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You searched for: degz=5

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1

New Number: 5.100 |  AESZ: 347  |  Superseeker: 15 27140/3  |  Hash: f00de20026c099e75b447c475ab287e4  

Degree: 5

\(\theta^4-3 x\left(213\theta^4+186\theta^3+149\theta^2+56\theta+8\right)+2^{3} 3^{3} x^{2}\left(702\theta^4+1078\theta^3+949\theta^2+392\theta+60\right)-2^{6} 3^{3} x^{3}\left(9277\theta^4+18432\theta^3+16008\theta^2+6000\theta+840\right)+2^{13} 3^{4} 5 x^{4}(2\theta+1)^2(51\theta^2+69\theta+32)-2^{14} 3^{6} 5^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1944, 218400, 28488600, ...
--> OEIS
Normalized instanton numbers (n0=1): 15, 1329/4, 27140/3, 220680, 5952570, ... ; Common denominator:...

Discriminant

\(-(192z-1)(1728z^2-207z+1)(-1+120z)^2\)

Local exponents

\(0\)\(\frac{ 23}{ 384}-\frac{ 11}{ 1152}\sqrt{ 33}\)\(\frac{ 1}{ 192}\)\(\frac{ 1}{ 120}\)\(\frac{ 23}{ 384}+\frac{ 11}{ 1152}\sqrt{ 33}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.100" from ...

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2

New Number: 5.101 |  AESZ: 348  |  Superseeker: -52 -44772  |  Hash: 8759f016475d17d0fc88f4b98a374d3f  

Degree: 5

\(\theta^4+2^{2} x\left(70\theta^4+194\theta^3+145\theta^2+48\theta+6\right)-2^{4} 3 x^{2}\left(141\theta^4-858\theta^3-2111\theta^2-1192\theta-206\right)-2^{8} 3^{2} x^{3}\left(18\theta^4-324\theta^3-2364\theta^2-1953\theta-403\right)-2^{10} 3^{4} x^{4}(3\theta+1)(3\theta+2)(42\theta^2+258\theta+223)+2^{14} 3^{6} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, 2160, -309120, 54608400, ...
--> OEIS
Normalized instanton numbers (n0=1): -52, 461/2, -44772, 3546761/2, -178670332, ... ; Common denominator:...

Discriminant

\((746496z^3+17280z^2+352z+1)(-1+36z)^2\)

Local exponents

≈\(-0.009925-0.017537I\) ≈\(-0.009925+0.017537I\) ≈\(-0.003299\)\(0\)\(\frac{ 1}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(1\)\(0\)\(3\)\(\frac{ 4}{ 3}\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.101" from ...

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3

New Number: 5.102 |  AESZ: 352  |  Superseeker: 1 -12  |  Hash: fc8b141522720827b1dd2cd28a232c1b  

Degree: 5

\(\theta^4-x\left(70\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+3 x^{2}\left(675\theta^4+1602\theta^3+1933\theta^2+1130\theta+258\right)-2^{2} 3^{3} x^{3}\left(271\theta^4+888\theta^3+1259\theta^2+831\theta+207\right)+2^{2} 3^{5} x^{4}\left(212\theta^4+808\theta^3+1189\theta^2+773\theta+186\right)-2^{4} 3^{7} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 492, 3510, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -7/8, -12, -131/4, 90, ... ; Common denominator:...

Discriminant

\(-(16z-1)(432z^2-36z+1)(-1+9z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\)\(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.102" from ...

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4

New Number: 5.103 |  AESZ: 354  |  Superseeker: 25 17175  |  Hash: 0d4263e8c85dceb5c51f8614f7c1bc79  

Degree: 5

\(\theta^4-5 x\left(170\theta^4+160\theta^3+125\theta^2+45\theta+6\right)+3 5^{3} x^{2}\left(725\theta^4+1220\theta^3+1105\theta^2+460\theta+68\right)-3^{2} 5^{5} x^{3}\left(1421\theta^4+3186\theta^3+3053\theta^2+1272\theta+188\right)+2^{2} 3^{3} 5^{7} x^{4}(3\theta+1)(3\theta+2)(34\theta^2+61\theta+36)-2^{2} 3^{4} 5^{9} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 3150, 462000, 78828750, ...
--> OEIS
Normalized instanton numbers (n0=1): 25, 2175/4, 17175, 351250, 23000351/5, ... ; Common denominator:...

