Summary

You searched for: c2h=72

Your search produced 19 matches

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1

New Number: 2.10 |  AESZ: 70  |  Superseeker: 27 18089  |  Hash: 3d2adae6eaf26a56c76b8b67d92cc5df  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1350, 156240, 22141350, ...
--> OEIS
Normalized instanton numbers (n0=1): 27, 432, 18089, 997785, 68438142, ... ; Common denominator:...

Discriminant

\((243z-1)(27z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 243}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast c$.

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2

New Number: 2.11 |  AESZ: 69  |  Superseeker: 64 246848  |  Hash: 729adc350de26d9415643078ed8d3867  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 6300, 1718640, 575675100, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, 2616, 246848, 32024824, 5160268864, ... ; Common denominator:...

Discriminant

\((576z-1)(64z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 576}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast c$

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3

New Number: 2.12 |  AESZ: 64  |  Superseeker: 432 78259376  |  Hash: 43991f21e20c16ab91690259b788b4cd  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(10\theta^2+10\theta+3)+2^{4} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 180, 207900, 379819440, 855338063580, ...
--> OEIS
Normalized instanton numbers (n0=1): 432, 130842, 78259376, 68104755558, 73096116588720, ... ; Common denominator:...

Discriminant

\((3888z-1)(432z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3888}\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product $B\ast c$.

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4

New Number: 2.1 |  AESZ: 45  |  Superseeker: 12 3204  |  Hash: cdf289f6febf84eb577a238542a57457  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 360, 22400, 1695400, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, 163, 3204, 107582, 4203360, ... ; Common denominator:...

Discriminant

\(-(16z+1)(128z-1)\)

Local exponents

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

Note:

Hadamard product $A \ast a$, where $A$ is (:case 2.1.1)

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5

New Number: 2.2 |  AESZ: 15  |  Superseeker: 21 15894  |  Hash: c8053e0e9c05ef468263fafd5e3fc764  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ...
--> OEIS
Normalized instanton numbers (n0=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...

Discriminant

\(-(27z+1)(216z-1)\)

Local exponents

\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 216}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(2\)\(0\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast a$.

A-Incarnation: diagonal of (3,3)-intersection in $P^2 \times P^2$

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6

New Number: 2.3 |  AESZ: 68  |  Superseeker: 52 220220  |  Hash: 13a48045ff0a42a9fcfbdb710baf1997  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 4200, 1034880, 311711400, ...
--> OEIS
Normalized instanton numbers (n0=1): 52, 2814, 220220, 29135058, 4512922272, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 512}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(0\)\(2\)\(\frac{ 7}{ 4}\)

Note:

C*a

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7

New Number: 2.4 |  AESZ: 62  |  Superseeker: 372 71562236  |  Hash: 07a3fd7577f878056e765831c6820f3d  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 120, 138600, 228708480, 463140798120, ...
--> OEIS
Normalized instanton numbers (n0=1): 372, 136182, 71562236, 63364481358, 65860679690400, ... ; Common denominator:...

Discriminant

\(-(432z+1)(3456z-1)\)

Local exponents

\(-\frac{ 1}{ 432}\)\(0\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(1\)\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(2\)\(0\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*a

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8

New Number: 2.53 |  AESZ: 29  |  Superseeker: 14 10424/3  |  Hash: 92e8a038051b3fb8e0cc6ad6a52b8bfb  

Degree: 2

\(\theta^4-2 x(2\theta+1)^2(17\theta^2+17\theta+5)+2^{2} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 438, 28900, 2310070, ...
--> OEIS
Normalized instanton numbers (n0=1): 14, 303/2, 10424/3, 113664, 4579068, ... ; Common denominator:...

Discriminant

\(1-136z+16z^2\)

Local exponents

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

Note:

Hadamard product $I \ast \gamma$

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9

New Number: 2.9 |  AESZ: 58  |  Superseeker: 16 11056/3  |  Hash: 1ca6d3d1c4514db0651efce420265f5a  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 540, 37200, 3131100, ...
--> OEIS
Normalized instanton numbers (n0=1): 16, 142, 11056/3, 121470, 4971792, ... ; Common denominator:...

