Calabi-Yau differential operator database v.3.0 - Search results

Summary

You searched for: Spectrum0=1/2,1,1,3/2

Your search produced 47 matches
1-30 31-47

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31

New Number: 5.75 | AESZ: 298 | Superseeker: 205/9 97622/9 | Hash: e52d50673ec5c795512e2bc3e1017b12

Degree: 5

\(3^{4} \theta^4-3^{2} x\left(1993\theta^4+3218\theta^3+2437\theta^2+828\theta+108\right)+2^{5} x^{2}\left(17486\theta^4+25184\theta^3+12239\theta^2+2790\theta+297\right)-2^{8} x^{3}\left(23620\theta^4+34776\theta^3+28905\theta^2+12447\theta+2106\right)+2^{15} x^{4}(2\theta+1)(340\theta^3+618\theta^2+455\theta+129)-2^{22} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 12, 708, 63840, 6989220, ...
--> OEIS
Normalized instanton numbers (n₀=1): 205/9, 3206/9, 97622/9, 496806, 254037095/9, ... ; Common denominator:...

Discriminant

\(-(z-1)(1024z^2-192z+1)(-9+128z)^2\)

Local exponents

\(0\) \(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\) \(\frac{ 9}{ 128}\) \(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\) \(1\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(0\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(0\) \(1\) \(3\) \(1\) \(1\) \(1\)
\(0\) \(2\) \(4\) \(2\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.75" from ...

32

New Number: 5.77 | AESZ: 307 | Superseeker: 69/11 8883/11 | Hash: 3a2dcd4c59d8fa5b7c57250efeecba62

Degree: 5

\(11^{2} \theta^4-3 11 x\left(361\theta^4+530\theta^3+419\theta^2+154\theta+22\right)+2^{2} x^{2}\left(47008\theta^4+45904\theta^3-3251\theta^2-17094\theta-4851\right)-2^{4} 3 x^{3}\left(31436\theta^4+86856\theta^3+160363\theta^2+122133\theta+30294\right)+2^{9} 3^{2} x^{4}(2\theta+1)(1252\theta^3+5442\theta^2+6767\theta+2625)-2^{14} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 6, 162, 6540, 314370, ...
--> OEIS
Normalized instanton numbers (n₀=1): 69/11, 620/11, 8883/11, 171916/11, 4334406/11, ... ; Common denominator:...

Discriminant

\(-(81z-1)(64z^2+1)(-11+96z)^2\)

Local exponents

\(0-\frac{ 1}{ 8}I\) \(0\) \(0+\frac{ 1}{ 8}I\) \(\frac{ 1}{ 81}\) \(\frac{ 11}{ 96}\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(0\) \(1\) \(1\) \(1\) \(1\)
\(1\) \(0\) \(1\) \(1\) \(3\) \(1\)
\(2\) \(0\) \(2\) \(2\) \(4\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.77" from ...

33

New Number: 5.78 | AESZ: 308 | Superseeker: 248/29 38708/29 | Hash: 94e96c5d238b2d22a633f4e05ec1ae9f

Degree: 5

\(29^{2} \theta^4-2 29 x\left(1318\theta^4+2336\theta^3+1806\theta^2+638\theta+87\right)-2^{2} x^{2}\left(90996\theta^4+744384\theta^3+1267526\theta^2+791584\theta+168345\right)+2^{2} 5^{2} x^{3}\left(34172\theta^4+77256\theta^3-46701\theta^2-110403\theta-36540\right)+2^{4} 5^{4} x^{4}(2\theta+1)(68\theta^3+1842\theta^2+2899\theta+1215)-2^{6} 5^{7} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 6, 210, 9780, 551250, ...
--> OEIS
Normalized instanton numbers (n₀=1): 248/29, 2476/29, 38708/29, 940480/29, 27926248/29, ... ; Common denominator:...

Discriminant

\(-(2000z^3+1024z^2+84z-1)(-29+100z)^2\)

Local exponents

≈\(-0.40534\) ≈\(-0.117186\) \(0\) ≈\(0.010526\) \(\frac{ 29}{ 100}\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(0\) \(1\) \(1\) \(1\)
\(1\) \(1\) \(0\) \(1\) \(3\) \(1\)
\(2\) \(2\) \(0\) \(2\) \(4\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.78" from ...