Discriminant

\(-(2278125z^3-84375z^2+550z-1)(-1+150z)^2\)

Local exponents

\(0\) ≈\(0.003863-0.000232I\) ≈\(0.003863+0.000232I\)\(\frac{ 1}{ 150}\) ≈\(0.029311\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.103" from ...

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5

New Number: 5.104 |  AESZ: 357  |  Superseeker: 7/13 21/13  |  Hash: afee0651c9b3b8e98079f5c2d5bfa8a5  

Degree: 5

\(13^{2} \theta^4-13 x\left(441\theta^4+690\theta^3+631\theta^2+286\theta+52\right)+2^{4} x^{2}\left(5121\theta^4+15576\theta^3+21215\theta^2+13702\theta+3445\right)-2^{10} x^{3}\left(640\theta^4+2847\theta^3+5078\theta^2+4056\theta+1196\right)+2^{14} x^{4}\left(125\theta^4+562\theta^3+905\theta^2+624\theta+157\right)-2^{21} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 20, 112, 916, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/13, -10/13, 21/13, 296/13, 608/13, ... ; Common denominator:...

Discriminant

\(-(16z-1)(128z^2-13z+1)(-13+32z)^2\)

Local exponents

\(0\)\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 1}{ 16}\)\(\frac{ 13}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 358/5.105

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6

New Number: 5.105 |  AESZ: 358  |  Superseeker: -336 -4761360  |  Hash: f026b6514e3be9b730646bc9410b1049  

Degree: 5

\(\theta^4-2^{4} x\left(125\theta^4-62\theta^3-31\theta^2+1\right)+2^{11} x^{2}\left(640\theta^4-287\theta^3+377\theta^2+119\theta+11\right)-2^{16} x^{3}\left(5121\theta^4+4908\theta^3+5213\theta^2+2484\theta+503\right)+2^{23} 13 x^{4}\left(441\theta^4+1074\theta^3+1207\theta^2+670\theta+148\right)-2^{34} 13^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, -880, -180992, -12537584, ...
--> OEIS
Normalized instanton numbers (n0=1): -336, -30306, -4761360, -962369202, -225176272240, ... ; Common denominator:...

Discriminant

\(-(128z-1)(32768z^2-208z+1)(-1+832z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 832}\)\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 357/5.04

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7

New Number: 5.106 |  AESZ: 360  |  Superseeker: 3169/17 16293835/17  |  Hash: 502b9ea354d34405e6925ab32d7f1cd2  

Degree: 5

\(17^{2} \theta^4+17 x\left(10622\theta^4-19904\theta^3-13913\theta^2-3961\theta-510\right)+3^{2} x^{2}\left(1596891\theta^4-10821444\theta^3+10580847\theta^2+6358884\theta+1355036\right)-3^{5} x^{3}\left(5472387\theta^4-81131922\theta^3-52565469\theta^2-9898488\theta+1434596\right)+2^{2} 3^{8} 127 x^{4}\left(318018\theta^4+157911\theta^3-445563\theta^2-476706\theta-130792\right)-2^{2} 3^{12} 5 127^{2} x^{5}(5\theta+3)(5\theta+4)(5\theta+6)(5\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 414, -73680, -4205250, ...
--> OEIS
Normalized instanton numbers (n0=1): 3169/17, -723497/68, 16293835/17, -1870341966/17, 251152956621/17, ... ; Common denominator:...

Discriminant

\(-(2278125z^3-33831z^2+182z-1)(17+6858z)^2\)

Local exponents

\(-\frac{ 17}{ 6858}\)\(0\) ≈\(0.001817-0.005986I\) ≈\(0.001817+0.005986I\) ≈\(0.011217\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 5}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 4}{ 5}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 6}{ 5}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 7}{ 5}\)

Note:

This is operator "5.106" from ...