Discriminant

\((144z-1)(16z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 144}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product A*c

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10

New Number: 3.10 |  AESZ: ~103  |  Superseeker: 10 664  |  Hash: 9239615e8ac132ca232c13367a39ae3b  

Degree: 3

\(\theta^4-2 x\left(86\theta^4+172\theta^3+143\theta^2+57\theta+9\right)+2^{2} 3^{2} x^{2}(\theta+1)^2(236\theta^2+472\theta+187)-2^{4} 3^{4} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 630, 28980, 1593270, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 24, 664, 9088, 234388, ... ; Common denominator:...

Discriminant

\(-(100z-1)(-1+36z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 100}\)\(\frac{ 1}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 103 =$c \ast c$.

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11

New Number: 3.8 |  AESZ: ~100  |  Superseeker: 5 454  |  Hash: 82a1ac6ac6fb9ab2e4d6b5d5790d1d9b  

Degree: 3

\(\theta^4+x\left(15\theta^4+30\theta^3+35\theta^2+20\theta+4\right)-2^{5} x^{2}(\theta+1)^2(66\theta^2+132\theta+53)-2^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 132, -1120, 72100, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 42, 454, 7498, 154351, ... ; Common denominator:...

Discriminant

\(-(49z-1)(1+32z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 1}{ 49}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(2\)
\(1\)\(0\)\(2\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 100= $ a \ast a$

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12

New Number: 5.3 |  AESZ: 20  |  Superseeker: 3 245/3  |  Hash: a9a698dc5c79ffda497a7897390408b0  

Degree: 5

\(\theta^4-3 x\left(48\theta^4+60\theta^3+53\theta^2+23\theta+4\right)+3^{2} x^{2}\left(873\theta^4+1980\theta^3+2319\theta^2+1344\theta+304\right)-2 3^{4} x^{3}\left(1269\theta^4+3888\theta^3+5259\theta^2+3348\theta+800\right)+2^{2} 3^{6} x^{4}\left(891\theta^4+3240\theta^3+4653\theta^2+2952\theta+688\right)-2^{3} 3^{11} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 252, 6600, 198540, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 33/2, 245/3, 879, 11829, ... ; Common denominator:...

Discriminant

\(-(54z-1)(27z-1)^2(18z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 54}\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 18}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 3}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 2}{ 3}\)\(3\)\(1\)
\(0\)\(2\)\(1\)\(4\)\(\frac{ 4}{ 3}\)

Note:

A-Incarnation: (3,0),(0,3),(1,1) intersection in $P^3 \times \P^3$.

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13

New Number: 5.40 |  AESZ: 226  |  Superseeker: 62/5 4060/3  |  Hash: 92f95cd33ac4bf18c2d05ce3040c5203  

Degree: 5

\(5^{2} \theta^4-2 5 x\left(328\theta^4+692\theta^3+551\theta^2+205\theta+30\right)+2^{2} 3 x^{2}\left(5352\theta^4+25416\theta^3+38387\theta^2+23020\theta+4860\right)-2^{4} 3^{3} x^{3}\left(352\theta^4+4520\theta^3+12108\theta^2+10205\theta+2630\right)-2^{6} 3^{3} x^{4}(2\theta+1)(586\theta^3+3039\theta^2+3947\theta+1527)-2^{8} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 396, 19920, 1241100, ...
--> OEIS
Normalized instanton numbers (n0=1): 62/5, 55, 4060/3, 28790, 861786, ... ; Common denominator:...

Discriminant

\(-(16z-1)(108z-1)(12z-1)(5+12z)^2\)

Local exponents

\(-\frac{ 5}{ 12}\)\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.40" from ...

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14

New Number: 5.84 |  AESZ: 318  |  Superseeker: 46/5 1126  |  Hash: 3fa38f629ecd5f39b585ce0c1bd88463  

Degree: 5

\(5^{2} \theta^4-5 x\left(473\theta^4+892\theta^3+696\theta^2+250\theta+35\right)+2 x^{2}\left(1973\theta^4-4636\theta^3-14417\theta^2-10895\theta-2745\right)+2 3^{2} x^{3}\left(343\theta^4+1920\theta^3+1147\theta^2-345\theta-320\right)-3^{4} x^{4}\left(83\theta^4-104\theta^3-458\theta^2-406\theta-114\right)-3^{8} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 7, 219, 9961, 546379, ...
--> OEIS
Normalized instanton numbers (n0=1): 46/5, 717/10, 1126, 51481/2, 3609772/5, ... ; Common denominator:...

Discriminant

\(-(z+1)(81z^2+92z-1)(-5+9z)^2\)

Local exponents

\(-\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\)\(-1\)\(0\)\(-\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\)\(\frac{ 5}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 319/5.85
Fibre product: 53211- x 632--1(1)

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15

New Number: 8.10 |  AESZ: 123  |  Superseeker: 12 1828/3  |  Hash: f0d76ab2b6b8808f4faa4ab8ecadff2c  

Degree: 8

\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+2^{4} x^{2}\left(209\theta^4+1052\theta^3+1471\theta^2+838\theta+183\right)+2^{7} 3^{2} x^{3}\left(30\theta^4-180\theta^3-551\theta^2-417\theta-111\right)-2^{10} 3^{2} x^{4}\left(227\theta^4+454\theta^3-550\theta^2-777\theta-261\right)+2^{12} 3^{4} x^{5}\left(30\theta^4+300\theta^3+169\theta^2-25\theta-35\right)+2^{14} 3^{4} x^{6}\left(209\theta^4-216\theta^3-431\theta^2-216\theta-27\right)-2^{17} 3^{6} x^{7}(3\theta^2+3\theta+1)(10\theta^2+10\theta+3)+2^{20} 3^{8} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 300, 10416, 431964, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, -47/2, 1828/3, -10813/4, 127948, ... ; Common denominator:...

Discriminant

\((36z-1)(8z-1)(72z-1)(4z-1)(-1+288z^2)^2\)

Local exponents

\(-\frac{ 1}{ 24}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 72}\)\(\frac{ 1}{ 36}\)\(\frac{ 1}{ 24}\sqrt{ 2}\)\(\frac{ 1}{ 8}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $c \ast d$. This operator has a second MUM-point at infinity with the same instanton numbers. It
can be reduced to an operator of degree 4 with a single
MUM-point defined over $\Q(\sqrt{?})$.

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16

New Number: 8.12 |  AESZ: 175  |  Superseeker: 17 1387  |  Hash: f6db11b5e593983f455489d5bb1003c5  

Degree: 8

\(\theta^4-x(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+3^{4} x^{2}\left(89\theta^4+452\theta^3+633\theta^2+362\theta+80\right)+2^{3} 3^{4} x^{3}\left(170\theta^4-1020\theta^3-3119\theta^2-2373\theta-648\right)-2^{4} 3^{8} x^{4}\left(97\theta^4+194\theta^3-238\theta^2-335\theta-114\right)+2^{6} 3^{8} x^{5}\left(170\theta^4+1700\theta^3+961\theta^2-125\theta-204\right)+2^{6} 3^{12} x^{6}\left(89\theta^4-96\theta^3-189\theta^2-96\theta-12\right)-2^{9} 3^{12} x^{7}(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+2^{12} 3^{16} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 630, 29016, 1529766, ...
--> OEIS
Normalized instanton numbers (n0=1): 17, -299/4, 1387, -47623/2, 500282, ... ; Common denominator:...

Discriminant

\((81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2\)

Local exponents

\(-\frac{ 1}{ 36}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 1}{ 72}\)\(\frac{ 1}{ 36}\sqrt{ 2}\)\(\frac{ 1}{ 9}\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $c \ast g$. This operator has a second MUM-point
at infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{?})$.