34

New Number: 5.80 | AESZ: 311 | Superseeker: 25/13 875/13 | Hash: 8219f3f4bd56f6c2b2cc3ab9093b65d1

Degree: 5

\(13^{2} \theta^4-13 x\left(327\theta^4+1038\theta^3+857\theta^2+338\theta+52\right)-2^{4} x^{2}\left(12848\theta^4+42008\theta^3+52082\theta^2+28548\theta+5707\right)-2^{11} x^{3}\left(122\theta^4-1872\theta^3-6341\theta^2-5772\theta-1547\right)+2^{16} x^{4}(2\theta+1)(76\theta^3+426\theta^2+570\theta+227)+2^{23} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 4, 84, 1840, 56980, ...
--> OEIS
Normalized instanton numbers (n₀=1): 25/13, 1359/52, 875/13, 36572/13, 256800/13, ... ; Common denominator:...

Discriminant

\((8192z^3-896z^2-35z+1)(13+64z)^2\)

Local exponents

\(-\frac{ 13}{ 64}\) ≈\(-0.045147\) \(0\) ≈\(0.020117\) ≈\(0.134405\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(0\) \(1\) \(1\) \(1\)
\(3\) \(1\) \(0\) \(1\) \(1\) \(1\)
\(4\) \(2\) \(0\) \(2\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.80" from ...

35

New Number: 5.82 | AESZ: 313 | Superseeker: 45 43531 | Hash: f8bfe82988e14680bdb775a3ce956216

Degree: 5

\(\theta^4-x(\theta+1)(285\theta^3+321\theta^2+128\theta+18)-2 x^{2}\left(1640\theta^4+1322\theta^3-1337\theta^2-1178\theta-240\right)-2^{2} 3^{2} x^{3}\left(213\theta^4-256\theta^3-286\theta^2-80\theta-5\right)+2^{3} 3^{3} x^{4}(2\theta+1)(22\theta^3+37\theta^2+24\theta+6)+2^{4} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 18, 1662, 236340, 40943070, ...
--> OEIS
Normalized instanton numbers (n₀=1): 45, 845, 43531, 3091112, 273471538, ... ; Common denominator:...

Discriminant

\((z-1)(48z^2+296z-1)(6z+1)^2\)

Local exponents

\(-\frac{ 37}{ 12}-\frac{ 7}{ 6}\sqrt{ 7}\) \(-\frac{ 1}{ 6}\) \(0\) \(-\frac{ 37}{ 12}+\frac{ 7}{ 6}\sqrt{ 7}\) \(1\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(0\) \(1\) \(1\) \(1\)
\(1\) \(3\) \(0\) \(1\) \(1\) \(1\)
\(2\) \(4\) \(0\) \(2\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.82" from ...

36

New Number: 5.86 | AESZ: 320 | Superseeker: 741/11 138745 | Hash: d19e7569ce62abdd5393977835e411a9

Degree: 5

\(11^{2} \theta^4-11 x\left(4843\theta^4+8918\theta^3+6505\theta^2+2046\theta+242\right)+2^{2} x^{2}\left(312184\theta^4+343456\theta^3-23371\theta^2-73942\theta-14883\right)-2^{4} x^{3}\left(511972\theta^4+256344\theta^3+144969\theta^2+78639\theta+15642\right)+2^{11} x^{4}(2\theta+1)(1964\theta^3+3078\theta^2+1853\theta+419)-2^{18} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 22, 2850, 568300, 138119170, ...
--> OEIS
Normalized instanton numbers (n₀=1): 741/11, 22232/11, 138745, 157326644/11, 19999995398/11, ... ; Common denominator:...

Discriminant

\(-(z-1)(64z^2-416z+1)(-11+128z)^2\)

Local exponents

\(0\) \(\frac{ 13}{ 4}-\frac{ 15}{ 8}\sqrt{ 3}\) \(\frac{ 11}{ 128}\) \(1\) \(\frac{ 13}{ 4}+\frac{ 15}{ 8}\sqrt{ 3}\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(0\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(0\) \(1\) \(3\) \(1\) \(1\) \(1\)
\(0\) \(2\) \(4\) \(2\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.86" from ...

