Calabi-Yau differential operator database v.3

New Number: 6.10 |  AESZ:  |  Superseeker: 23 16723  |  Hash: 23025d094839fb9d8e76076bd9a0bfa7  

Degree: 6

\(\theta^4-x\left(254\theta^4+508\theta^3+391\theta^2+137\theta+18\right)+x^{2}\left(4657\theta^4+18628\theta^3+27265\theta^2+17274\theta+3672\right)-2^{2} 3 x^{3}\left(2920\theta^4+17520\theta^3+36833\theta^2+31659\theta+8235\right)+2^{3} 3^{4} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{5} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{6} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1242, 138420, 18954810, ...
--> OEIS
Normalized instanton numbers (n₀=1): 23, 462, 16723, 923487, 61874817, ... ; Common denominator:...

Discriminant

\((3z-1)(3888z^3-1944z^2+243z-1)(4z-1)^2\)

Local exponents

\(0\)	≈\(0.004259\)	≈\(0.215449\)	\(\frac{ 1}{ 4}\)	≈\(0.280292\)	\(\frac{ 1}{ 3}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 5}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 7}{ 2}\)
\(0\)	\(2\)	\(2\)	\(1\)	\(2\)	\(2\)	\(\frac{ 11}{ 2}\)

Note:

This is operator "6.10" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

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 ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.12 |  AESZ:  |  Superseeker: 19 2263  |  Hash: 86993fb7955dee498aab7e103a0f457e  

Degree: 6

\(\theta^4-x\left(33\theta^4+258\theta^3+199\theta^2+70\theta+10\right)-2^{2} x^{2}\left(1380\theta^4+2400\theta^3-173\theta^2-634\theta-185\right)-2^{4} x^{3}\left(7325\theta^4+2670\theta^3-668\theta^2-1035\theta-290\right)-2^{7} x^{4}\left(897\theta^4-3504\theta^3-10058\theta^2-8492\theta-2435\right)+2^{12} x^{5}(\theta+1)^2(858\theta^2+1566\theta+745)-2^{17} 5^{2} x^{6}(\theta+1)^2(\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 310, 14860, 869590, ...
--> OEIS
Normalized instanton numbers (n₀=1): 19, -18, 2263, 4184, 1097345, ... ; Common denominator:...

Discriminant

\(-(z-1)(8z+1)(100z-1)(4z-1)(1+32z)^2\)

Local exponents

\(-\frac{ 1}{ 8}\)	\(-\frac{ 1}{ 32}\)	\(0\)	\(\frac{ 1}{ 100}\)	\(\frac{ 1}{ 4}\)	\(1\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(2\)
\(2\)	\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(2\)

Note:

This is operator "6.12" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.14 |  AESZ:  |  Superseeker: 8 9928/3  |  Hash: 44968de144621e2fa74ce3964a5435f7  

Degree: 6

\(\theta^4-2^{2} x(5\theta^2+5\theta+2)(13\theta^2+13\theta+3)+2^{5} x^{2}\left(533\theta^4+2132\theta^3+3137\theta^2+2010\theta+432\right)-2^{8} 3 x^{3}\left(652\theta^4+3912\theta^3+8229\theta^2+7083\theta+1845\right)+2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{15} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{17} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1224, 96000, 9633960, ...
--> OEIS
Normalized instanton numbers (n₀=1): 8, 471/2, 9928/3, 185385, 6071232, ... ; Common denominator:...

Discriminant

\((12z-1)(24z-1)(2304z^2-192z+1)(-1+16z)^2\)

Local exponents

\(0\)	\(\frac{ 1}{ 24}-\frac{ 1}{ 48}\sqrt{ 3}\)	\(\frac{ 1}{ 24}\)	\(\frac{ 1}{ 16}\)	\(\frac{ 1}{ 24}+\frac{ 1}{ 48}\sqrt{ 3}\)	\(\frac{ 1}{ 12}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 5}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 7}{ 2}\)
\(0\)	\(2\)	\(2\)	\(1\)	\(2\)	\(2\)	\(\frac{ 11}{ 2}\)

Note:

This is operator "6.14" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.15 |  AESZ:  |  Superseeker: 64 76608  |  Hash: 0130ee676bad42a2e117bca3367f8cf0  

Degree: 6

\(\theta^4+2^{4} x\left(56\theta^4+16\theta^3+22\theta^2+14\theta+3\right)+2^{10} x^{2}\left(308\theta^4+272\theta^3+347\theta^2+174\theta+35\right)+2^{18} x^{3}\left(212\theta^4+384\theta^3+473\theta^2+282\theta+69\right)+2^{26} x^{4}\left(77\theta^4+232\theta^3+327\theta^2+226\theta+62\right)+2^{35} x^{5}(7\theta^2+17\theta+13)(\theta+1)^2+2^{42} x^{6}(\theta+1)^2(\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -48, 3088, -231168, 19207440, ...
--> OEIS
Normalized instanton numbers (n₀=1): 64, -1732, 76608, -4429212, 296488640, ... ; Common denominator:...

Discriminant

\((64z+1)^2(128z+1)^2(256z+1)^2\)

Local exponents

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

Note:

This is operator "6.15" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.16 |  AESZ:  |  Superseeker: 2272 434311008  |  Hash: f30ffc268310c175e914066ee270f47b  

Degree: 6

\(\theta^4+2^{4} x\left(448\theta^4-544\theta^3-332\theta^2-60\theta-5\right)+2^{12} x^{2}\left(2576\theta^4-8416\theta^3+2808\theta^2+668\theta+35\right)-2^{20} x^{3}\left(9088\theta^4+5568\theta^3+5392\theta^2+3180\theta+667\right)-2^{28} 3^{2} x^{4}(2\theta+1)(744\theta^3+940\theta^2+798\theta+167)+2^{38} 3^{3} 5 x^{5}(16\theta^2+40\theta+33)(\theta+1)^2+2^{48} 3^{3} 5^{2} x^{6}(\theta+1)^2(\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 80, 30480, 9850112, 4649741584, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2272, -719992, 434311008, -343376572072, 316225589496736, ... ; Common denominator:...

Discriminant

\((768z-1)(256z-1)(256z+1)^2(3840z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)	\(-\frac{ 1}{ 3840}\)	\(0\)	\(\frac{ 1}{ 768}\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(\frac{ 1}{ 2}\)	\(3\)	\(0\)	\(1\)	\(1\)	\(2\)
\(1\)	\(4\)	\(0\)	\(2\)	\(2\)	\(2\)

Note:

This is operator "6.16" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.17 |  AESZ:  |  Superseeker: 2 224/9  |  Hash: bbcabbebf6c04783d4ec5d0a5664f174  

Degree: 6

\(\theta^4-x\left(14+73\theta+154\theta^2+162\theta^3+81\theta^4\right)+x^{2}\left(3256+11390\theta+15571\theta^2+9876\theta^3+2469\theta^4\right)-x^{3}\left(162708+457536\theta+476503\theta^2+215994\theta^3+35999\theta^4\right)+2 3 5 x^{4}\left(8837\theta^4+70696\theta^3+200535\theta^2+236572\theta+98316\right)-2^{2} 3^{2} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(151\theta^2+755\theta+850)+2^{3} 3^{3} 5^{3} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 14, 220, 3800, 70840, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -4, 224/9, -112, 4446/5, ... ; Common denominator:...

Discriminant

\((6z-1)(14z-1)(30z-1)(21z-1)(-1+5z)^2\)

Local exponents

\(0\)	\(\frac{ 1}{ 30}\)	\(\frac{ 1}{ 21}\)	\(\frac{ 1}{ 14}\)	\(\frac{ 1}{ 6}\)	\(\frac{ 1}{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(2\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(4\)
\(0\)	\(2\)	\(2\)	\(2\)	\(2\)	\(1\)	\(5\)

Note:

This is operator "6.17" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.18 |  AESZ:  |  Superseeker: 3 64  |  Hash: b127e33287ed87a366c178fc4678cdc4  

Degree: 6

\(\theta^4-x\left(18+94\theta+199\theta^2+210\theta^3+105\theta^4\right)+2 x^{2}\left(2095\theta^4+8380\theta^3+13298\theta^2+9836\theta+2850\right)-2^{2} 3^{2} x^{3}\left(2310\theta^4+13860\theta^3+30739\theta^2+29847\theta+10763\right)+2^{3} 3^{3} x^{4}\left(4044\theta^4+32352\theta^3+91997\theta^2+109172\theta+45693\right)-2^{4} 3^{3} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(61\theta^2+305\theta+345)+2^{5} 3^{5} 5^{2} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 348, 7320, 168840, ...
--> OEIS
Normalized instanton numbers (n₀=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...

Discriminant

\((6z-1)(15z-1)(14z-1)(42z-1)(18z-1)(10z-1)\)

Local exponents

\(0\)	\(\frac{ 1}{ 42}\)	\(\frac{ 1}{ 18}\)	\(\frac{ 1}{ 15}\)	\(\frac{ 1}{ 14}\)	\(\frac{ 1}{ 10}\)	\(\frac{ 1}{ 6}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(2\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(4\)
\(0\)	\(2\)	\(2\)	\(2\)	\(2\)	\(2\)	\(2\)	\(5\)

Note:

This is operator "6.18" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.19 |  AESZ:  |  Superseeker: 2/23 27/23  |  Hash: 38a2cec750ea75c0fd64ef0a4286a801  

Degree: 6

\(23^{6} \theta^4+2 23^{5} x\left(224\theta^4+448\theta^3+449\theta^2+225\theta+45\right)+2^{2} 23^{4} x^{2}\left(6271\theta^4+25084\theta^3+40435\theta^2+30702\theta+9035\right)-23^{3} x^{3}\left(8650483\theta^4+51902898\theta^3+114278033\theta^2+109271058\theta+38421000\right)-2^{2} 5 23^{2} x^{4}\left(37482007\theta^4+299856056\theta^3+854051365\theta^2+1017357012\theta+426206376\right)-2^{4} 3 5^{2} 7 11 19 23 x^{5}(\theta+4)(\theta+1)(10889\theta^2+54445\theta+62408)-2^{6} 3^{2} 5^{3} 7^{2} 11^{2} 19^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -90/23, 13390/529, -2157300/12167, 398261070/279841, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2/23, 18/23, 27/23, 136/23, 395/23, ... ; Common denominator:...

Discriminant

\(-(228z+23)(21z+23)(140z-23)(44z+23)(5225z^2+6785z+529)\)

Local exponents

\(-\frac{ 1357}{ 2090}-\frac{ 529}{ 2090}\sqrt{ 5}\)	\(-\frac{ 23}{ 21}\)	\(-\frac{ 23}{ 44}\)	\(-\frac{ 23}{ 228}\)	\(-\frac{ 1357}{ 2090}+\frac{ 529}{ 2090}\sqrt{ 5}\)	\(0\)	\(\frac{ 23}{ 140}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(2\)
\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(4\)
\(2\)	\(2\)	\(2\)	\(2\)	\(2\)	\(0\)	\(2\)	\(5\)

Note:

This is operator "6.19" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.1 |  AESZ:  |  Superseeker: -2 -70/3  |  Hash: 28ce9053a8969d292554c4f160bc469e  

Degree: 6

\(\theta^4-x\left(112\theta^4+224\theta^3+280\theta^2+168\theta+39\right)+3 x^{2}\left(1568\theta^4+6272\theta^3+11538\theta^2+10532\theta+3923\right)-2^{3} x^{3}\left(11552\theta^4+69312\theta^3+172218\theta^2+204750\theta+96687\right)+x^{4}\left(872704\theta^4+6981632\theta^3+21940576\theta^2+31909248\theta+18039321\right)-2^{7} 3^{2} x^{5}(784\theta^2+3920\theta+5547)(2\theta+5)^2+2^{14} 3^{4} x^{6}(2\theta+5)(2\theta+7)(\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 39, 2541/2, 80689/2, 10329363/8, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2, -9/2, -70/3, -145, -1060, ... ; Common denominator:...

Discriminant

\((4z-1)^2(36z-1)^2(16z-1)^2\)

Local exponents

\(0\)	\(\frac{ 1}{ 36}\)	\(\frac{ 1}{ 16}\)	\(\frac{ 1}{ 4}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 5}{ 2}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(3\)
\(0\)	\(1\)	\(1\)	\(1\)	\(3\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 7}{ 2}\)

Note:

YY-pullback of AESZ:130

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.20 |  AESZ:  |  Superseeker: 0 -1/3  |  Hash: 5169c67af7361bf7e6467dabea9612bd  

Degree: 6

\(\theta^4+x\left(11\theta+26\theta^3+2+13\theta^4+24\theta^2\right)-x^{2}(141\theta^2+282\theta+296)(\theta+1)^2-2 x^{3}(\theta+2)(\theta+1)(407\theta^2+1221\theta+654)+2^{2} 7 x^{4}(\theta+3)(\theta+1)(389\theta^2+1556\theta+1460)-2^{3} 3 7^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+166)+2^{5} 3 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2, 28, -224, 2464, ...
--> OEIS
Normalized instanton numbers (n₀=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...

