}\)\(\frac{ 13}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 358/5.105

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117

New Number: 5.105 |  AESZ: 358  |  Superseeker: -336 -4761360  |  Hash: f026b6514e3be9b730646bc9410b1049  

Degree: 5

\(\theta^4-2^{4} x\left(125\theta^4-62\theta^3-31\theta^2+1\right)+2^{11} x^{2}\left(640\theta^4-287\theta^3+377\theta^2+119\theta+11\right)-2^{16} x^{3}\left(5121\theta^4+4908\theta^3+5213\theta^2+2484\theta+503\right)+2^{23} 13 x^{4}\left(441\theta^4+1074\theta^3+1207\theta^2+670\theta+148\right)-2^{34} 13^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, -880, -180992, -12537584, ...
--> OEIS
Normalized instanton numbers (n0=1): -336, -30306, -4761360, -962369202, -225176272240, ... ; Common denominator:...

Discriminant

\(-(128z-1)(32768z^2-208z+1)(-1+832z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 832}\)\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 357/5.04

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118

New Number: 5.106 |  AESZ: 360  |  Superseeker: 3169/17 16293835/17  |  Hash: 502b9ea354d34405e6925ab32d7f1cd2  

Degree: 5

\(17^{2} \theta^4+17 x\left(10622\theta^4-19904\theta^3-13913\theta^2-3961\theta-510\right)+3^{2} x^{2}\left(1596891\theta^4-10821444\theta^3+10580847\theta^2+6358884\theta+1355036\right)-3^{5} x^{3}\left(5472387\theta^4-81131922\theta^3-52565469\theta^2-9898488\theta+1434596\right)+2^{2} 3^{8} 127 x^{4}\left(318018\theta^4+157911\theta^3-445563\theta^2-476706\theta-130792\right)-2^{2} 3^{12} 5 127^{2} x^{5}(5\theta+3)(5\theta+4)(5\theta+6)(5\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 414, -73680, -4205250, ...
--> OEIS
Normalized instanton numbers (n0=1): 3169/17, -723497/68, 16293835/17, -1870341966/17, 251152956621/17, ... ; Common denominator:...

Discriminant

\(-(2278125z^3-33831z^2+182z-1)(17+6858z)^2\)

Local exponents

\(-\frac{ 17}{ 6858}\)\(0\) ≈\(0.001817-0.005986I\) ≈\(0.001817+0.005986I\) ≈\(0.011217\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 5}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 4}{ 5}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 6}{ 5}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 7}{ 5}\)

Note:

This is operator "5.106" from ...

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119

New Number: 5.107 |  AESZ: 364  |  Superseeker: 11/5 71/5  |  Hash: c5b4bc60bc9d39ea420bd49fad182557  

Degree: 5

\(5^{2} \theta^4-5 x\left(553\theta^4+722\theta^3+611\theta^2+250\theta+40\right)+2^{6} x^{2}\left(1914\theta^4+4722\theta^3+5519\theta^2+3010\theta+610\right)-2^{12} x^{3}\left(685\theta^4+2400\theta^3+3466\theta^2+2220\theta+500\right)+2^{19} x^{4}(2\theta+1)(30\theta^3+105\theta^2+122\theta+46)-2^{25} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 8, 120, 2240, 50680, ...
--> OEIS
Normalized instanton numbers (n0=1): 11/5, -8/5, 71/5, 738, 26841/5, ... ; Common denominator:...

Discriminant

\(-(32768z^3-2560z^2+85z-1)(-5+64z)^2\)

Local exponents

\(0\) ≈\(0.023029\) ≈\(0.027548-0.023797I\) ≈\(0.027548+0.023797I\)\(\frac{ 5}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.107" from ...

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120

New Number: 5.108 |  AESZ: 365  |  Superseeker: 4 1268  |  Hash: f84624e83cd4eb2cc90693bd5627efcf  

Degree: 5

\(\theta^4-2^{2} x\left(99\theta^4+78\theta^3+65\theta^2+26\theta+4\right)+2^{6} x^{2}\left(938\theta^4+1382\theta^3+1269\theta^2+554\theta+92\right)-2^{10} x^{3}\left(4171\theta^4+8736\theta^3+8690\theta^2+3948\theta+680\right)+2^{15} 5 x^{4}(2\theta+1)(418\theta^3+951\theta^2+846\theta+260)-2^{19} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 16, 720, 44800, 3245200, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 107/2, 1268, 89439/4, 396908, ... ; Common denominator:...

Discriminant

\(-(108z-1)(2048z^2-128z+1)(-1+80z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 2}\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 80}\)\(\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.108" from ...

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