37

New Number: 5.87 | AESZ: 321 | Superseeker: 35/9 3002/9 | Hash: b786027c217dd5d5c5abac7b1ecc570b

Degree: 5

\(3^{4} \theta^4-3^{2} x\left(191\theta^4+862\theta^3+683\theta^2+252\theta+36\right)-2^{5} x^{2}\left(7225\theta^4+24835\theta^3+30634\theta^2+16173\theta+3069\right)-2^{8} x^{3}\left(13251\theta^4+35856\theta^3+27641\theta^2+6966\theta+180\right)-2^{12} 5 x^{4}(2\theta+1)(314\theta^3+363\theta^2+68\theta-31)+2^{16} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 4, 132, 4000, 179620, ...
--> OEIS
Normalized instanton numbers (n₀=1): 35/9, 261/4, 3002/9, 126800/9, 1727129/9, ... ; Common denominator:...

Discriminant

\((32z+1)(32z^2-71z+1)(9+80z)^2\)

Local exponents

\(-\frac{ 9}{ 80}\) \(-\frac{ 1}{ 32}\) \(0\) \(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) \(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(0\) \(1\) \(1\) \(1\)
\(3\) \(1\) \(0\) \(1\) \(1\) \(1\)
\(4\) \(2\) \(0\) \(2\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.87" from ...

38

New Number: 5.89 | AESZ: 329 | Superseeker: 48 25200 | Hash: 8c526b3b825d5ad6a3d0fb83ee4e6059

Degree: 5

\(\theta^4-2^{4} x\left(8\theta^4+34\theta^3+25\theta^2+8\theta+1\right)-2^{8} x^{2}\left(87\theta^4+150\theta^3+32\theta^2-2\theta-1\right)-2^{12} x^{3}\left(202\theta^4+240\theta^3+211\theta^2+102\theta+19\right)-2^{16} 3 x^{4}(2\theta+1)(22\theta^3+45\theta^2+38\theta+12)-2^{20} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 16, 1200, 136960, 19010320, ...
--> OEIS
Normalized instanton numbers (n₀=1): 48, 270, 25200, 968066, 80892688, ... ; Common denominator:...

Discriminant

\(-(16384z^3+3072z^2+224z-1)(1+48z)^2\)

Local exponents

≈\(-0.095858-0.072741I\) ≈\(-0.095858+0.072741I\) \(-\frac{ 1}{ 48}\) \(0\) ≈\(0.004215\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(1\) \(0\) \(1\) \(1\)
\(1\) \(1\) \(3\) \(0\) \(1\) \(1\)
\(2\) \(2\) \(4\) \(0\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.89" from ...

39

New Number: 5.90 | AESZ: 330 | Superseeker: 352 3284448 | Hash: ba5b66d5fe92237e6416a117563571e9

Degree: 5

\(\theta^4+2^{4} x\left(112\theta^4-64\theta^3-32\theta^2+1\right)+2^{14} x^{2}\left(56\theta^4-64\theta^3+3\theta^2-10\theta-4\right)+2^{20} x^{3}\left(32\theta^4-384\theta^3-436\theta^2-264\theta-55\right)-2^{29} 3 x^{4}(2\theta+1)(10\theta+7)(2\theta^2+4\theta+3)-2^{38} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, -16, 4368, -344320, 107445520, ...
--> OEIS
Normalized instanton numbers (n₀=1): 352, -23368, 3284448, -578330224, 120252731680, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 1}{ 256}\) \(-\frac{ 1}{ 768}\) \(0\) \(\frac{ 1}{ 256}\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\) \(1\) \(0\) \(1\) \(1\)
\(\frac{ 1}{ 2}\) \(3\) \(0\) \(1\) \(1\)
\(1\) \(4\) \(0\) \(2\) \(\frac{ 3}{ 2}\)

Note:

B-Incarnation as double octic D.O.20

40

New Number: 5.91 | AESZ: 331 | Superseeker: 112 186800 | Hash: a30093d8c1ab2f66122cef8935b79efb

Degree: 5

\(\theta^4+2^{4} x\left(18\theta^4-48\theta^3-33\theta^2-9\theta-1\right)-2^{9} x^{2}\left(86\theta^4+512\theta^3+125\theta^2+45\theta+10\right)-2^{14} x^{3}\left(1138\theta^4+2040\theta^3+1883\theta^2+879\theta+157\right)-2^{19} 7 x^{4}(2\theta+1)(186\theta^3+375\theta^2+317\theta+100)-2^{27} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 16, 1488, 183040, 27611920, ...
--> OEIS
Normalized instanton numbers (n₀=1): 112, -2242, 186800, -11675813, 1250599376, ... ; Common denominator:...

