Summary

You searched for: Spectrum0=1/4,3/4,5/4,7/4

Your search produced 8 matches

You can download all data as plain text or as JSON

1

New Number: 2.11 |  AESZ: 69  |  Superseeker: 64 246848  |  Hash: 729adc350de26d9415643078ed8d3867  

Degree: 2

\(\theta^4-2^{2} x(4\theta+1)(4\theta+3)(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 6300, 1718640, 575675100, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, 2616, 246848, 32024824, 5160268864, ... ; Common denominator:...

Discriminant

\((576z-1)(64z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 576}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast c$

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

2

New Number: 2.15 |  AESZ: 38  |  Superseeker: 48 73328  |  Hash: 9ce26bb7405c3b98d8aeae5b1102c611  

Degree: 2

\(\theta^4-2^{4} x(4\theta+1)(4\theta+3)(3\theta^2+3\theta+1)+2^{9} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 8400, 2069760, 609008400, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 998, 73328, 7388135, 857248528, ... ; Common denominator:...

Discriminant

\((512z-1)(256z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 512}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast d$

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

3

New Number: 2.22 |  AESZ: 135  |  Superseeker: 36 -206716/3  |  Hash: 85e55291bd94bb32087b43f104c60645  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 388080, 8108100, ...
--> OEIS
Normalized instanton numbers (n0=1): 36, -477, -206716/3, -4431924, -27005472, ... ; Common denominator:...

Discriminant

\(1-576z+110592z^2\)

Local exponents

\(0\)\(\frac{ 1}{ 384}-\frac{ 1}{ 1152}\sqrt{ 3}I\)\(\frac{ 1}{ 384}+\frac{ 1}{ 1152}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

4

New Number: 2.26 |  AESZ: 139  |  Superseeker: 44 22500  |  Hash: f5d9215987323abcff6ed8709927af5d  

Degree: 2

\(\theta^4-2^{2} x(4\theta+1)(4\theta+3)(17\theta^2+17\theta+6)+2^{7} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 72, 17640, 5765760, 2156754600, ...
--> OEIS
Normalized instanton numbers (n0=1): 44, 607, 22500, 1444678, 128626784, ... ; Common denominator:...

Discriminant

\((576z-1)(512z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 576}\)\(\frac{ 1}{ 512}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C \ast g$

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

5

New Number: 2.33 |  AESZ:  |  Superseeker: -160 -539680  |  Hash: 83a66e92381baa083f87a13e02375bc9  

Degree: 2

\(\theta^4-2^{4} x(4\theta+1)(4\theta+3)(32\theta^2+32\theta+13)+2^{16} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 624, 1251600, 3268151040, 9627237219600, ...
--> OEIS
Normalized instanton numbers (n0=1): -160, -6920, -539680, -54568560, -6402958560, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 3}{ 4}\)
\(0\)\(\frac{ 3}{ 4}\)\(\frac{ 5}{ 4}\)
\(0\)\(1\)\(\frac{ 7}{ 4}\)

Note:

This is operator "2.33" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

6

New Number: 2.37 |  AESZ:  |  Superseeker: -2592 81451104  |  Hash: fb56d2f39692cfb98f66d467355b3c99  

Degree: 2

\(\theta^4-2^{4} 3 x(4\theta+1)(4\theta+3)(72\theta^2+72\theta+31)+2^{12} 3^{6} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4464, 62430480, 1125574813440, 22774986122288400, ...
--> OEIS
Normalized instanton numbers (n0=1): -2592, -307800, 81451104, 144135316512, 98667659422368, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 27648}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(\frac{ 1}{ 6}\)\(\frac{ 3}{ 4}\)
\(0\)\(\frac{ 5}{ 6}\)\(\frac{ 5}{ 4}\)
\(0\)\(1\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product $B\ast c$.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

7

New Number: 2.3 |  AESZ: 68  |  Superseeker: 52 220220  |  Hash: 13a48045ff0a42a9fcfbdb710baf1997  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 4200, 1034880, 311711400, ...
--> OEIS
Normalized instanton numbers (n0=1): 52, 2814, 220220, 29135058, 4512922272, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 512}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(0\)\(2\)\(\frac{ 7}{ 4}\)

Note:

C*a

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

8

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

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex