Summary

You searched for: Spectrum0=1/2,1,2,5/2

Your search produced 19 matches

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1

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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2

New Number: 3.15 |  AESZ:  |  Superseeker: -32 -16288  |  Hash: e21c92d8f9a2222be40fdc71ea51ee35  

Degree: 3

\(\theta^4+2^{3} x\left(21\theta^4+42\theta^3+30\theta^2+9\theta+1\right)-2^{6} x^{2}(\theta+1)^2(96\theta^2+192\theta+77)+2^{9} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 720, -68480, 8123920, ...
--> OEIS
Normalized instanton numbers (n0=1): -32, 468, -16288, 1681645/2, -53608288, ... ; Common denominator:...

Discriminant

\((200z+1)(-1+16z)^2\)

Local exponents

\(-\frac{ 1}{ 200}\)\(0\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 6}\)\(1\)
\(1\)\(0\)\(\frac{ 5}{ 6}\)\(2\)
\(2\)\(0\)\(1\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 328

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3

New Number: 3.16 |  AESZ: 386  |  Superseeker: 10 18328  |  Hash: 7d032616d3bd41272e22a4d23747d7a0  

Degree: 3

\(\theta^4-2 x\left(422\theta^4+844\theta^3+751\theta^2+329\theta+57\right)+2^{2} 3^{4} x^{2}(\theta+1)^2(716\theta^2+1432\theta+579)-2^{4} 3^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 114, 22518, 5236980, 1321024950, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -872, 18328, -432528, 13706388, ... ; Common denominator:...

Discriminant

\(-(196z-1)(-1+324z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 324}\)\(\frac{ 1}{ 196}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(0\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

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4

New Number: 3.17 |  AESZ: 387  |  Superseeker: 68 125636/3  |  Hash: 06864aab02693f4b84eb494138bb3428  

Degree: 3

\(\theta^4-2^{2} x\left(228\theta^4+456\theta^3+385\theta^2+157\theta+26\right)+2^{11} x^{2}(\theta+1)^2(132\theta^2+264\theta+109)-2^{18} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 104, 18600, 3925760, 906368680, ...
--> OEIS
Normalized instanton numbers (n0=1): 68, 204, 125636/3, 841384, 123715360, ... ; Common denominator:...

Discriminant

\(-(400z-1)(-1+256z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 400}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "3.17" from ...

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5

New Number: 3.18 |  AESZ: 388  |  Superseeker: 266 11433160/3  |  Hash: 7e11db69c1b7bd8781e54a5eadb0e307  

Degree: 3

\(\theta^4-2 x\left(582\theta^4+1164\theta^3+815\theta^2+233\theta+25\right)+2^{2} x^{2}(\theta+1)^2(2316\theta^2+4632\theta+1907)-2^{4} 17^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 50, 17142, 9383540, 6301530550, ...
--> OEIS
Normalized instanton numbers (n0=1): 266, 19320, 11433160/3, 1106069392, 397606861972, ... ; Common denominator:...

Discriminant

\(-(1156z-1)(4z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 1156}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "3.18" from ...

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6

New Number: 3.20 |  AESZ: 390  |  Superseeker: 19 4455  |  Hash: cd8ca8746f3610e70893770a090533f9  

Degree: 3

\(\theta^4-x\left(561\theta^4+1122\theta^3+975\theta^2+414\theta+70\right)+2^{2} 7^{2} x^{2}(\theta+1)^2(534\theta^2+1068\theta+433)-2^{2} 7^{4} 13^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 70, 8442, 1192660, 182057050, ...
--> OEIS
Normalized instanton numbers (n0=1): 19, -276, 4455, -104648, 2969383, ... ; Common denominator:...

Discriminant

\(-(169z-1)(-1+196z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 196}\)\(\frac{ 1}{ 169}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 6}\)\(1\)\(1\)
\(0\)\(\frac{ 5}{ 6}\)\(1\)\(2\)
\(0\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "3.20" from ...

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7

New Number: 3.11 |  AESZ:  |  Superseeker: 37 15270  |  Hash: e7db0935aa1b331d8fb696a009d2d7bb  

Degree: 3

\(\theta^4-x\left(865\theta^4+1730\theta^3+1501\theta^2+636\theta+108\right)+2^{5} 3^{2} x^{2}(\theta+1)^2(866\theta^2+1732\theta+709)-2^{8} 3^{4} 17^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 108, 19908, 4278240, 990152100, ...
--> OEIS
Normalized instanton numbers (n0=1): 37, -570, 15270, -529994, 21300463, ... ; Common denominator:...