Discriminant

\(-(32z+1)(256z-1)(64z+1)(1+224z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\) \(-\frac{ 1}{ 64}\) \(-\frac{ 1}{ 224}\) \(0\) \(\frac{ 1}{ 256}\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(1\) \(0\) \(1\) \(1\)
\(1\) \(1\) \(3\) \(0\) \(1\) \(1\)
\(2\) \(2\) \(4\) \(0\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.91" from ...

41

New Number: 5.93 | AESZ: 333 | Superseeker: 1 2668/3 | Hash: dc274781605ee4262d8745e3fa3a8057

Degree: 5

\(\theta^4+x\theta^2(71\theta^2-2\theta-1)+2^{3} 3 x^{2}\left(154\theta^4+334\theta^3+461\theta^2+248\theta+48\right)+2^{6} 3^{2} x^{3}(5\theta+3)(31\theta^3+39\theta^2-25\theta-21)+2^{9} 3^{4} x^{4}(2\theta+1)(2\theta^3-33\theta^2-56\theta-24)-2^{12} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 0, -72, 1440, 22680, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, -66, 2668/3, -2774, -167786, ... ; Common denominator:...

Discriminant

\(-(9z-1)(2304z^2+32z+1)(1+24z)^2\)

Local exponents

\(-\frac{ 1}{ 24}\) \(-\frac{ 1}{ 144}-\frac{ 1}{ 72}\sqrt{ 2}I\) \(-\frac{ 1}{ 144}+\frac{ 1}{ 72}\sqrt{ 2}I\) \(0\) \(\frac{ 1}{ 9}\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(1\) \(0\) \(1\) \(1\)
\(3\) \(1\) \(1\) \(0\) \(1\) \(1\)
\(4\) \(2\) \(2\) \(0\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.93" from ...

42

New Number: 5.95 | AESZ: 338 | Superseeker: -140/3 -66092 | Hash: eb4f6d6e59fafa4e794fb664dbdeab3f

Degree: 5

\(3^{2} \theta^4+2^{2} 3 x\left(278\theta^4+424\theta^3+311\theta^2+99\theta+12\right)+2^{5} x^{2}\left(5210\theta^4+3944\theta^3-2635\theta^2-2433\theta-492\right)+2^{8} x^{3}\left(8190\theta^4-3528\theta^3-3991\theta^2-585\theta+114\right)-2^{11} 11 x^{4}(2\theta+1)(86\theta^3+57\theta^2-39\theta-32)+2^{15} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, -16, 1608, -243520, 44810920, ...
--> OEIS
Normalized instanton numbers (n₀=1): -140/3, 1293, -66092, 5236719, -1553321056/3, ... ; Common denominator:...

Discriminant

\((2048z^3-640z^2+312z+1)(3+88z)^2\)

Local exponents

\(-\frac{ 3}{ 88}\) ≈\(-0.003184\) \(0\) ≈\(0.157842-0.358378I\) ≈\(0.157842+0.358378I\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(0\) \(1\) \(1\) \(1\)
\(3\) \(1\) \(0\) \(1\) \(1\) \(1\)
\(4\) \(2\) \(0\) \(2\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.95" from ...

43

New Number: 5.99 | AESZ: 342 | Superseeker: -4 3856/9 | Hash: 009a00efdd065ef9ea58db999d777786

Degree: 5

\(\theta^4+2 x\left(50\theta^4+64\theta^3+52\theta^2+20\theta+3\right)+2^{2} 3 x^{2}\left(380\theta^4+992\theta^3+1166\theta^2+612\theta+117\right)+2^{2} 3^{2} x^{3}\left(2140\theta^4+5832\theta^3+5651\theta^2+2349\theta+360\right)+2^{4} 3^{6} x^{4}(2\theta+1)(20\theta^3+42\theta^2+35\theta+11)+2^{6} 3^{7} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, -6, 54, 660, -69930, ...
--> OEIS
Normalized instanton numbers (n₀=1): -4, -16, 3856/9, -3864, -20784, ... ; Common denominator:...