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8

New Number: 5.107 |  AESZ: 364  |  Superseeker: 11/5 71/5  |  Hash: c5b4bc60bc9d39ea420bd49fad182557  

Degree: 5

\(5^{2} \theta^4-5 x\left(553\theta^4+722\theta^3+611\theta^2+250\theta+40\right)+2^{6} x^{2}\left(1914\theta^4+4722\theta^3+5519\theta^2+3010\theta+610\right)-2^{12} x^{3}\left(685\theta^4+2400\theta^3+3466\theta^2+2220\theta+500\right)+2^{19} x^{4}(2\theta+1)(30\theta^3+105\theta^2+122\theta+46)-2^{25} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 120, 2240, 50680, ...
--> OEIS
Normalized instanton numbers (n0=1): 11/5, -8/5, 71/5, 738, 26841/5, ... ; Common denominator:...

Discriminant

\(-(32768z^3-2560z^2+85z-1)(-5+64z)^2\)

Local exponents

\(0\) ≈\(0.023029\) ≈\(0.027548-0.023797I\) ≈\(0.027548+0.023797I\)\(\frac{ 5}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.107" from ...

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9

New Number: 5.108 |  AESZ: 365  |  Superseeker: 4 1268  |  Hash: f84624e83cd4eb2cc90693bd5627efcf  

Degree: 5

\(\theta^4-2^{2} x\left(99\theta^4+78\theta^3+65\theta^2+26\theta+4\right)+2^{6} x^{2}\left(938\theta^4+1382\theta^3+1269\theta^2+554\theta+92\right)-2^{10} x^{3}\left(4171\theta^4+8736\theta^3+8690\theta^2+3948\theta+680\right)+2^{15} 5 x^{4}(2\theta+1)(418\theta^3+951\theta^2+846\theta+260)-2^{19} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 720, 44800, 3245200, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 107/2, 1268, 89439/4, 396908, ... ; Common denominator:...

Discriminant

\(-(108z-1)(2048z^2-128z+1)(-1+80z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 2}\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 80}\)\(\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.108" from ...

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10

New Number: 5.109 |  AESZ: 373  |  Superseeker: 50 68472  |  Hash: 8b0fbfc0016c3fb02fd42d4ff919e0f8  

Degree: 5

\(\theta^4-2 x\left(190\theta^4+308\theta^3+227\theta^2+73\theta+9\right)+2^{2} x^{2}\left(4780\theta^4+6304\theta^3+2395\theta^2+642\theta+135\right)-2^{4} 3 x^{3}\left(6700\theta^4+8472\theta^3+7607\theta^2+3615\theta+648\right)+2^{7} 3^{2} x^{4}(2\theta+1)(760\theta^3+1464\theta^2+1211\theta+375)-2^{10} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1782, 276660, 52396470, ...
--> OEIS
Normalized instanton numbers (n0=1): 50, 1299, 68472, 5536032, 555252324, ... ; Common denominator:...

Discriminant

\(-(-1+324z)(24z-1)^2(4z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 324}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(2\)\(4\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.109" from ...

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11

New Number: 5.10 |  AESZ: 59  |  Superseeker: 30/7 124  |  Hash: f47563daeb0f7328bd675f13cfb84a55  

Degree: 5

\(7^{2} \theta^4-2 7 x\left(257\theta^4+520\theta^3+435\theta^2+175\theta+28\right)+2^{2} x^{2}\left(13497\theta^4+55536\theta^3+81222\theta^2+50337\theta+11396\right)-2^{3} x^{3}\left(17201\theta^4+114996\theta^3+248466\theta^2+202629\theta+55412\right)-2^{4} x^{4}\left(5762\theta^4+29668\theta^3+48150\theta^2+31741\theta+7412\right)-2^{5} 3 x^{5}(4\theta+5)(3\theta+2)(3\theta+4)(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 144, 3680, 114400, ...
--> OEIS
Normalized instanton numbers (n0=1): 30/7, 129/14, 124, 72129/56, 130434/7, ... ; Common denominator:...

Discriminant

\(-(4z-1)(16z-1)(54z-1)(7+2z)^2\)

Local exponents

\(-\frac{ 7}{ 2}\)\(0\)\(\frac{ 1}{ 54}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.10" from ...