Discriminant

\(-(289z-1)(-1+288z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 289}\)\(\frac{ 1}{ 288}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 144=c \ast c$

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8

New Number: 3.19 |  AESZ: 389  |  Superseeker: 66 69048  |  Hash: c5cca5b7bfc61c4e8b38fab025244078  

Degree: 3

\(\theta^4-2 x\left(742\theta^4+1484\theta^3+1295\theta^2+553\theta+95\right)+2^{2} 5^{3} x^{2}(\theta+1)^2(1468\theta^2+2936\theta+1211)-2^{4} 5^{6} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 190, 61170, 22892500, 9212271250, ...
--> OEIS
Normalized instanton numbers (n0=1): 66, -1780, 69048, -3847892, 244783420, ... ; Common denominator:...

Discriminant

\(-(484z-1)(-1+500z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 500}\)\(\frac{ 1}{ 484}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(0\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "3.19" from ...

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9

New Number: 3.34 |  AESZ:  |  Superseeker: 16 1744  |  Hash: 931a876bfe4d4aa192c6e18e74047640  

Degree: 3

\(\theta^4-2^{4} x\left(25\theta^4+50\theta^3+43\theta^2+18\theta+3\right)+2^{11} x^{2}(26\theta^2+52\theta+21)(\theta+1)^2-2^{16} 3^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 3984, 387840, 40818960, ...
--> OEIS
Normalized instanton numbers (n0=1): 16, -110, 1744, -29526, 644016, ... ; Common denominator:...

Discriminant

\(-(144z-1)(-1+128z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 144}\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 107 $=d \ast d$

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10

New Number: 3.4 |  AESZ:  |  Superseeker: -9 -748  |  Hash: 350ef7c6e038467a3f50bfbe164fa73a  

Degree: 3

\(\theta^4+3^{2} x\left(33\theta^4+66\theta^3+57\theta^2+24\theta+4\right)+2^{3} 3^{6} x^{2}(\theta+1)^2(5\theta^2+10\theta+4)+2^{2} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -36, 2268, -168840, 13664700, ...
--> OEIS
Normalized instanton numbers (n0=1): -9, -279/4, -748, -9612, -155448, ... ; Common denominator:...

Discriminant

\((81z+1)(1+108z)^2\)

Local exponents

\(-\frac{ 1}{ 81}\)\(-\frac{ 1}{ 108}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(0\)\(2\)
\(2\)\(1\)\(0\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 165= $f \ast f$.

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11

New Number: 3.5 |  AESZ:  |  Superseeker: 26 103520/9  |  Hash: 4ed9bc316d49a71649da0a1148f7ea9d  

Degree: 3

\(\theta^4-2 x\left(102\theta^4+204\theta^3+155\theta^2+53\theta+7\right)+2^{2} x^{2}(\theta+1)^2(396\theta^2+792\theta+311)-2^{4} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 14, 834, 78260, 8970850, ...
--> OEIS
Normalized instanton numbers (n0=1): 26, 348, 103520/9, 539764, 31290280, ... ; Common denominator:...

Discriminant

\(-(196z-1)(4z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 196}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 4}\)\(1\)
\(0\)\(1\)\(\frac{ 3}{ 4}\)\(2\)
\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 214

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12

New Number: 3.7 |  AESZ: ~73  |  Superseeker: 90 151648  |  Hash: 9f672e1168859bdcc8ddc7a201c57968  

Degree: 3

\(\theta^4-2 3^{2} x\left(6\theta^4+12\theta^3+3\theta^2-3\theta-1\right)-2^{2} 3^{6} x^{2}(\theta+1)^2(20\theta^2+40\theta+17)-2^{4} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -18, 2754, 37620, 43789410, ...
--> OEIS
Normalized instanton numbers (n0=1): 90, 2196, 151648, 14813388, 1820806056, ... ; Common denominator:...