Discriminant

\((3888z^3+2592z^2+76z+1)(1+12z)^2\)

Local exponents

≈\(-0.636595\) \(-\frac{ 1}{ 12}\) ≈\(-0.015036-0.01334I\) ≈\(-0.015036+0.01334I\) \(0\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(1\) \(1\) \(0\) \(1\)
\(1\) \(3\) \(1\) \(1\) \(0\) \(1\)
\(2\) \(4\) \(2\) \(2\) \(0\) \(\frac{ 3}{ 2}\)

Note:

This is operator "5.99" from ...

44

New Number: 7.11 | AESZ: | Superseeker: -8 -3784/3 | Hash: cb1bf6566f9c1a0dbfe98fb55f81944c

Degree: 7

\(\theta^4+2^{2} x\left(23\theta^4-34\theta^3-30\theta^2-13\theta-2\right)+2^{5} x^{2}\left(177\theta^4+108\theta^3+577\theta^2+518\theta+116\right)+2^{10} x^{3}\left(355\theta^4+960\theta^3+1178\theta^2+139\theta-44\right)+2^{15} x^{4}\left(451\theta^4+1228\theta^3+997\theta^2+489\theta+103\right)+2^{20} x^{5}\left(285\theta^4+720\theta^3+766\theta^2+410\theta+83\right)+2^{26} x^{6}(2\theta+1)(20\theta^3+50\theta^2+49\theta+17)+2^{31} x^{7}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 8, -120, -4480, 55720, ...
--> OEIS
Normalized instanton numbers (n₀=1): -8, 43/2, -3784/3, 51036, -1659840, ... ; Common denominator:...

Discriminant

\((8z+1)(32768z^3+3072z^2-12z+1)(32z+1)^3\)

Local exponents

\(-\frac{ 1}{ 8}\) ≈\(-0.100423\) \(-\frac{ 1}{ 32}\) \(0\) ≈\(0.003336-0.01711I\) ≈\(0.003336+0.01711I\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(2\) \(0\) \(1\) \(1\) \(1\)
\(1\) \(1\) \(3\) \(0\) \(1\) \(1\) \(1\)
\(2\) \(2\) \(5\) \(0\) \(2\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "7.11" from ...

45

New Number: 8.30 | AESZ: 314 | Superseeker: 229/4 297111/4 | Hash: 893692ba7eb3effcbc0c3b48d405456a

Degree: 8

\(2^{4} \theta^4-2^{2} x\left(1282\theta^4+2618\theta^3+1909\theta^2+600\theta+72\right)-3^{2} x^{2}\left(9503\theta^4+26810\theta^3+31755\theta^2+15944\theta+2936\right)+3^{4} x^{3}\left(15627\theta^4-18288\theta^3-91412\theta^2-53256\theta-9688\right)+2 3^{6} x^{4}\left(15106\theta^4+20300\theta^3-20421\theta^2-23443\theta-5907\right)-2^{2} 3^{8} x^{5}\left(2072\theta^4-18256\theta^3-2563\theta^2+4626\theta+1495\right)-2^{2} 3^{10} x^{6}\left(6204\theta^4+360\theta^3-281\theta^2+1017\theta+434\right)-2^{5} 3^{12} x^{7}(2\theta+1)(100\theta^3+162\theta^2+95\theta+21)+2^{8} 3^{14} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 18, 1926, 310860, 61060230, ...
--> OEIS
Normalized instanton numbers (n₀=1): 229/4, 1293, 297111/4, 6150238, 2540085295/4, ... ; Common denominator:...

Discriminant

\((z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2\)

Local exponents

≈\(-0.168156-0.022431I\) ≈\(-0.168156+0.022431I\) \(\frac{ 1}{ 144}-\frac{ 1}{ 144}\sqrt{ 129}\) \(0\) \(\frac{ 1}{ 18}2^(\frac{ 1}{ 3})+\frac{ 1}{ 36}2^(\frac{ 2}{ 3})-\frac{ 1}{ 9}\) \(\frac{ 1}{ 144}+\frac{ 1}{ 144}\sqrt{ 129}\) \(1\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(1\) \(0\) \(1\) \(1\) \(1\) \(1\)
\(1\) \(1\) \(3\) \(0\) \(1\) \(3\) \(1\) \(1\)
\(2\) \(2\) \(4\) \(0\) \(2\) \(4\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "8.30" from ...