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12

New Number: 5.110 |  AESZ: 377  |  Superseeker: 32/3 6752/3  |  Hash: 4b8e1b4341fae957e1766a0071de5ba5  

Degree: 5

\(3^{2} \theta^4-2^{3} 3 x\left(61\theta^4+74\theta^3+58\theta^2+21\theta+3\right)+2^{4} x^{2}\left(3883\theta^4+5356\theta^3+3451\theta^2+1278\theta+228\right)-2^{7} x^{3}\left(8067\theta^4+13410\theta^3+12875\theta^2+6336\theta+1236\right)+2^{14} x^{4}\left(413\theta^4+1069\theta^3+1206\theta^2+658\theta+140\right)-2^{19} 3 x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 264, 13760, 873640, ...
--> OEIS
Normalized instanton numbers (n0=1): 32/3, 731/6, 6752/3, 355219/6, 5936896/3, ... ; Common denominator:...

Discriminant

\(-(4z-1)(108z-1)(8z-1)(-3+64z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 3}{ 64}\)\(\frac{ 1}{ 8}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.110" from ...

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13

New Number: 5.111 |  AESZ: 380  |  Superseeker: 12 2320  |  Hash: 85214e3836a67470a05358a4d38fb124  

Degree: 5

\(\theta^4-2 x\left(60\theta^4+90\theta^3+68\theta^2+23\theta+3\right)+2^{2} x^{2}\left(313\theta^4-398\theta^3-1417\theta^2-1033\theta-252\right)+2^{3} x^{3}\left(654\theta^4+5064\theta^3+3574\theta^2+129\theta-405\right)-2^{4} 5 x^{4}\left(628\theta^4-40\theta^3-1699\theta^2-1661\theta-480\right)-2^{6} 3 5^{2} x^{5}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 246, 13020, 832950, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, 511/4, 2320, 63507, 2180312, ... ; Common denominator:...

Discriminant

\(-(108z-1)(4z+1)^2(10z-1)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 10}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(3\)\(1\)
\(1\)\(0\)\(2\)\(4\)\(\frac{ 7}{ 6}\)

Note:

This is operator "5.111" from ...

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14

New Number: 5.112 |  AESZ: 395  |  Superseeker: 4 940  |  Hash: 2d13c01eaf16983977dfb0325c5f376e  

Degree: 5

\(\theta^4-2^{2} x\theta(22\theta^3+8\theta^2+5\theta+1)+2^{5} x^{2}\left(34\theta^4-152\theta^3-265\theta^2-163\theta-36\right)+2^{8} x^{3}\left(142\theta^4+600\theta^3+335\theta^2-39\theta-54\right)-2^{11} 3 x^{4}\left(68\theta^4-56\theta^3-295\theta^2-261\theta-72\right)-2^{15} 3^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 72, 1728, 72360, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 60, 940, 19091, 463904, ... ; Common denominator:...

Discriminant

\(-(16z+1)(8z+1)(64z-1)(-1+24z)^2\)

Local exponents

\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.112" from ...

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15

New Number: 5.113 |  AESZ: 403  |  Superseeker: -29/5 -1481/5  |  Hash: 492c8a69e87d470c87b9557834f0fc5b  

Degree: 5

\(5^{2} \theta^4+5 x\left(487\theta^4+878\theta^3+709\theta^2+270\theta+40\right)+2^{5} x^{2}\left(1013\theta^4+2639\theta^3+2943\theta^2+1520\theta+280\right)-2^{8} x^{3}\left(2169\theta^4+14880\theta^3+30789\theta^2+22440\theta+5240\right)-2^{12} x^{4}(2\theta+1)(518\theta^3+2397\theta^2+2940\theta+1048)-2^{16} 3 x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 216, -8000, 359800, ...
--> OEIS
Normalized instanton numbers (n0=1): -29/5, 229/5, -1481/5, 43173/5, -155267, ... ; Common denominator:...

Discriminant

\(-(27z+1)(1024z^2-64z-1)(5+16z)^2\)

Local exponents

\(-\frac{ 5}{ 16}\)\(-\frac{ 1}{ 27}\)\(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(3\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(4\)\(2\)\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.113" from ...