Discriminant

\((-1+2z)(4z-1)(21z^2-9z+1)(1+14z)^2\)

Local exponents

\(-\frac{ 1}{ 14}\)	\(0\)	\(\frac{ 3}{ 14}-\frac{ 1}{ 42}\sqrt{ 3}I\)	\(\frac{ 3}{ 14}+\frac{ 1}{ 42}\sqrt{ 3}I\)	\(\frac{ 1}{ 4}\)	\(\frac{ 1}{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(2\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(4\)
\(1\)	\(0\)	\(2\)	\(2\)	\(2\)	\(2\)	\(5\)

Note:

This is operator "6.20" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.21 |  AESZ:  |  Superseeker: 1 11  |  Hash: 319d6b2f1541de5252840442cc6f8dcd  

Degree: 6

\(\theta^4+x\left(6+27\theta+47\theta^2+40\theta^3+20\theta^4\right)-x^{2}(143\theta^2+286\theta+120)(\theta+1)^2-2 3^{2} x^{3}(\theta+2)(\theta+1)(291\theta^2+873\theta+766)-2^{2} 3^{3} 5 x^{4}(\theta+3)(\theta+1)(41\theta^2+164\theta+196)+2^{3} 3^{3} 5^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+150)+2^{5} 3^{5} 5^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 60, -480, 5040, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...

Discriminant

\((6z-1)(15z-1)(9z+1)(12z+1)(10z+1)^2\)

Local exponents

\(-\frac{ 1}{ 9}\)	\(-\frac{ 1}{ 10}\)	\(-\frac{ 1}{ 12}\)	\(0\)	\(\frac{ 1}{ 15}\)	\(\frac{ 1}{ 6}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(1\)	\(1\)	\(2\)
\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(1\)	\(1\)	\(4\)
\(2\)	\(1\)	\(2\)	\(0\)	\(2\)	\(2\)	\(5\)

Note:

This is operator "6.21" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.22 |  AESZ: 376  |  Superseeker: 5/4 35/2  |  Hash: 24fee66b67ff1a8a852f7a562f7665c1  

Degree: 6

\(2^{12} \theta^4-2^{10} x\left(106\theta^4+212\theta^3+183\theta^2+77\theta+13\right)+2^{8} x^{2}\left(19\theta^4+76\theta^3-43\theta^2-238\theta-141\right)+2^{6} 3 x^{3}\left(2988\theta^4+17928\theta^3+39970\theta^2+39234\theta+14267\right)+2^{4} 3^{3} x^{4}\left(309\theta^4+2472\theta^3+7618\theta^2+10696\theta+5311\right)-2^{2} 3^{3} 5 7^{2} x^{5}(\theta+4)(\theta+1)(22\theta^2+110\theta+123)-3^{5} 5^{2} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 13/4, 489/16, 25429/64, 1591057/256, ...
--> OEIS
Normalized instanton numbers (n₀=1): 5/4, 57/16, 35/2, 459/4, 3615/4, ... ; Common denominator:...

Discriminant

\(-(7z+4)(5z-4)(105z-4)(9z-4)(4+3z)^2\)

Local exponents

\(-\frac{ 4}{ 3}\)	\(-\frac{ 4}{ 7}\)	\(0\)	\(\frac{ 4}{ 105}\)	\(\frac{ 4}{ 9}\)	\(\frac{ 4}{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(\frac{ 1}{ 3}\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(2\)
\(\frac{ 2}{ 3}\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(4\)
\(1\)	\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(5\)

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.23 |  AESZ:  |  Superseeker: 24/29 284/29  |  Hash: 83e67651e4ea5ee123354c2989ff7460  

Degree: 6

\(29^{6} \theta^4-2 29^{5} x(2\theta^2+2\theta+1)(152\theta^2+152\theta+41)-2^{2} 29^{4} x^{2}\left(4104\theta^4+16416\theta^3+23786\theta^2+14740\theta+3267\right)+2^{2} 29^{3} x^{3}\left(517492\theta^4+3104952\theta^3+6923513\theta^2+6798255\theta+2465928\right)-2^{4} 3 29^{2} x^{4}\left(3104764\theta^4+24838112\theta^3+70273625\theta^2+82389604\theta+33870303\right)+2^{8} 3^{2} 19 23 29 x^{5}(\theta+4)(\theta+1)(5408\theta^2+27040\theta+30585)-2^{12} 3^{4} 19^{2} 23^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 82/29, 18498/841, 5789116/24389, 2183601010/707281, ...
--> OEIS
Normalized instanton numbers (n₀=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...

