Summary

You searched for: dim_h=3

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1

New Number: 4.47 |  AESZ: 239  |  Superseeker: 1584 171534960  |  Hash: 8e610c3437d7f38e552038bc55399495  

Degree: 4

\(\theta^4+2^{4} 3 x\left(9\theta^4-198\theta^3-131\theta^2-32\theta-3\right)-2^{11} 3^{2} x^{2}\left(486\theta^4+1215\theta^3+81\theta^2-27\theta-5\right)-2^{16} 3^{5} x^{3}\left(891\theta^4+972\theta^3+675\theta^2+216\theta+25\right)-2^{23} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, 144, 147600, 239904000, 479672701200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1584, -17874, 171534960, 30012731550, 105934107802896, ... ; Common denominator:...

Discriminant

\(-(432z+1)(3456z-1)(1+1728z)^2\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 1}{ 1728}\)\(0\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 3}\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(2\)\(4\)\(0\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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2

New Number: 4.48 |  AESZ: 241  |  Superseeker: 320 19748928  |  Hash: b4d16d8dd1eb7839630ecf8e8d242023  

Degree: 4

\(\theta^4-2^{4} x\left(152\theta^4+160\theta^3+110\theta^2+30\theta+3\right)+2^{10} 3 x^{2}\left(428\theta^4+176\theta^3-299\theta^2-170\theta-25\right)-2^{17} 3^{2} x^{3}\left(136\theta^4-216\theta^3-180\theta^2-51\theta-5\right)-2^{24} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

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Coefficients of the holomorphic solution: 1, 48, 26640, 21907200, 22048765200, ...
--> OEIS
Normalized instanton numbers (n0=1): 320, 61084, 19748928, 9428973876, 5618509433280, ... ; Common denominator:...

Discriminant

\(-(64z+1)(1728z-1)(-1+384z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 1728}\)\(\frac{ 1}{ 384}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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3

New Number: 4.51 |  AESZ:  |  Superseeker: 992 63721056  |  Hash: 1d45a05c9bcf007b5042b0f7a5672551  

Degree: 4

\(\theta^4-2^{4} x\left(112\theta^4+416\theta^3+280\theta^2+72\theta+7\right)-2^{12} x^{2}\left(656\theta^4+896\theta^3-216\theta^2-160\theta-23\right)-2^{23} x^{3}\left(96\theta^4+24\theta^3+12\theta^2+6\theta+1\right)-2^{30} x^{4}\left((2\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 112, 93456, 124614400, 204621667600, ...
--> OEIS
Normalized instanton numbers (n0=1): 992, 98792, 63721056, 40943244128, 36122052633760, ... ; Common denominator:...

Discriminant

\(-(65536z^2+2816z-1)(1+512z)^2\)

Local exponents

\(-\frac{ 11}{ 512}-\frac{ 5}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 512}\)\(0\)\(s_2\)\(s_1\)\(-\frac{ 11}{ 512}+\frac{ 5}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point
hiding at infinity, corresponding to Operator
AESZ 256/4.50

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4

New Number: 4.60 |  AESZ: 288  |  Superseeker: 3616 264403872  |  Hash: 3373ebdbe30d220b5562cfd77d4e8f96  

Degree: 4

\(\theta^4-2^{4} x\left(496\theta^4+1568\theta^3+1060\theta^2+276\theta+27\right)-2^{15} 3 x^{2}\left(32\theta^4-760\theta^3-1570\theta^2-651\theta-81\right)+2^{22} 3^{2} x^{3}\left(1616\theta^4+6912\theta^3+5092\theta^2+1416\theta+135\right)+2^{34} 3^{3} x^{4}(4\theta+1)(3\theta+1)(3\theta+2)(4\theta+3)\)

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Coefficients of the holomorphic solution: 1, 432, 982800, 3259872000, 12958462717200, ...
--> OEIS
Normalized instanton numbers (n0=1): 3616, 114144, 264403872, 424149521656, 710239010095456, ... ; Common denominator:...

