Summary

You searched for: Spectrum0=0,-1/2,1,3/2

Your search produced 57 matches
 1-30  31-57 

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1

New Number: 2.39 |  AESZ: ~80,~81  |  Superseeker: -2450 -623291900  |  Hash: a4500006693bca99ed7ce6d889944382  

Degree: 2

\(\theta^4-2 5 x\left(2500\theta^4+5000\theta^3+5875\theta^2+3375\theta+738\right)+2^{2} 5^{6} x^{2}(5\theta+4)(5\theta+6)(10\theta+9)(10\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 7380, 71382150, 753157832000, 8295076883047500, ...
--> OEIS
Normalized instanton numbers (n0=1): -2450, -1825075/2, -623291900, -559511912750, -584671005670010, ... ; Common denominator:...

Discriminant

\((12500z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 12500}\)\(\infty\)
\(0\)\(0\)\(\frac{ 4}{ 5}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 9}{ 10}\)
\(0\)\(1\)\(\frac{ 11}{ 10}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 6}{ 5}\)

Note:

Operator equivalent to $\hat{1}$ of AESZ

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2

New Number: 2.40 |  AESZ:  |  Superseeker: -791200 -4288711075194400  |  Hash: 43d26d7aa358d5634e12c133ddc42a01  

Degree: 2

\(\theta^4-2^{4} 5 x\left(80000\theta^4+160000\theta^3+186000\theta^2+106000\theta+22811\right)+2^{16} 5^{6} x^{2}(10\theta+7)(10\theta+9)(10\theta+11)(10\theta+13)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1824880, 4485741488400, 12079072308276832000, 33999719248816985649610000, ...
--> OEIS
Normalized instanton numbers (n0=1): -791200, -41486886600, -4288711075194400, -585926703697412494000, -93381074165698184340671200, ... ; Common denominator:...

Discriminant

\((3200000z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 3200000}\)\(\infty\)
\(0\)\(0\)\(\frac{ 7}{ 10}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 9}{ 10}\)
\(0\)\(1\)\(\frac{ 11}{ 10}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 13}{ 10}\)

Note:

Operator equivalent to $\hat{2}$ of AESZ.

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3

New Number: 2.41 |  AESZ:  |  Superseeker: -522 -9879192  |  Hash: 73d9f98b2c49f1c35df531f020cf1721  

Degree: 2

\(\theta^4-2 3^{2} x\left(324\theta^4+648\theta^3+765\theta^2+441\theta+97\right)+2^{2} 3^{10} x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1746, 3951990, 9740271348, 25043989159350, ...
--> OEIS
Normalized instanton numbers (n0=1): -522, -105291/2, -9879192, -2420127936, -689420749716, ... ; Common denominator:...

Discriminant

\((2916z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 2916}\)\(\infty\)
\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 7}{ 6}\)

Note:

Operator equivalent to $\hat{4}$

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4

New Number: 2.42 |  AESZ: ~98  |  Superseeker: -288 -2339616  |  Hash: acfee9d4b5fefd1a945cfa6b1bc61373  

Degree: 2

\(\theta^4-2^{2} 3 x\left(288\theta^4+576\theta^3+682\theta^2+394\theta+87\right)+2^{4} 3^{2} x^{2}(12\theta+11)^2(12\theta+13)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1044, 1403100, 2051002800, 3126485684700, ...
--> OEIS
Normalized instanton numbers (n0=1): -288, -19260, -2339616, -369882612, -67925445408, ... ; Common denominator:...