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16

New Number: 5.114 |  AESZ: 412  |  Superseeker: -1312 -127846048  |  Hash: 4a9870395db313fa368bbafcfc6a7435  

Degree: 5

\(\theta^4-2^{4} x\left(560\theta^4-32\theta^3+56\theta^2+72\theta+15\right)+2^{15} x^{2}\left(896\theta^4+272\theta^3+604\theta^2+196\theta+21\right)-2^{24} 3^{2} x^{3}\left(288\theta^4+352\theta^3+364\theta^2+164\theta+29\right)+2^{35} 3^{3} x^{4}(2\theta+1)(16\theta^3+32\theta^2+28\theta+9)-2^{46} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 118032, 72810240, 50454043920, ...
--> OEIS
Normalized instanton numbers (n0=1): -1312, -301048, -127846048, -70845744192, -45645879602784, ... ; Common denominator:...

Discriminant

\(-(-1+768z)(3072z-1)^2(1024z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 3072}\)\(\frac{ 1}{ 1024}\)\(\frac{ 1}{ 768}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(4\)\(1\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as double octic D.O.256

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17

New Number: 5.115 |  AESZ: 413  |  Superseeker: -3843 -2715123387  |  Hash: 2cc16ba9e49744872ae72bfd6b36d064  

Degree: 5

\(\theta^4-3^{2} x\left(2835\theta^4-162\theta^3+261\theta^2+342\theta+68\right)+2^{2} 3^{9} x^{2}\left(3024\theta^4+918\theta^3+1977\theta^2+606\theta+64\right)-2^{2} 3^{16} x^{3}\left(5832\theta^4+7128\theta^3+7137\theta^2+3087\theta+524\right)+2^{4} 3^{25} x^{4}(2\theta+1)(72\theta^3+144\theta^2+121\theta+36)-2^{6} 3^{31} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 612, 836244, 1455469200, 2860801391700, ...
--> OEIS
Normalized instanton numbers (n0=1): -3843, -9668061/4, -2715123387, -3984527414448, -6798579266503881, ... ; Common denominator:...

Discriminant

\(-(-1+2187z)(8748z-1)^2(2916z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 8748}\)\(\frac{ 1}{ 2916}\)\(\frac{ 1}{ 2187}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(4\)\(1\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.115" from ...

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18

New Number: 5.116 |  AESZ: 414  |  Superseeker: -22432 -425234532128  |  Hash: 973fceefe183415b5d0e15e5a0bd12f5  

Degree: 5

\(\theta^4-2^{4} x\left(8960\theta^4-512\theta^3+736\theta^2+992\theta+183\right)+2^{19} x^{2}\left(14336\theta^4+4352\theta^3+9008\theta^2+2544\theta+261\right)-2^{32} 3^{2} x^{3}\left(4608\theta^4+5632\theta^3+5408\theta^2+2208\theta+351\right)+2^{49} 3^{3} x^{4}(2\theta+1)^2(32\theta^2+48\theta+27)-2^{64} 3^{3} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2928, 21778704, 210543916800, 2314156512099600, ...
--> OEIS
Normalized instanton numbers (n0=1): -22432, -74752296, -425234532128, -3159114140624208, -27288043319514722784, ... ; Common denominator:...

Discriminant

\(-(-1+12288z)(49152z-1)^2(16384z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 49152}\)\(\frac{ 1}{ 16384}\)\(\frac{ 1}{ 12288}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(4\)\(1\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.116" from ...

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19

New Number: 5.117 |  AESZ: 415  |  Superseeker: -1083168 -32204207145918624  |  Hash: 480ebcdf255c1fe6ad1cac7896e482fa  

Degree: 5

\(\theta^4-2^{4} 3^{2} x\left(45360\theta^4-2592\theta^3+3096\theta^2+4392\theta+695\right)+2^{15} 3^{9} x^{2}\left(24192\theta^4+7344\theta^3+14340\theta^2+3516\theta+335\right)-2^{24} 3^{16} x^{3}\left(23328\theta^4+28512\theta^3+25740\theta^2+9540\theta+1325\right)+2^{35} 3^{25} x^{4}(2\theta+1)(144\theta^3+288\theta^2+212\theta+45)-2^{46} 3^{31} x^{5}(2\theta+1)(3\theta+1)(3\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 100080, 32388472080, 14040210456518400, 6986717866758049635600, ...
--> OEIS
Normalized instanton numbers (n0=1): -1083168, -148187321784, -32204207145918624, -9094164085684648886400, -2986312705706358630596895840, ... ; Common denominator:...