Discriminant

\(-(324z-1)(1+108z)^2\)

Local exponents

\(-\frac{ 1}{ 108}\)\(0\)\(\frac{ 1}{ 324}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(0\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(2\)
\(1\)\(0\)\(2\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 73

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13

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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14

New Number: 3.9 |  AESZ: ~101  |  Superseeker: 13 2650  |  Hash: a6878d847acf199583e8168a33967174  

Degree: 3

\(\theta^4-x\left(113\theta^4+226\theta^3+173\theta^2+60\theta+8\right)-2^{3} x^{2}(\theta+1)^2(119\theta^2+238\theta+92)-2^{2} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 336, 19880, 1420720, ...
--> OEIS
Normalized instanton numbers (n0=1): 13, 128, 2650, 79400, 2921395, ... ; Common denominator:...

Discriminant

\(-(121z-1)(4z+1)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 121}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(2\)
\(1\)\(0\)\(2\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to $AESZ 101=$b \ast b$.

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15

New Number: 6.11 |  AESZ:  |  Superseeker: 27296 369676901920  |  Hash: 480dfd541eda896f1434450e820ef263  

Degree: 6

\(\theta^4+2^{4} x\left(4480\theta^4-6016\theta^3-3632\theta^2-624\theta-57\right)+2^{14} x^{2}\left(56512\theta^4-238208\theta^3+88016\theta^2+21584\theta+2943\right)-2^{24} 3^{2} x^{3}\left(93952\theta^4+21248\theta^3+15264\theta^2+2176\theta+155\right)-2^{34} 3^{3} x^{4}\left(41664\theta^4+57088\theta^3+4448\theta^2-21248\theta-7191\right)+2^{48} 3^{3} 13 x^{5}(\theta+1)(808\theta^3+2352\theta^2+2099\theta+582)-2^{58} 3^{5} 13^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 912, 2320656, 9507313920, 49468269165840, ...
--> OEIS
Normalized instanton numbers (n0=1): 27296, -70540912, 369676901920, -2547102730999216, 20534034788092596960, ... ; Common denominator:...

Discriminant

\(-(3072z+1)(9216z-1)(39936z+1)^2(1024z-1)^2\)

Local exponents

\(-\frac{ 1}{ 3072}\)\(-\frac{ 1}{ 39936}\)\(0\)\(\frac{ 1}{ 9216}\)\(\frac{ 1}{ 1024}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(2\)
\(2\)\(4\)\(0\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.11" from ...

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16

New Number: 6.40 |  AESZ:  |  Superseeker: 24586 329889747608  |  Hash: 36fe35d15f62636c9a59974b02c3c153  

Degree: 6

\(\theta^4+2 x\left(31252\theta^4-47788\theta^3-30351\theta^2-6457\theta-777\right)+2^{2} x^{2}\left(141990396\theta^4-851496456\theta^3+348245465\theta^2+120244516\theta+24723417\right)-2^{4} 7 x^{3}\left(114890001328\theta^4-55808058864\theta^3-39178895096\theta^2-22533986391\theta-2840254281\right)+2^{6} 7^{2} x^{4}\left(12756705884284\theta^4+28777665785840\theta^3+28025191186334\theta^2+13259372733985\theta+2453710035513\right)+2^{8} 3^{4} 7^{3} 13 101 x^{5}(\theta+1)(6017971352\theta^3+13862309856\theta^2+7944674578\theta+1672187649)-2^{10} 3^{10} 5^{2} 7^{5} 13^{2} 37^{2} 101^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1554, 4332150, 14528884020, 53714646216630, ...
--> OEIS
Normalized instanton numbers (n0=1): 24586, -65016808, 329889747608, -2211583844012928, 17318548806048850836, ... ; Common denominator:...

Discriminant

\(-(2916z-1)(5476z-1)(2268z+1)(4900z-1)(1+36764z)^2\)

Local exponents

\(-\frac{ 1}{ 2268}\)\(-\frac{ 1}{ 36764}\)\(0\)\(\frac{ 1}{ 5476}\)\(\frac{ 1}{ 4900}\)\(\frac{ 1}{ 2916}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(2\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.40" from ...