Discriminant

\((1728z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(\frac{ 11}{ 12}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 12}\)
\(0\)\(1\)\(\frac{ 13}{ 12}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 13}{ 12}\)

Note:

Operator equivalent to $\hat{5}$

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5

New Number: 2.43 |  AESZ: ~77, ~78,~97  |  Superseeker: -736 -26911072  |  Hash: 3d2cd06eccf32145816b35cb63878900  

Degree: 2

\(\theta^4-2^{4} x\left(512\theta^4+1024\theta^3+1208\theta^2+696\theta+153\right)+2^{12} x^{2}(8\theta+7)^2(8\theta+9)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2448, 7779600, 26927622400, 97242114301200, ...
--> OEIS
Normalized instanton numbers (n0=1): -736, -104512, -26911072, -9061573696, -3547993303456, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(\frac{ 7}{ 8}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 8}\)
\(0\)\(1\)\(\frac{ 9}{ 8}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 9}{ 8}\)

Note:

Operator equivalent to $\hat{6}$

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6

New Number: 2.44 |  AESZ:  |  Superseeker: -57760 -3869123234080  |  Hash: db68f352287fb91ca91e65eb38318ac4  

Degree: 2

\(\theta^4-2^{4} x\left(32768\theta^4+65536\theta^3+76544\theta^2+43776\theta+9495\right)+2^{26} x^{2}(4\theta+3)(4\theta+5)(8\theta+7)(8\theta+9)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 151920, 30692221200, 6779721385465600, 1564471951791288368400, ...
--> OEIS
Normalized instanton numbers (n0=1): -57760, -354010600, -3869123234080, -56296618019665040, -953499788550226132960, ... ; Common denominator:...

Discriminant

\((262144z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 262144}\)\(\infty\)
\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 8}\)
\(0\)\(1\)\(\frac{ 9}{ 8}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{7}$

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7

New Number: 2.45 |  AESZ: ~82  |  Superseeker: -10080 -24400330080  |  Hash: 11afa89027677e0616228cad62a9f990  

Degree: 2

\(\theta^4-2^{2} 3^{2} x\left(2592\theta^4+5184\theta^3+6066\theta^2+3474\theta+755\right)+2^{4} 3^{10} x^{2}(4\theta+3)(4\theta+5)(12\theta+11)(12\theta+13)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 27180, 978471900, 38487760088400, 1581137831289447900, ...
--> OEIS
Normalized instanton numbers (n0=1): -10080, -11338740, -24400330080, -69157402598340, -228492096441648480, ... ; Common denominator:...

Discriminant

\((46656z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 46656}\)\(\infty\)
\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 12}\)
\(0\)\(1\)\(\frac{ 13}{ 12}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{8}$

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8

New Number: 2.46 |  AESZ:  |  Superseeker: -2710944 -302270555492914464  |  Hash: a06fc8c91c1e4c766fdb1e79370bef7a  

Degree: 2

\(\theta^4-2^{4} 3^{2} x\left(165888\theta^4+331776\theta^3+386496\theta^2+220608\theta+47711\right)+2^{22} 3^{10} x^{2}(4\theta+3)(4\theta+5)(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6870384, 63135105483024, 634962415293388429056, 6673257595142837863377354000, ...
--> OEIS
Normalized instanton numbers (n0=1): -2710944, -717640301160, -302270555492914464, -171507700573958028578832, -113303073680022744870130144224, ... ; Common denominator:...

Discriminant

\((11943936z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 11943936}\)\(\infty\)
\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{9}$

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9

New Number: 2.47 |  AESZ:  |  Superseeker: -3488 -1142687008  |  Hash: 413005461e43cfa75125577c2d4c2fde  

Degree: 2

\(\theta^4-2^{4} x\left(2048\theta^4+4096\theta^3+4800\theta^2+2752\theta+599\right)+2^{24} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9584, 121274640, 1675847866112, 24182028281658640, ...
--> OEIS
Normalized instanton numbers (n0=1): -3488, -1406056, -1142687008, -1211614451216, -1500013956719584, ... ; Common denominator:...