Discriminant

\(-(-1+559872z)(2239488z-1)^2(746496z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 2239488}\)\(\frac{ 1}{ 746496}\)\(\frac{ 1}{ 559872}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(4\)\(1\)\(2\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.117" from ...

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20

New Number: 5.118 |  AESZ: 416  |  Superseeker: 1312 127846048  |  Hash: 3ae3241981d64d9c9cc38b29974fa202  

Degree: 5

\(\theta^4+2^{4} x\left(560\theta^4-32\theta^3+56\theta^2+72\theta+15\right)+2^{15} x^{2}\left(896\theta^4+272\theta^3+604\theta^2+196\theta+21\right)+2^{24} 3^{2} x^{3}\left(288\theta^4+352\theta^3+364\theta^2+164\theta+29\right)+2^{35} 3^{3} x^{4}(2\theta+1)(16\theta^3+32\theta^2+28\theta+9)+2^{46} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -240, 118032, -72810240, 50454043920, ...
--> OEIS
Normalized instanton numbers (n0=1): 1312, -301376, 127846048, -70845744192, 45645879602784, ... ; Common denominator:...

Discriminant

\((1+768z)(1024z+1)^2(3072z+1)^2\)

Local exponents

\(-\frac{ 1}{ 768}\)\(-\frac{ 1}{ 1024}\)\(-\frac{ 1}{ 3072}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)
\(2\)\(1\)\(4\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.118" from ...

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21

New Number: 5.119 |  AESZ:  |  Superseeker: 138 278872  |  Hash: 61d7a82df3cf3c429b6286bc39ccb426  

Degree: 5

\(\theta^4-2 3 x\left(42\theta^4+204\theta^3+145\theta^2+43\theta+5\right)-2^{2} x^{2}\left(26932\theta^4+40768\theta^3-6943\theta^2-8482\theta-1635\right)-2^{4} 3^{2} 5 x^{3}\left(11156\theta^4+3848\theta^3+1777\theta^2+901\theta+180\right)-2^{7} 3^{3} 5^{2} x^{4}(2\theta+1)(304\theta^3+356\theta^2+97\theta-15)+2^{10} 3^{3} 5^{5} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 4530, 1074900, 312527250, ...
--> OEIS
Normalized instanton numbers (n0=1): 138, 1139, 278872, 21493934, 3832908140, ... ; Common denominator:...

Discriminant

\((4z-1)(500z-1)(12z+1)(1+120z)^2\)

Local exponents

\(-\frac{ 1}{ 12}\)\(-\frac{ 1}{ 120}\)\(0\)\(\frac{ 1}{ 500}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.119" from ...

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22

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

Degree: 5

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

Maple   LaTex

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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23

New Number: 5.120 |  AESZ:  |  Superseeker: 48 171120  |  Hash: 3eb6b52ff225f7b2f94716d73344b578  

Degree: 5

\(\theta^4-2^{4} x\left(41\theta^4+34\theta^3+25\theta^2+8\theta+1\right)+2^{10} x^{2}\left(126\theta^4+108\theta^3+33\theta^2+6\theta+1\right)-2^{14} x^{3}\left(564\theta^4+504\theta^3+429\theta^2+195\theta+34\right)+2^{21} x^{4}(2\theta+1)(44\theta^3+78\theta^2+59\theta+17)-2^{28} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1680, 298240, 64975120, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 2286, 171120, 17540830, 2229934864, ... ; Common denominator:...

