Summary

You searched for: c2h=32

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1

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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2

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

Degree: 4

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

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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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3

New Number: 5.11 |  AESZ: 71  |  Superseeker: 112 378800  |  Hash: cf4de65b0566a4f6294132c167d227eb  

Degree: 5

\(\theta^4+2^{4} x\left(39\theta^4-42\theta^3-29\theta^2-8\theta-1\right)+2^{11} x^{2}\theta(37\theta^3-137\theta^2-10\theta-1)-2^{16} x^{3}\left(181\theta^4+456\theta^3+353\theta^2+132\theta+19\right)-2^{23} 5 x^{4}\left(36\theta^4+60\theta^3+36\theta^2+6\theta-1\right)+2^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 16, 656, 40192, 3006736, ...
--> OEIS
Normalized instanton numbers (n0=1): 112, -4570, 378800, -40565898, 5098744272, ... ; Common denominator:...

Discriminant

\((16z-1)(128z-1)(128z+1)(1+320z)^2\)

Local exponents

\(-\frac{ 1}{ 128}\)\(-\frac{ 1}{ 320}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(1\)

Note:

This is operator "5.11" from ...

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4

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

Degree: 1

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

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

Discriminant

\(1-27648z\)

Local exponents

\(0\)\(\frac{ 1}{ 27648}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(2\)\(\frac{ 5}{ 6}\)

Note:

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

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