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17

New Number: 6.3 |  AESZ:  |  Superseeker: 178/7 129516/7  |  Hash: ec9e21dc2ccd3b4b4156ae1438454b96  

Degree: 6

\(7^{2} \theta^4-2 7 x\left(1488\theta^4+1452\theta^3+1125\theta^2+399\theta+56\right)+2^{2} x^{2}\left(766392\theta^4+1184952\theta^3+1010797\theta^2+454076\theta+83776\right)-2^{4} x^{3}\left(12943616\theta^4+28354200\theta^3+30710572\theta^2+16054731\theta+3215254\right)+2^{6} x^{4}\left(105973188\theta^4+333359304\theta^3+436182381\theta^2+261265857\theta+57189166\right)-2^{11} 127 x^{5}(\theta+1)(390972\theta^3+1350660\theta^2+1486781\theta+460439)+2^{14} 23^{2} 127^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 864, 80800, 9624160, ...
--> OEIS
Normalized instanton numbers (n0=1): 178/7, 3375/7, 129516/7, 6515900/7, 409239710/7, ... ; Common denominator:...

Discriminant

\((1-248z+8464z^2)(508z-7)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 31}{ 2116}-\frac{ 3}{ 529}\sqrt{ 3}\)\(\frac{ 7}{ 508}\)\(\frac{ 31}{ 2116}+\frac{ 3}{ 529}\sqrt{ 3}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 3}\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(\frac{ 2}{ 3}\)\(2\)
\(0\)\(2\)\(4\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.3" from ...

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18

New Number: 6.4 |  AESZ:  |  Superseeker: 370/19 140636/19  |  Hash: 0f3ddf420018e2870561a3e9fd2551cc  

Degree: 6

\(19^{2} \theta^4-19 x\left(4333\theta^4+6212\theta^3+4778\theta^2+1672\theta+228\right)+x^{2}\left(4307495\theta^4+7600484\theta^3+6216406\theta^2+2802424\theta+530556\right)-x^{3}\left(93729369\theta^4+213316800\theta^3+236037196\theta^2+125748612\theta+25260804\right)+2^{2} x^{4}\left(240813800\theta^4+778529200\theta^3+1041447759\theta^2+631802809\theta+138510993\right)-2^{2} 409 x^{5}(\theta+1)(2851324\theta^3+10035516\theta^2+11221241\theta+3481470)+2^{2} 3^{2} 19^{2} 409^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, 12, 588, 46200, 4446540, ...
--> OEIS
Normalized instanton numbers (n0=1): 370/19, 276, 140636/19, 5568700/19, 277119292/19, ... ; Common denominator:...

Discriminant

\((9z-1)(5776z^3-1920z^2+176z-1)(-19+409z)^2\)

Local exponents

\(0\) ≈\(0.006077\)\(\frac{ 19}{ 409}\)\(\frac{ 1}{ 9}\) ≈\(0.163166-0.043179I\) ≈\(0.163166+0.043179I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.4" from ...

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19

New Number: 6.8 |  AESZ:  |  Superseeker: 567/13 512341/13  |  Hash: 00104510dfaa4ae75940f08df0a52bf5  

Degree: 6

\(13^{2} \theta^4-13 x\left(5041\theta^4+7634\theta^3+5767\theta^2+1950\theta+260\right)+2^{3} x^{2}\left(744635\theta^4+1560842\theta^3+1510101\theta^2+768170\theta+156078\right)-2^{6} 3 x^{3}\left(1232985\theta^4+3409302\theta^3+4189688\theta^2+2419209\theta+518414\right)+2^{9} x^{4}\left(9225025\theta^4+33675338\theta^3+49289090\theta^2+31849807\theta+7296732\right)-2^{12} 3 17 x^{5}(\theta+1)(222704\theta^3+833160\theta^2+989659\theta+317310)+2^{15} 3^{2} 17^{2} 23^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, 20, 1524, 196400, 31587220, ...
--> OEIS
Normalized instanton numbers (n0=1): 567/13, 11392/13, 512341/13, 34191454/13, 2850663840/13, ... ; Common denominator:...

Discriminant

\((1-293z+4232z^2)(408z-13)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 293}{ 8464}-\frac{ 41}{ 8464}\sqrt{ 41}\)\(\frac{ 13}{ 408}\)\(\frac{ 1}{ 16}\)\(\frac{ 293}{ 8464}+\frac{ 41}{ 8464}\sqrt{ 41}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(2\)
\(0\)\(2\)\(4\)\(1\)\(2\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.8" from ...

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