Discriminant

\(-(16z-1)(4096z^2-384z+1)(-1+128z)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\)\(\frac{ 1}{ 128}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- x 821--1

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24

New Number: 5.121 |  AESZ:  |  Superseeker: 272 1143760  |  Hash: 36da1ed5dd29b416116a3ac9f4b4c4da  

Degree: 5

\(\theta^4-2^{4} x\left(17\theta^4+130\theta^3+91\theta^2+26\theta+3\right)-2^{11} x^{2}\left(150\theta^4+204\theta^3-163\theta^2-110\theta-21\right)-2^{16} x^{3}\left(564\theta^4-648\theta^3-595\theta^2-189\theta-18\right)+2^{24} x^{4}(2\theta+1)(52\theta^3+66\theta^2+29\theta+3)-2^{32} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 10128, 3521280, 1516853520, ...
--> OEIS
Normalized instanton numbers (n0=1): 272, -142, 1143760, 76778666, 28997783216, ... ; Common denominator:...

Discriminant

\(-(16z-1)(16384z^2-768z+1)(1+256z)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0\)\(\frac{ 3}{ 128}-\frac{ 1}{ 64}\sqrt{ 2}\)\(\frac{ 3}{ 128}+\frac{ 1}{ 64}\sqrt{ 2}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- x 182--1

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25

New Number: 5.122 |  AESZ:  |  Superseeker: 19 18641/3  |  Hash: 7cc1a0411f21ffd93f1a9f6468627432  

Degree: 5

\(\theta^4+x\left(119\theta^4-194\theta^3-143\theta^2-46\theta-6\right)-2^{2} 3^{2} x^{2}\left(46\theta^4+748\theta^3+379\theta^2+150\theta+27\right)-2^{2} 3^{4} x^{3}\left(2164\theta^4+6264\theta^3+7421\theta^2+4131\theta+846\right)-2^{5} 3^{8} x^{4}(2\theta+1)(76\theta^3+222\theta^2+235\theta+85)-2^{8} 3^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 162, 7620, 334530, ...
--> OEIS
Normalized instanton numbers (n0=1): 19, -170, 18641/3, -163734, 6446745, ... ; Common denominator:...

Discriminant

\(-(81z-1)(1296z^2+56z+1)(1+72z)^2\)

Local exponents

\(-\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I\)\(-\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I\)\(-\frac{ 1}{ 72}\)\(0\)\(\frac{ 1}{ 81}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- 623--1

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26

New Number: 5.123 |  AESZ:  |  Superseeker: 96 266464  |  Hash: b9a4a4eae678c9ce13a407517f92c30e  

Degree: 5

\(\theta^4+2^{4} x\left(28\theta^4-40\theta^3-28\theta^2-8\theta-1\right)+2^{13} x^{2}\left(6\theta^4-12\theta^3+17\theta^2+10\theta+2\right)+2^{18} x^{3}\left(12\theta^4+72\theta^3+35\theta^2-3\theta-4\right)+2^{26} x^{4}(2\theta+1)(4\theta^3-6\theta^2-15\theta-7)-2^{34} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, -240, -24320, 2075920, ...
--> OEIS
Normalized instanton numbers (n0=1): 96, -4200, 266464, -20295944, 1778341408, ... ; Common denominator:...

Discriminant

\(-(64z-1)(16384z^2+1)(1+256z)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0-\frac{ 1}{ 128}I\)\(0\)\(0+\frac{ 1}{ 128}I\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- x 812--1

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27

New Number: 5.124 |  AESZ:  |  Superseeker: 307 4336475  |  Hash: 782c2ecb639a2462baac59dfaf17de0e  

Degree: 5

\(\theta^4-x\left(1081\theta^4+2594\theta^3+1807\theta^2+510\theta+54\right)-2^{2} 3^{2} x^{2}\left(4686\theta^4+4908\theta^3-2213\theta^2-1738\theta-293\right)-2^{2} 3^{4} x^{3}\left(18484\theta^4-3336\theta^3-4883\theta^2-1101\theta-50\right)+2^{5} 3^{7} x^{4}(2\theta+1)(92\theta^3+134\theta^2+79\theta+17)-2^{8} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 54, 19746, 11427300, 8114331330, ...
--> OEIS
Normalized instanton numbers (n0=1): 307, 19410, 4336475, 1291393654, 484327566649, ... ; Common denominator:...