Discriminant

\((16384z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 16384}\)\(\infty\)
\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{10}$

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10

New Number: 2.48 |  AESZ: ~94  |  Superseeker: -1344 -109320512  |  Hash: 892e497a83d12667b7f189a3d743fb7c  

Degree: 2

\(\theta^4-2^{2} 3 x\left(1152\theta^4+2304\theta^3+2710\theta^2+1558\theta+341\right)+2^{4} 3^{2} x^{2}(24\theta+19)(24\theta+23)(24\theta+25)(24\theta+29)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4092, 21900060, 127808119824, 778493560064220, ...
--> OEIS
Normalized instanton numbers (n0=1): -1344, -278040, -109320512, -56290146024, -33748229589312, ... ; Common denominator:...

Discriminant

\((6912z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 6912}\)\(\infty\)
\(0\)\(0\)\(\frac{ 19}{ 24}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 23}{ 24}\)
\(0\)\(1\)\(\frac{ 25}{ 24}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 29}{ 24}\)

Note:

Operator equivalent to $\hat{11}$

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11

New Number: 2.49 |  AESZ:  |  Superseeker: -26400 -230398034080  |  Hash: ffdc338b55d1f4e1f989f4359b06df6c  

Degree: 2

\(\theta^4-2^{4} 3 x\left(4608\theta^4+9216\theta^3+10744\theta^2+6136\theta+1325\right)+2^{12} 3^{2} x^{2}(24\theta+17)(24\theta+23)(24\theta+25)(24\theta+31)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 63600, 5412963600, 504140776339200, 49063316029156400400, ...
--> OEIS
Normalized instanton numbers (n0=1): -26400, -52511160, -230398034080, -1287524740195200, -8504689433002312800, ... ; Common denominator:...

Discriminant

\((110592z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 110592}\)\(\infty\)
\(0\)\(0\)\(\frac{ 17}{ 24}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 23}{ 24}\)
\(0\)\(1\)\(\frac{ 25}{ 24}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 31}{ 24}\)

Note:

Operator equivalent to $\hat{12}$

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12

New Number: 2.50 |  AESZ:  |  Superseeker: -201888 -40177844666400  |  Hash: 5309f0b5a4362f22faafad07a0eb1bb8  

Degree: 2

\(\theta^4-2^{4} 3^{2} x\left(10368\theta^4+20736\theta^3+24048\theta^2+13680\theta+2927\right)+2^{20} 3^{10} x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 421488, 241251334416, 151434902650832640, 99396938275247309913360, ...
--> OEIS
Normalized instanton numbers (n0=1): -201888, -1567499400, -40177844666400, -988883543512335600, -35724019937142805037280, ... ; Common denominator:...

Discriminant

\((746496z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 746496}\)\(\infty\)
\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 4}{ 3}\)

Note:

Operator equivalent to $\hat{13}$ of AESZ

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13

New Number: 2.51 |  AESZ: ~88,~89  |  Superseeker: -5472 -6444589536  |  Hash: 02d09c6c320ab036e45834cf0d3951e7  

Degree: 2

\(\theta^4-2^{4} 3 x\left(1152\theta^4+2304\theta^3+2704\theta^2+1552\theta+339\right)+2^{16} 3^{2} x^{2}(6\theta+5)^2(6\theta+7)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16272, 347859216, 8115450239232, 197661638029770000, ...
--> OEIS
Normalized instanton numbers (n0=1): -5472, -4476528, -6444589536, -12228845295024, -27012506850929952, ... ; Common denominator:...

Discriminant

\((27648z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 27648}\)\(\infty\)
\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 7}{ 6}\)

Note:

Operator equivalent to $\widehat{14}$
B-Incarnations:
Double octics: D.O.267, D.O.275

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14

New Number: 3.26 |  AESZ: 407  |  Superseeker: 2 440  |  Hash: c46d32ba4b3738ba34fe1e6c16e6f242  

Degree: 3

\(\theta^4+2 x\left(132\theta^4+264\theta^3+293\theta^2+161\theta+35\right)+2^{2} 5^{2} x^{2}(\theta+1)^2(228\theta^2+456\theta+335)+2^{6} 5^{4} x^{3}(\theta+1)(\theta+2)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -70, 5650, -484900, 43071250, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -44, 440, -4844, 46268, ... ; Common denominator:...