Discriminant

\((6912z-1)(4096z-1)(1+1536z)^2\)

Local exponents

\(-\frac{ 1}{ 1536}\)\(0\)\(\frac{ 1}{ 6912}\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 3}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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5

New Number: 4.66 |  AESZ: 300  |  Superseeker: -1616 -283183120  |  Hash: edc54887effd2ebcaa636dcc93baf0b7  

Degree: 4

\(\theta^4+2^{4} x\left(371\theta^4+862\theta^3+591\theta^2+160\theta+15\right)+2^{11} 5 x^{2}\left(224\theta^4+2069\theta^3+3277\theta^2+1363\theta+159\right)-2^{16} 5^{2} x^{3}\left(2089\theta^4+7500\theta^3+5533\theta^2+1500\theta+135\right)+2^{23} 5^{3} x^{4}(5\theta+1)(5\theta+2)(5\theta+3)(5\theta+4)\)

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Coefficients of the holomorphic solution: 1, -240, 378000, -941740800, 2908743037200, ...
--> OEIS
Normalized instanton numbers (n0=1): -1616, 265534, -283183120, 351860487150, -525536710386800, ... ; Common denominator:...

Discriminant

\((6400000z^2+6576z+1)(-1+320z)^2\)

Local exponents

≈\(-0.000842\) ≈\(-0.000186\)\(0\)\(s_2\)\(s_1\)\(\frac{ 1}{ 320}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 5}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 5}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 3}{ 5}\)
\(2\)\(2\)\(0\)\(2\)\(2\)\(4\)\(\frac{ 4}{ 5}\)

Note:

Sporadic Operator.

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6

New Number: 5.22 |  AESZ: 193  |  Superseeker: 129/7 41441/7  |  Hash: 44e6fc2823d5ff31e66059ba6b37f2ae  

Degree: 5

\(7^{2} \theta^4-7 x\left(1135\theta^4+2204\theta^3+1683\theta^2+581\theta+77\right)+x^{2}\left(28723\theta^4+40708\theta^3+13260\theta^2-1337\theta-896\right)-x^{3}\left(32126\theta^4+38514\theta^3+26511\theta^2+10731\theta+1806\right)+7 11 x^{4}\left(130\theta^4+254\theta^3+192\theta^2+65\theta+8\right)+11^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 11, 559, 42923, 3996751, ...
--> OEIS
Normalized instanton numbers (n0=1): 129/7, 1557/7, 41441/7, 1594332/7, 75470601/7, ... ; Common denominator:...

Discriminant

\((z^3+84z^2-159z+1)(-7+11z)^2\)

Local exponents

≈\(-85.852157\)\(0\) ≈\(0.00631\)\(\frac{ 7}{ 11}\) ≈\(1.845846\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 198/5.25

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7

New Number: 5.29 |  AESZ: 208  |  Superseeker: 274/7 281388/7  |  Hash: f1d6dfa8a5cdcc2513dfca4243565b2f  

Degree: 5

\(7^{2} \theta^4-2 7 x\left(1056\theta^4+1884\theta^3+1397\theta^2+455\theta+56\right)+2^{2} 3 x^{2}\left(22760\theta^4+13672\theta^3-22537\theta^2-18116\theta-3584\right)-2^{4} x^{3}\left(53312\theta^4-162120\theta^3-195172\theta^2-78561\theta-11130\right)-2^{6} 19 x^{4}(1189\theta^2+2533\theta+1646)(2\theta+1)^2+2^{11} 19^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 16, 1440, 196000, 32418400, ...
--> OEIS
Normalized instanton numbers (n0=1): 274/7, 6115/7, 281388/7, 2815228, 1699166270/7, ... ; Common denominator:...

Discriminant

\((4z+1)(512z^2-284z+1)(-7+76z)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 71}{ 256}-\frac{ 17}{ 256}\sqrt{ 17}\)\(\frac{ 7}{ 76}\)\(\frac{ 71}{ 256}+\frac{ 17}{ 256}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.29" from ...

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8

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

\(\)

No data for singularities

Note:

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

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9

New Number: 1.2 |  AESZ: 2  |  Superseeker: 231200 1700894366474400  |  Hash: 709cba5c90462e9488c8a3dbbee8f89c  

Degree: 1

\(\theta^4-2^{4} 5 x(10\theta+1)(10\theta+3)(10\theta+7)(10\theta+9)\)

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Coefficients of the holomorphic solution: 1, 15120, 3491888400, 1304290155168000, 601680868708529610000, ...
--> OEIS
Normalized instanton numbers (n0=1): 231200, 12215785600, 1700894366474400, 350154658851324656000, 89338191421813572850115680, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

A-incarnation: X(10) in P^4(1,1,1,2,5)

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