Summary

You searched for: sol=720

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1

New Number: 2.13 |  AESZ: 36  |  Superseeker: 16 1232  |  Hash: dea6fdf568a5907a24ba30fef2caf124  

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 16, 720, 44800, 3312400, ...
--> OEIS
Normalized instanton numbers (n0=1): 16, 42, 1232, 32159, 990128, ... ; Common denominator:...

Discriminant

\((128z-1)(64z-1)\)

Local exponents

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

Note:

A*d

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2

New Number: 2.19 |  AESZ: 112  |  Superseeker: -288 -96055968  |  Hash: 9a988f0cb0ca922885043cdadf98dd79  

Degree: 2

\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(8\theta^2+8\theta+3)+2^{12} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

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Coefficients of the holomorphic solution: 1, 720, 2273040, 9605756160, 46308725583120, ...
--> OEIS
Normalized instanton numbers (n0=1): -288, 162504, -96055968, 106571782296, -135291308081760, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 6912}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 6}\)
\(0\)\(\frac{ 1}{ 2}\)\(\frac{ 7}{ 6}\)
\(0\)\(1\)\(\frac{ 11}{ 6}\)

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3

New Number: 3.15 |  AESZ:  |  Superseeker: -32 -16288  |  Hash: e21c92d8f9a2222be40fdc71ea51ee35  

Degree: 3

\(\theta^4+2^{3} x\left(21\theta^4+42\theta^3+30\theta^2+9\theta+1\right)-2^{6} x^{2}(\theta+1)^2(96\theta^2+192\theta+77)+2^{9} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, -8, 720, -68480, 8123920, ...
--> OEIS
Normalized instanton numbers (n0=1): -32, 468, -16288, 1681645/2, -53608288, ... ; Common denominator:...

Discriminant

\((200z+1)(-1+16z)^2\)

Local exponents

\(-\frac{ 1}{ 200}\)\(0\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 6}\)\(1\)
\(1\)\(0\)\(\frac{ 5}{ 6}\)\(2\)
\(2\)\(0\)\(1\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 328

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4

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

Degree: 5

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

Maple   LaTex

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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5

New Number: 5.34 |  AESZ: 217  |  Superseeker: 17/7 5095/21  |  Hash: e8743aeac19deca699ff90aaef6b8ea7  

Degree: 5

\(7^{2} \theta^4+7 x\theta(-14-73\theta-118\theta^2+13\theta^3)-2^{3} 3 x^{2}\left(3378\theta^4+13446\theta^3+18869\theta^2+11158\theta+2352\right)-2^{4} 3^{3} x^{3}\left(3628\theta^4+17920\theta^3+31668\theta^2+22596\theta+5383\right)-2^{8} 3^{3} x^{4}(2\theta+1)(572\theta^3+2370\theta^2+2896\theta+1095)-2^{10} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 72, 720, 37800, ...
--> OEIS
Normalized instanton numbers (n0=1): 17/7, 254/7, 5095/21, 29600/7, 491991/7, ... ; Common denominator:...

Discriminant

\(-(16z+1)(27z+1)(48z-1)(7+24z)^2\)

Local exponents

\(-\frac{ 7}{ 24}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 48}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(3\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(4\)\(2\)\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.34" from ...

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6

New Number: 1.12 |  AESZ: 12  |  Superseeker: 7776 66942277344  |  Hash: ad7e2e881b3939396323eb746eb17a58  

Degree: 1

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 720, 5821200, 75473798400, 1205906199498000, ...
--> OEIS
Normalized instanton numbers (n0=1): 7776, 13952088, 66942277344, 475338414733416, 4184555647748620320, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

A-incarnation: X(3,4) in P^5(1,1,1,1,1,2)

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