Discriminant

\((64z+1)(1+100z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 100}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(1\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 5}{ 4}\)
\(1\)\(1\)\(0\)\(\frac{ 7}{ 4}\)
\(2\)\(\frac{ 3}{ 2}\)\(0\)\(2\)

Note:

This is operator "3.26" from ...

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15

New Number: 3.30 |  AESZ: 422  |  Superseeker: 124 2152276/9  |  Hash: b37ac82ae57415849cb59beac4cd6adf  

Degree: 3

\(\theta^4+2^{2} x\left(380\theta^4+760\theta^3+907\theta^2+527\theta+117\right)+2^{4} 3 x^{2}(8\theta+7)(8\theta+9)(184\theta^2+368\theta+183)-2^{8} 3^{2} x^{3}(8\theta+7)(8\theta+9)(8\theta+15)(8\theta+17)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -468, 280260, -182276400, 123566444100, ...
--> OEIS
Normalized instanton numbers (n0=1): 124, -3752, 2152276/9, -18042588, 1647569184, ... ; Common denominator:...

Discriminant

\(-(16z-1)(1+768z)^2\)

Local exponents

\(-\frac{ 1}{ 768}\)\(0\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 7}{ 8}\)
\(-\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 9}{ 8}\)
\(1\)\(0\)\(1\)\(\frac{ 15}{ 8}\)
\(\frac{ 3}{ 2}\)\(0\)\(2\)\(\frac{ 17}{ 8}\)

Note:

This is operator "3.30" from ...

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16

New Number: 3.32 |  AESZ:  |  Superseeker: 128 382592  |  Hash: 9b39b616939718654c472dbfb37cdd4e  

Degree: 3

\(\theta^4-2^{4} x(6\theta^2+6\theta-1)(2\theta+1)^2-2^{10} x^{2}(60\theta^2+120\theta+97)(\theta+1)^2-2^{21} x^{3}(\theta+1)^2(\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -16, 4624, 678656, 238896400, ...
--> OEIS
Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...

Discriminant

\(-(512z-1)(1+64z)^2\)

Local exponents

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

Note:

Operator equivalent to AESZ 220
B-Incarnation:
Double octic:D.O.244

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17

New Number: 3.33 |  AESZ:  |  Superseeker: 4 1580/9  |  Hash: da01a7b2dfcebe6e332be6c29ed2a8e5  

Degree: 3

\(\theta^4+2^{2} x\left(36\theta^4+72\theta^3+85\theta^2+49\theta+11\right)+2^{4} x^{2}(8\theta^2+16\theta+11)(48\theta^2+96\theta+49)+2^{8} x^{3}(4\theta+7)^2(4\theta+5)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -44, 2244, -122576, 6952516, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, -25, 1580/9, -1580, 17120, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 5}{ 4}\)
\(1\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 5}{ 4}\)
\(1\)\(1\)\(0\)\(\frac{ 7}{ 4}\)
\(2\)\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 7}{ 4}\)

Note:

Operator equivalent to AESZ 353

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18

New Number: 4.10 |  AESZ:  |  Superseeker: -84 -148820  |  Hash: fc2837f1001e57a5cc53749a08d4f2bf  

Degree: 4

\(\theta^4-2 3 x\left(216\theta^4+432\theta^3+516\theta^2+300\theta+67\right)+2^{2} 3^{2} x^{2}\left(12312\theta^4+49248\theta^3+76374\theta^2+54252\theta+15017\right)-2^{6} 3^{10} x^{3}(\theta^2+3\theta+3)(2\theta+3)^2+2^{4} 3^{10} x^{4}(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 402, 197010, 104962956, 58311249066, ...
--> OEIS
Normalized instanton numbers (n0=1): -84, -5271/2, -148820, -41373213/4, -836813460, ... ; Common denominator:...

