Summary

You searched for: h3=8

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1

New Number: 2.16 |  AESZ: 65  |  Superseeker: 240 19105840  |  Hash: 13ba368bcbb10731ac8727b510731ff2  

Degree: 2

\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{9} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

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Coefficients of the holomorphic solution: 1, 240, 277200, 457416960, 904864680720, ...
--> OEIS
Normalized instanton numbers (n0=1): 240, 57102, 19105840, 14810143935, 10017820614480, ... ; Common denominator:...

Discriminant

\((3456z-1)(1728z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3456}\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*d

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2

New Number: 4.41 |  AESZ: 220  |  Superseeker: 128 382592  |  Hash: 671a1aa788ead53985e13ad6774d0189  

Degree: 4

\(\theta^4-2^{4} x\left(20\theta^4+56\theta^3+38\theta^2+10\theta+1\right)-2^{10} x^{2}\left(84\theta^4+240\theta^3+261\theta^2+134\theta+25\right)-2^{16} x^{3}(2\theta+1)^2(23\theta^2+55\theta+39)-2^{23} x^{4}(2\theta+1)^2(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 16, 3600, 851200, 257328400, ...
--> OEIS
Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...

Discriminant

\(-(512z-1)(64z+1)^3\)

Local exponents

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

Note:

Sporadic Operator.
Reducible to 3.32, so not a primary operator.
B-Incarnation: 81111- x 82--11

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3

New Number: 4.46 |  AESZ: 237  |  Superseeker: 208 1218192  |  Hash: 52c18dd4477f6548dd3b185e97b94c20  

Degree: 4

\(\theta^4-2^{4} x\left(46\theta^4+128\theta^3+91\theta^2+27\theta+3\right)-2^{9} 3 x^{2}\left(74\theta^4-16\theta^3-231\theta^2-127\theta-20\right)+2^{14} 3^{2} x^{3}\left(14\theta^4+216\theta^3+175\theta^2+51\theta+5\right)+2^{19} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 12240, 4972800, 2489533200, ...
--> OEIS
Normalized instanton numbers (n0=1): 208, 5874, 1218192, 220754467, 56417503216, ... ; Common denominator:...

Discriminant

\((864z-1)(64z-1)(1+96z)^2\)

Local exponents

\(-\frac{ 1}{ 96}\)\(0\)\(\frac{ 1}{ 864}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

This is operator "4.46" from ...

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4

New Number: 4.52 |  AESZ: 258  |  Superseeker: 480 4215904  |  Hash: bfb9f01124fd9980817cbf1b50f789c3  

Degree: 4

\(\theta^4-2^{4} x\left(16\theta^4+224\theta^3+156\theta^2+44\theta+5\right)-2^{14} x^{2}\left(48\theta^4+48\theta^3-120\theta^2-66\theta-11\right)-2^{22} x^{3}\left(16\theta^4-192\theta^3-156\theta^2-48\theta-5\right)+2^{32} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 80, 24336, 11398400, 6632189200, ...
--> OEIS
Normalized instanton numbers (n0=1): 480, -16536, 4215904, -242723592, 151800032928, ... ; Common denominator:...

Discriminant

\((1024z-1)(256z-1)(1+512z)^2\)

Local exponents

\(-\frac{ 1}{ 512}\)\(0\)\(\frac{ 1}{ 1024}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator.

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5

New Number: 5.19 |  AESZ: 180  |  Superseeker: -624 -43406256  |  Hash: c174fb2dfd87730e48b4ae8b57ac66df  

Degree: 5

\(\theta^4-2^{4} 3 x\left(198\theta^4+72\theta^3+69\theta^2+33\theta+5\right)+2^{9} 3^{2} x^{2}\left(7614\theta^4+7128\theta^3+6813\theta^2+2529\theta+340\right)-2^{14} 3^{5} x^{3}\left(15714\theta^4+27216\theta^3+26343\theta^2+11151\theta+1685\right)+2^{19} 3^{9} x^{4}(3\theta+1)(3\theta+2)(576\theta^2+1008\theta+605)-2^{27} 3^{13} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 173520, 170016000, 193451504400, ...
--> OEIS
Normalized instanton numbers (n0=1): -624, -137190, -43406256, -18281817141, -9083828410320, ... ; Common denominator:...

Discriminant

\(-(-1+864z)(2592z-1)^2(1728z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 2592}\)\(\frac{ 1}{ 1728}\)\(\frac{ 1}{ 864}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(4\)\(1\)\(2\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.19" from ...

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6

New Number: 1.6 |  AESZ: 6  |  Superseeker: 160 1956896  |  Hash: 483b4ca5270ed3bfca9243827b62064e  

Degree: 1

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 15120, 7392000, 4414410000, ...
--> OEIS
Normalized instanton numbers (n0=1): 160, 11536, 1956896, 485487816, 148865410272, ... ; Common denominator:...

Discriminant

\(1-1024z\)

Local exponents

\(0\)\(\frac{ 1}{ 1024}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(2\)\(\frac{ 3}{ 4}\)

Note:

A-incarnation of $X(2,4)$ in $P^5$.

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