Discriminant

\(-(z-1)(1296z^2-1224z+1)(1+72z)^2\)

Local exponents

\(-\frac{ 1}{ 72}\)\(0\)\(\frac{ 17}{ 36}-\frac{ 1}{ 3}\sqrt{ 2}\)\(\frac{ 17}{ 36}+\frac{ 1}{ 3}\sqrt{ 2}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- x 263--1

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28

New Number: 5.125 |  AESZ:  |  Superseeker: 229 10128562/3  |  Hash: ce147b64cc67dee1204a2d16f6ac4210  

Degree: 5

\(\theta^4-x\left(1217\theta^4+2050\theta^3+1437\theta^2+412\theta+44\right)+2^{5} x^{2}(\theta+1)(4550\theta^3-186\theta^2-899\theta-171)-2^{8} x^{3}\left(18484\theta^4+3192\theta^3+1005\theta^2+1107\theta+258\right)+2^{14} x^{4}(2\theta+1)(268\theta^3+414\theta^2+267\theta+65)-2^{20} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 44, 14532, 7508960, 4749338020, ...
--> OEIS
Normalized instanton numbers (n0=1): 229, 18542, 10128562/3, 938391582, 323686899951, ... ; Common denominator:...

Discriminant

\(-(z-1)(1024z^2-1088z+1)(-1+64z)^2\)

Local exponents

\(0\)\(\frac{ 17}{ 32}-\frac{ 3}{ 8}\sqrt{ 2}\)\(\frac{ 1}{ 64}\)\(1\)\(\frac{ 17}{ 32}+\frac{ 3}{ 8}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- x 362--1

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29

New Number: 5.126 |  AESZ:  |  Superseeker: 110 729096  |  Hash: 511069e41e6328e47a1ea996049096b4  

Degree: 5

\(\theta^4-x\left(881\theta^4+1222\theta^3+878\theta^2+267\theta+30\right)+3 x^{2}\left(50601\theta^4+60024\theta^3+17189\theta^2+280\theta-340\right)-3^{2} 5 x^{3}\left(195867\theta^4+207846\theta^3+142719\theta^2+49068\theta+6316\right)+2^{2} 3^{4} 5^{2} x^{4}(3\theta+1)(3\theta+2)(1902\theta^2+1767\theta+386)+2^{2} 3^{6} 5^{4} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

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Coefficients of the holomorphic solution: 1, 30, 6210, 2004240, 789638850, ...
--> OEIS
Normalized instanton numbers (n0=1): 110, 12935/2, 729096, 247828991/2, 26419290920, ... ; Common denominator:...

Discriminant

\((675z-1)(27z-1)(z+1)(-1+90z)^2\)

Local exponents

\(-1\)\(0\)\(\frac{ 1}{ 675}\)\(\frac{ 1}{ 90}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(\frac{ 4}{ 3}\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Operator London 18.
B-Incarnation: Laurent-polynomial.

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30

New Number: 5.127 |  AESZ:  |  Superseeker: 957/10 1581774/5  |  Hash: 8b1c933faa73767af598d82d1e214624  

Degree: 5

\(2^{2} 5^{2} \theta^4-2 3 5 x\left(1812\theta^4+3858\theta^3+2799\theta^2+870\theta+100\right)-3 x^{2}\left(293697\theta^4-124614\theta^3-930203\theta^2-562390\theta-95700\right)+3^{3} x^{3}\left(62631\theta^4+977400\theta^3+677140\theta^2+104550\theta-6300\right)+3^{5} 5 13 x^{4}(3\theta+1)(3\theta+2)(308\theta^2-16\theta-231)-3^{8} 13^{2} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

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Coefficients of the holomorphic solution: 1, 30, 5130, 1369200, 446603850, ...
--> OEIS
Normalized instanton numbers (n0=1): 957/10, 32493/10, 1581774/5, 423123141/10, 14142369903/2, ... ; Common denominator:...

Discriminant

\(-(6561z^3-4320z^2+567z-1)(10+117z)^2\)

Local exponents

\(-\frac{ 10}{ 117}\)\(0\) ≈\(0.001788\) ≈\(0.178154\) ≈\(0.478494\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Operator London 9.
B-Incarnation as Laurent-polynomial.

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