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You searched for: degz=2

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61

New Number: 2.65 |  AESZ: 183  |  Superseeker: -4 -556/9  |  Hash: 04a3788c3f9ed53281ae824deb33d833  

Degree: 2

\(\theta^4+2^{2} x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{4} 3 x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, -12, 324, -11280, 447300, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, 8, -556/9, 624, -8928, ... ; Common denominator:...

Discriminant

\((48z+1)(64z+1)\)

Local exponents

\(-\frac{ 1}{ 48}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(0\)\(\frac{ 5}{ 4}\)
\(2\)\(2\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "2.65" from ...

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62

New Number: 2.66 |  AESZ:  |  Superseeker: -192 -229568  |  Hash: 0fb32be57a9fcd1b243f9e1341b39d45  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(2\theta^2+2\theta+1)+2^{4} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

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Coefficients of the holomorphic solution: 1, 60, 13860, 4084080, 1338557220, ...
--> OEIS
Normalized instanton numbers (n0=1): -192, 4182, -229568, 19136058, -2006581440, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(1\)\(\frac{ 11}{ 6}\)

Note:

This is operator "2.66" from ...

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63

New Number: 2.67 |  AESZ: 245  |  Superseeker: -6 -170  |  Hash: 0ef0bca0dbecbedad92696fd7c0f9e42  

Degree: 2

\(\theta^4-2 3 x\left(36\theta^4+66\theta^3+61\theta^2+28\theta+5\right)+2^{2} 3^{2} x^{2}(3\theta+2)^2(6\theta+7)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 1764, 127776, 10248750, ...
--> OEIS
Normalized instanton numbers (n0=1): -6, -33, -170, -1029, -3246, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(\frac{ 1}{ 6}\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(\frac{ 7}{ 6}\)\(\frac{ 7}{ 6}\)

Note:

This is operator "2.67" from ...

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64

New Number: 2.68 |  AESZ: 406  |  Superseeker: -12 -1668  |  Hash: d3a5c69671a7189e15cf1394437380a2  

Degree: 2

\(\theta^4-2^{2} x\left(128\theta^4+224\theta^3+197\theta^2+85\theta+14\right)+2^{7} x^{2}(2\theta+1)(4\theta+5)(8\theta+5)(8\theta+9)\)

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Coefficients of the holomorphic solution: 1, 56, 7272, 1200000, 222009000, ...
--> OEIS
Normalized instanton numbers (n0=1): -12, -186, -1668, -25974, -243552, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 5}{ 8}\)
\(0\)\(1\)\(\frac{ 9}{ 8}\)
\(0\)\(\frac{ 5}{ 4}\)\(\frac{ 5}{ 4}\)

Note:

This is operator "2.68" from ...

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65

New Number: 2.69 |  AESZ: 205  |  Superseeker: 1 5  |  Hash: 4fb2e7002e630237d0458c3985cd6a18  

Degree: 2

\(\theta^4-x\left(59\theta^4+118\theta^3+105\theta^2+46\theta+8\right)+2^{5} 3 x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...

Discriminant

\((32z-1)(27z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "2.69" from ...

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66

New Number: 2.6 |  AESZ: 24  |  Superseeker: 36 41421  |  Hash: 5e8f8f32b5e99693a2956e1240b9fdff  

Degree: 2

\(\theta^4-3 x(3\theta+1)(3\theta+2)(11\theta^2+11\theta+3)-3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1710, 246960, 43347150, ...
--> OEIS
Normalized instanton numbers (n0=1): 36, 837, 41421, 2992851, 266362506, ... ; Common denominator:...

Discriminant

\(1-297z-729z^2\)

Local exponents

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

Note:

Hadamard product B*b
Related to 7.19, 8.18
This operator corresponds to $(Grass(2,5)\vert 1,1,3)_{-150}$ from arXiv:0802.2908

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67

New Number: 2.70 |  AESZ:  |  Superseeker: 20 28820/3  |  Hash: 336ddc1188eadae2f4b4c470a17f4ec1  

Degree: 2

\(\theta^4-2^{2} x\left(128\theta^4+352\theta^3+413\theta^2+237\theta+54\right)+2^{7} x^{2}(4\theta+5)(2\theta+3)(8\theta+9)(8\theta+13)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 216, 49896, 11872896, 2872063656, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 290, 28820/3, 454190, 26517920, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(\frac{ 9}{ 8}\)
\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 5}{ 4}\)
\(0\)\(-\frac{ 3}{ 4}\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(\frac{ 13}{ 8}\)

Note:

Operator equivalent to (:aesz 255)

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68

New Number: 2.7 |  AESZ: 51  |  Superseeker: 92 585396  |  Hash: e09b9b149b6845daa8d5ef03df33f22d  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 7980, 2716560, 1127025900, ...
--> OEIS
Normalized instanton numbers (n0=1): 92, 5052, 585396, 99982012, 21054159152, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\)\(0\)\(-\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(0\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product C*b
Related to 8.139
A-Incarnation: double cover of $B_5$.

A:Incarnation: double cover of B

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69

New Number: 2.8 |  AESZ: 63  |  Superseeker: 684 195638820  |  Hash: 06c1a4c0aa33f5051126908a9898430d  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(11\theta^2+11\theta+3)-2^{4} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 180, 263340, 600359760, 1674535082220, ...
--> OEIS
Normalized instanton numbers (n0=1): 684, 253314, 195638820, 225040578570, 319342448936304, ... ; Common denominator:...

Discriminant

\(1-4752z-186624z^2\)

No data for singularities

Note:

Hadamard product D*b

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70

New Number: 2.9 |  AESZ: 58  |  Superseeker: 16 11056/3  |  Hash: 1ca6d3d1c4514db0651efce420265f5a  

Degree: 2

\(\theta^4-2^{2} x(2\theta+1)^2(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 540, 37200, 3131100, ...
--> OEIS
Normalized instanton numbers (n0=1): 16, 142, 11056/3, 121470, 4971792, ... ; Common denominator:...

Discriminant

\((144z-1)(16z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 144}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product A*c

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71

New Number: 2.71 |  AESZ:  |  Superseeker: 0 0  |  Hash: 757b011780c5986bd45a5bf434c76c28  

Degree: 2

\(\theta^4-2^{5} x(2\theta+1)^2(2\theta^2+2\theta+1)+2^{8} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 32, 2160, 181760, 17021200, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, -20, 0, -865, 0, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 3}{ 4}\)
\(0\)\(\frac{ 3}{ 4}\)\(\frac{ 5}{ 4}\)
\(0\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator is equivalent to [2.33]. Transformation:.....

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