Discriminant

\((1-648z+11664z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 2}\)\(\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 170=$d \ast h \tilde B \ast \epsilon$

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19

New Number: 4.11 |  AESZ:  |  Superseeker: -63 -96866  |  Hash: 39ed55f37672c58e7ce182c4c33d4a66  

Degree: 4

\(\theta^4-x\left(972\theta^4+1944\theta^3+2322\theta^2+1350\theta+603/2\right)+x^{2}\left(196830\theta^4+787320\theta^3+2110455/2\theta^2+535815\theta+237897/4\right)+3^{14} x^{3}(\theta^2+3\theta+3)(2\theta+3)^2+x^{4}43046721/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 603/2, 1008855/8, 898513875/16, 3331190162475/128, ...
--> OEIS
Normalized instanton numbers (n0=1): -63, -8757/4, -96866, -6253821, -446217723, ... ; Common denominator:...

Discriminant

\((-1+486z+19683z^2)^2\)

Local exponents

\(-\frac{ 1}{ 81}-\frac{ 2}{ 243}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 1}{ 81}+\frac{ 2}{ 243}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

This is operator "4.11" from ...

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20

New Number: 4.12 |  AESZ:  |  Superseeker: -45 7080  |  Hash: 6c95cb50a57e8a1c96a5a4e3e353cb85  

Degree: 4

\(\theta^4-x\left(1188\theta^4+2376\theta^3+2874\theta^2+1686\theta+765/2\right)+x^{2}\left(535086\theta^4+2140344\theta^3+7708527/2\theta^2+3427839\theta+4938345/4\right)-3^{8} 5^{3} x^{3}(33\theta^2+99\theta+100)(2\theta+3)^2+x^{4}922640625/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 765/2, 1009575/8, 627988725/16, 1505754528075/128, ...
--> OEIS
Normalized instanton numbers (n0=1): -45, -135, 7080, 406035, 17168436, ... ; Common denominator:...

Discriminant

\((1-594z+91125z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 3375}-\frac{ 2}{ 3375}I\)\(\frac{ 11}{ 3375}+\frac{ 2}{ 3375}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-operator equivalent to AESZ $=b \ast h ~B \ast \eta$

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21

New Number: 4.13 |  AESZ: ~37  |  Superseeker: -128 -1546624/3  |  Hash: c03e4e4ca58f9f1f76c98c8616bc2cbd  

Degree: 4

\(\theta^4-2^{2} x\left(640\theta^4+1280\theta^3+1534\theta^2+894\theta+201\right)+2^{4} 3 x^{2}\left(45056\theta^4+180224\theta^3+308352\theta^2+256256\theta+86363\right)-2^{19} x^{3}(320\theta^2+960\theta+957)(2\theta+3)^2+2^{30} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

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Coefficients of the holomorphic solution: 1, 804, 655260, 563879792, 505573095132, ...
--> OEIS
Normalized instanton numbers (n0=1): -128, -5232, -1546624/3, -64705008, -7960717440, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 1024}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 37$=C \ast \alpha ~tilde c \ast i$

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22

New Number: 4.14 |  AESZ:  |  Superseeker: -340 -15174100/3  |  Hash: a961869d91c2f73091913e8f8c4b5fa0  

Degree: 4

\(\theta^4-2^{2} x\left(1088\theta^4+2176\theta^3+2579\theta^2+1491\theta+330\right)+2^{7} 3 x^{2}\left(12352\theta^4+49408\theta^3+74070\theta^2+49324\theta+12325\right)-2^{12} x^{3}(1088\theta^2+3264\theta+3225)(2\theta+3)^2+2^{18} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1320, 2233320, 4108451200, 7880762169000, ...
--> OEIS
Normalized instanton numbers (n0=1): -340, -31985, -15174100/3, -1036481610, -246612212640, ... ; Common denominator:...