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17

New Number: 8.2 |  AESZ: 104  |  Superseeker: 7 1271/3  |  Hash: d6bd0d1524954c8ce0a6421d295e9795  

Degree: 8

\(\theta^4-x(10\theta^2+10\theta+3)(7\theta^2+7\theta+2)-x^{2}\left(71\theta^4+1148\theta^3+1591\theta^2+886\theta+192\right)-2^{3} 3^{2} x^{3}\left(70\theta^4-420\theta^3-1289\theta^2-963\theta-240\right)-2^{4} 3^{2} x^{4}\left(143\theta^4+286\theta^3-1138\theta^2-1281\theta-414\right)+2^{6} 3^{4} x^{5}\left(70\theta^4+700\theta^3+391\theta^2-75\theta-76\right)-2^{6} 3^{4} x^{6}\left(71\theta^4-864\theta^3-1427\theta^2-864\theta-180\right)+2^{9} 3^{6} x^{7}(10\theta^2+10\theta+3)(7\theta^2+7\theta+2)+2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 150, 5208, 221094, ...
--> OEIS
Normalized instanton numbers (n0=1): 7, 93/2, 1271/3, 18507/2, 190710, ... ; Common denominator:...

Discriminant

\((9z+1)(8z-1)(72z-1)(z+1)(1+72z^2)^2\)

Local exponents

\(-1\)\(-\frac{ 1}{ 9}\)\(0-\frac{ 1}{ 12}\sqrt{ 2}I\)\(0\)\(0+\frac{ 1}{ 12}\sqrt{ 2}I\)\(\frac{ 1}{ 72}\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $a \ast c$. This operator has a second MUM-point at infinity with the same instanton point.
It is reducible to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{-2})$

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18

New Number: 8.3 |  AESZ: 105  |  Superseeker: 8 -104  |  Hash: 7b27135451cf2016217211c633b7ab83  

Degree: 8

\(\theta^4-2^{2} x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{5} 3 x^{2}\left(15\theta^4+28\theta^3+39\theta^2+22\theta+4\right)-2^{10} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{14} x^{4}\left(37\theta^4+74\theta^3+50\theta^2+13\theta+6\right)+2^{18} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{21} 3 x^{6}\left(15\theta^4+32\theta^3+45\theta^2+32\theta+8\right)+2^{26} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{32} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 8, 200, 6272, 233896, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 71/2, -104, 4202, 50112, ... ; Common denominator:...

Discriminant

\((8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 8}\)\(0-\frac{ 1}{ 16}I\)\(0\)\(0+\frac{ 1}{ 16}I\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $a \ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{-1})$.

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19

New Number: 8.5 |  AESZ: 173  |  Superseeker: 11 -2434/3  |  Hash: afa82ed9ee239bb5fcac960f8884db01  

Degree: 8

\(\theta^4-x(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{6} x^{2}\left(55\theta^4+112\theta^3+155\theta^2+86\theta+15\right)-2^{6} 3^{2} x^{3}\left(119\theta^4-714\theta^3-2185\theta^2-1656\theta-444\right)+2^{12} 3^{2} x^{4}\left(92\theta^4+184\theta^3+98\theta^2+6\theta+9\right)+2^{12} 3^{4} x^{5}\left(119\theta^4+1190\theta^3+671\theta^2-96\theta-140\right)+2^{18} 3^{4} x^{6}\left(55\theta^4+108\theta^3+149\theta^2+108\theta+27\right)+2^{18} 3^{6} x^{7}(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{24} 3^{8} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 12, 420, 17472, 828324, ...
--> OEIS
Normalized instanton numbers (n0=1): 11, 229/4, -2434/3, 7512, 54801, ... ; Common denominator:...

Discriminant

\((72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2\)

Local exponents

\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 9}\)\(0-\frac{ 1}{ 24}I\)\(0\)\(0+\frac{ 1}{ 24}I\)\(\frac{ 1}{ 72}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $a \ast g$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{?})$.

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