46

New Number: 8.48 | AESZ: | Superseeker: 359/13 393749/13 | Hash: de7301c14448dbf584c01cc3722d0e58

Degree: 8

\(13^{2} \theta^4-13 x\left(5249\theta^4+4930\theta^3+3687\theta^2+1222\theta+156\right)+2^{4} 3 x^{2}\left(175601\theta^4+188064\theta^3+90243\theta^2+19422\theta+1547\right)-2^{7} x^{3}\left(3336915\theta^4+3777024\theta^3+2377229\theta^2+746148\theta+94185\right)+2^{10} x^{4}\left(8591694\theta^4+11872968\theta^3+7381951\theta^2+2132674\theta+236280\right)-2^{12} x^{5}\left(15421829\theta^4+18326342\theta^3+7032841\theta^2+833608\theta-2718\right)+2^{16} 3^{2} x^{6}\left(334895\theta^4+615600\theta^3+867965\theta^2+590850\theta+138536\right)-2^{19} 3^{4} 7 x^{7}(\theta+1)(2\theta+1)(646\theta^2+1715\theta+1044)+2^{22} 3^{6} 7^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 12, 852, 94800, 12860820, ...
--> OEIS
Normalized instanton numbers (n₀=1): 359/13, 9162/13, 393749/13, 23364200/13, 1734245216/13, ... ; Common denominator:...

Discriminant

\((1-261z+6896z^2-6656z^3+36864z^4)(13-928z+4032z^2)^2\)

Local exponents

\(0\) \(\frac{ 29}{ 252}-\frac{ 1}{ 504}\sqrt{ 2545}\) \(\frac{ 29}{ 252}+\frac{ 1}{ 504}\sqrt{ 2545}\) \(#ND+#NDI\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(0\) \(1\) \(1\) \(1\) \(1\)
\(0\) \(3\) \(3\) \(1\) \(1\)
\(0\) \(4\) \(4\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "8.48" from ...

47

New Number: 8.49 | AESZ: | Superseeker: 56/3 17704/3 | Hash: 4fa01cbee2fc74e3a62e00386e6fa1c0

Degree: 8

\(3^{2} \theta^4-2^{2} 3 x\left(29\theta^4+178\theta^3+134\theta^2+45\theta+6\right)-2^{5} x^{2}\left(2233\theta^4+2536\theta^3+607\theta^2+132\theta+12\right)-2^{10} x^{3}\left(1274\theta^4+7425\theta^3+20002\theta^2+12717\theta+2670\right)+2^{13} x^{4}\left(2539\theta^4-36538\theta^3-52775\theta^2-31122\theta-6192\right)+2^{20} x^{5}\left(1617\theta^4+9771\theta^3+4484\theta^2-674\theta-556\right)+2^{25} x^{6}\left(1135\theta^4+4272\theta^3+3439\theta^2+858\theta+16\right)-2^{31} 3 x^{7}(2\theta+1)(110\theta^3+225\theta^2+184\theta+57)+2^{37} 3^{2} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Coefficients of the holomorphic solution: 1, 8, 264, 16640, 1130920, ...
--> OEIS
Normalized instanton numbers (n₀=1): 56/3, -83/6, 17704/3, -25024/3, 13408832/3, ... ; Common denominator:...

Discriminant

\((4z-1)(131072z^3+2048z^2+88z-1)(48z+1)^2(64z-3)^2\)

Local exponents

\(-\frac{ 1}{ 48}\) ≈\(-0.01214-0.027095I\) ≈\(-0.01214+0.027095I\) \(0\) ≈\(0.008655\) \(\frac{ 3}{ 64}\) \(\frac{ 1}{ 4}\) \(\infty\)
\(0\) \(0\) \(0\) \(0\) \(0\) \(0\) \(0\) \(\frac{ 1}{ 2}\)
\(1\) \(1\) \(1\) \(0\) \(1\) \(1\) \(1\) \(1\)
\(3\) \(1\) \(1\) \(0\) \(1\) \(3\) \(1\) \(1\)
\(4\) \(2\) \(2\) \(0\) \(2\) \(4\) \(2\) \(\frac{ 3}{ 2}\)

Note:

This is operator "8.49" from ...

1-30 31-47