Summary

You searched for: c2h=40

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1

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

Degree: 5

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

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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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2

New Number: 5.14 |  AESZ: 116  |  Superseeker: 64 23360  |  Hash: 0b366ad8c78b6697205c5a7fff270f5b  

Degree: 5

\(\theta^4-2^{5} x\left(10\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(52\theta^4+472\theta^3+832\theta^2+492\theta+103\right)+2^{16} x^{3}\left(14\theta^4+12\theta^3-96\theta^2-105\theta-29\right)-2^{18} x^{4}(2\theta+1)(56\theta^3+468\theta^2+646\theta+249)-2^{24} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 32, 2448, 273920, 38525200, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, 12, 23360, 654490, 53956288, ... ; Common denominator:...

Discriminant

\(-(-1+256z)(32z+1)^2(64z-1)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 4}\)
\(3\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 4}\)
\(4\)\(0\)\(2\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.14" from ...

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3

New Number: 5.37 |  AESZ: 221  |  Superseeker: 492/5 872164/5  |  Hash: b7ce7a734c057660ce3d6341a7572078  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(404\theta^4+1096\theta^3+773\theta^2+225\theta+25\right)-2^{4} x^{2}\left(66896\theta^4+137408\theta^3+101096\theta^2+52800\theta+11625\right)-2^{8} 3 5 x^{3}(2\theta+1)(5672\theta^3+9500\theta^2+8422\theta+2689)-2^{15} 3^{2} x^{4}(2\theta+1)(1208\theta^3+2892\theta^2+2842\theta+969)-2^{20} 3^{3} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 20, 2988, 618320, 156299500, ...
--> OEIS
Normalized instanton numbers (n0=1): 492/5, 10376/5, 872164/5, 91316176/5, 12181916784/5, ... ; Common denominator:...

Discriminant

\(-(-1+432z)(16z+1)^2(192z+5)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 5}{ 192}\)\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 4}\)\(1\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(\frac{ 3}{ 4}\)\(3\)\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(1\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.37" from ...

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4

New Number: 5.91 |  AESZ: 331  |  Superseeker: 112 186800  |  Hash: a30093d8c1ab2f66122cef8935b79efb  

Degree: 5

\(\theta^4+2^{4} x\left(18\theta^4-48\theta^3-33\theta^2-9\theta-1\right)-2^{9} x^{2}\left(86\theta^4+512\theta^3+125\theta^2+45\theta+10\right)-2^{14} x^{3}\left(1138\theta^4+2040\theta^3+1883\theta^2+879\theta+157\right)-2^{19} 7 x^{4}(2\theta+1)(186\theta^3+375\theta^2+317\theta+100)-2^{27} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 16, 1488, 183040, 27611920, ...
--> OEIS
Normalized instanton numbers (n0=1): 112, -2242, 186800, -11675813, 1250599376, ... ; Common denominator:...

Discriminant

\(-(32z+1)(256z-1)(64z+1)(1+224z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 224}\)\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.91" from ...

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5

New Number: 1.10 |  AESZ: 10  |  Superseeker: 928 170869536  |  Hash: 51f8135aba94201bd0bbe9b2287a92d5  

Degree: 1

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

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Coefficients of the holomorphic solution: 1, 144, 176400, 341510400, 811620810000, ...
--> OEIS
Normalized instanton numbers (n0=1): 928, 245616, 170869536, 174999877936, 221984814405088, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

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

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