Discriminant

\((1-2176z+4096z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 17}{ 64}-\frac{ 3}{ 16}\sqrt{ 2}\)\(\frac{ 17}{ 64}+\frac{ 3}{ 16}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 52 $=C \ast \gamma \tilde g \ast i$

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23

New Number: 4.15 |  AESZ:  |  Superseeker: -76 415420  |  Hash: d8c866a60b2b4edb0c88e03315fa2a7b  

Degree: 4

\(\theta^4-2^{2} x\left(448\theta^4+896\theta^3+1077\theta^2+629\theta+142\right)+2^{7} x^{2}\left(11456\theta^4+45824\theta^3+86434\theta^2+81220\theta+30693\right)-2^{12} 3^{4} x^{3}(448\theta^2+1344\theta+1343)(2\theta+3)^2+2^{18} 3^{8} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

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Coefficients of the holomorphic solution: 1, 568, 207720, 25669504, -32774007128, ...
--> OEIS
Normalized instanton numbers (n0=1): -76, 2958, 415420, 17891650, -1211214176, ... ; Common denominator:...

Discriminant

\((331776z^2-896z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 7}{ 5184}-\frac{ 1}{ 1296}\sqrt{ 2}I\)\(\frac{ 7}{ 5184}+\frac{ 1}{ 1296}\sqrt{ 2}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 152 $=C \ast \delta ~tilde \alpha \ast i$

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24

New Number: 4.16 |  AESZ:  |  Superseeker: -208 -1863312  |  Hash: ff22b96c1af3d06292a97d4dee085628  

Degree: 4

\(\theta^4-2^{4} x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{9} x^{2}\left(4864\theta^4+19456\theta^3+30088\theta^2+21264\theta+5849\right)-2^{18} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{26} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 944, 1093840, 1379945728, 1816122981136, ...
--> OEIS
Normalized instanton numbers (n0=1): -208, -15098, -1863312, -284211001, -50414626800, ... ; Common denominator:...

Discriminant

\((1-1536z+65536z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 3}{ 256}-\frac{ 1}{ 128}\sqrt{ 2}\)\(\frac{ 3}{ 256}+\frac{ 1}{ 128}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \epsilon ~d \ast i$

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25

New Number: 4.17 |  AESZ:  |  Superseeker: -156 -1229332  |  Hash: 245e2566c8da93abbfc4296923ccba12  

Degree: 4

\(\theta^4-2^{2} 3 x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{4} 3^{2} x^{2}\left(7680\theta^4+30720\theta^3+41040\theta^2+20640\theta+2203\right)+2^{12} 3^{4} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{18} 3^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 708, 700740, 738956400, 811309522500, ...
--> OEIS
Normalized instanton numbers (n0=1): -156, -12549, -1229332, -175559052, -27542017056, ... ; Common denominator:...

Discriminant

\((-1+1152z+110592z^2)^2\)

Local exponents

\(-\frac{ 1}{ 192}-\frac{ 1}{ 288}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 1}{ 192}+\frac{ 1}{ 288}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \zeta ~tilde f \ast i$

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26

New Number: 4.18 |  AESZ:  |  Superseeker: -100 126580  |  Hash: 3ab4956c5da76dad5e104e338e7c0128  

Degree: 4

\(\theta^4-2^{2} x\left(704\theta^4+1408\theta^3+1697\theta^2+993\theta+225\right)+2^{4} x^{2}\left(187904\theta^4+751616\theta^3+1350224\theta^2+1197216\theta+429975\right)-2^{12} 5^{3} x^{3}(704\theta^2+2112\theta+2115)(2\theta+3)^2+2^{18} 5^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 900, 701100, 515510800, 365497137900, ...
--> OEIS
Normalized instanton numbers (n0=1): -100, -1260, 126580, 12033300, 1211646512, ... ; Common denominator:...

Discriminant

\((512000z^2-1408z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 8000}-\frac{ 1}{ 4000}I\)\(\frac{ 11}{ 8000}+\frac{ 1}{ 4000}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \eta ~b \ast i$

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27

New Number: 4.19 |  AESZ: ~66  |  Superseeker: -864 -147560800  |  Hash: b9b85f803521c6af3b5f7572d309f89a  

Degree: 4

\(\theta^4-2^{2} 3 x\left(1440\theta^4+2880\theta^3+3434\theta^2+1994\theta+447\right)+2^{4} 3^{4} x^{2}\left(76032\theta^4+304128\theta^3+518496\theta^2+428736\theta+143785\right)-2^{15} 3^{8} x^{3}(240\theta^2+720\theta+709)(2\theta+3)^2+2^{26} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5364, 29367900, 170217457200, 1029027458497500, ...
--> OEIS
Normalized instanton numbers (n0=1): -864, -261684, -147560800, -120568926924, -88009904955744, ... ; Common denominator:...

Discriminant

\((6912z-1)^2(1728z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 6912}\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $AESZ 66 =$D \ast \alpha \tilde c \ast j$

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28

New Number: 4.1 |  AESZ: ~39  |  Superseeker: -32 -8736  |  Hash: 462066f711fc3742db1ea9befa2fe01b  

Degree: 4

\(\theta^4-2^{2} x\left(160\theta^4+320\theta^3+386\theta^2+226\theta+51\right)+2^{4} 3 x^{2}\left(2816\theta^4+11264\theta^3+19360\theta^2+16192\theta+5491\right)-2^{15} x^{3}(80\theta^2+240\theta+243)(2\theta+3)^2+2^{26} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 204, 41820, 9022160, 2025179100, ...
--> OEIS
Normalized instanton numbers (n0=1): -32, -284, -8736, -283900, -10041888, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 39=$A \ast \alpha$.

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29

New Number: 4.20 |  AESZ:  |  Superseeker: -2484 -1327731388  |  Hash: 80035e90a6f24cd6da3d4c5adc98379f  

Degree: 4

\(\theta^4-2^{2} 3 x\left(2448\theta^4+4896\theta^3+5773\theta^2+3325\theta+732\right)+2^{6} 3^{4} x^{2}\left(41688\theta^4+166752\theta^3+248973\theta^2+164442\theta+40616\right)-2^{8} 3^{8} x^{3}(816\theta^2+2448\theta+2389)(2\theta+3)^2+2^{14} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8784, 99982728, 1239742123200, 16039070549564328, ...
--> OEIS
Normalized instanton numbers (n0=1): -2484, -1446309, -1327731388, -1580284433106, -2187358898922144, ... ; Common denominator:...

Discriminant

\((1-14688z+186624z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 17}{ 432}-\frac{ 1}{ 36}\sqrt{ 2}\)\(\frac{ 17}{ 432}+\frac{ 1}{ 36}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 149=$D \ast \gamma ~tilde g \ast j$

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30

New Number: 4.21 |  AESZ:  |  Superseeker: -492 136094428  |  Hash: 595707be6cb20abc1dfeecf72492ae5f  

Degree: 4

\(\theta^4-2^{2} 3 x\left(1008\theta^4+2016\theta^3+2411\theta^2+1403\theta+316\right)+2^{6} 3^{2} x^{2}\left(115992\theta^4+463968\theta^3+872325\theta^2+816714\theta+307516\right)-2^{8} 3^{12} x^{3}(336\theta^2+1008\theta+995)(2\theta+3)^2+2^{14} 3^{18} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 3792, 9275400, 7430606400, -68166524583000, ...
--> OEIS
Normalized instanton numbers (n0=1): -492, 128514, 136094428, 32416215738, -16919954920032, ... ; Common denominator:...

Discriminant

\((15116544z^2-6048z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 7}{ 34992}-\frac{ 1}{ 8748}\sqrt{ 2}I\)\(\frac{ 7}{ 34992}+\frac{ 1}{ 8748}\sqrt{ 2}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

This is operator "4.21" from ...

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