Discriminant

\(-(92z+29)(1195632z^3-467248z^2+548332z-24389)(24z-29)^2\)

Local exponents

\(-\frac{ 29}{ 92}\)	\(0\)	≈\(0.046074\)	≈\(0.172361-0.642668I\)	≈\(0.172361+0.642668I\)	\(\frac{ 29}{ 24}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(2\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(4\)
\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(1\)	\(5\)

Note:

This is operator "6.23" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.24 |  AESZ:  |  Superseeker: 1/3 5/3  |  Hash: aebe18b25bf886c4483ce54370c0fcbe  

Degree: 6

\(3^{6} \theta^4+3^{5} x\left(7\theta^2+7\theta+2\right)-3^{4} x^{2}\left(1095\theta^4+4380\theta^3+7227\theta^2+5694\theta+1760\right)-2 3^{3} x^{3}(\theta+2)(\theta+1)(4165\theta^2+12495\theta+11148)+2^{2} 3^{2} x^{4}(47961\theta^2+191844\theta+148643)(\theta+2)^2+2^{3} 3^{2} 5 7 17 73 x^{5}(\theta+1)(\theta+2)(\theta+3)(\theta+4)-2^{5} 5^{2} 7^{2} 17^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2/3, 112/9, -8/27, 29500/81, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...

Discriminant

\(-(7z-3)(34z-3)(17z+3)(20z+3)(10z-3)(14z+3)\)

Local exponents

\(-\frac{ 3}{ 14}\)	\(-\frac{ 3}{ 17}\)	\(-\frac{ 3}{ 20}\)	\(0\)	\(\frac{ 3}{ 34}\)	\(\frac{ 3}{ 10}\)	\(\frac{ 3}{ 7}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(2\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(4\)
\(2\)	\(2\)	\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(5\)

Note:

This is operator "6.24" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.25 |  AESZ:  |  Superseeker: -11/13 -385/39  |  Hash: 47050ee8c9a3655ea77ba8df999a7459  

Degree: 6

\(13^{6} \theta^4+13^{5} x(48\theta^2+48\theta+11)(3\theta^2+3\theta+1)-13^{4} x^{2}\left(20766\theta^4+83064\theta^3+129875\theta^2+93622\theta+26145\right)+13^{3} x^{3}\left(1368558\theta^4+8211348\theta^3+18296041\theta^2+17937057\theta+6515866\right)-13^{2} x^{4}\left(48595515\theta^4+388764120\theta^3+1109406129\theta^2+1327511556\theta+560261752\right)+7 13 31 229 x^{5}(\theta+4)(\theta+1)(19935\theta^2+99675\theta+113198)-2^{2} 7^{2} 31^{2} 229^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -11/13, 2149/169, -279167/2197, 42641173/28561, ...
--> OEIS
Normalized instanton numbers (n₀=1): -11/13, 131/52, -385/39, 672/13, -4437/13, ... ; Common denominator:...

Discriminant

\(-(28z-13)(1603z^2-559z+169)(220069z^3-108004z^2+36335z+2197)\)

Local exponents

≈\(-0.051688\)	\(0\)	\(\frac{ 559}{ 3206}-\frac{ 507}{ 3206}\sqrt{ 3}I\)	\(\frac{ 559}{ 3206}+\frac{ 507}{ 3206}\sqrt{ 3}I\)	≈\(0.27123-0.345803I\)	≈\(0.27123+0.345803I\)	\(\frac{ 13}{ 28}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(2\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(4\)
\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(2\)	\(2\)	\(5\)

Note:

This is operator "6.25" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.26 |  AESZ:  |  Superseeker: 58/43 1024/43  |  Hash: 38ef7a13fad0ecbb53ba25dafe26b113  

Degree: 6

\(43^{2} \theta^4-43 x\left(830\theta^4+1750\theta^3+1434\theta^2+559\theta+86\right)-x^{2}\left(1342738\theta^3+368510+1383525\theta+354697\theta^4+2007703\theta^2\right)-x^{3}\left(2348230+6951423\theta+774028\theta^4+3928308\theta^3+7763518\theta^2\right)-3 5 x^{4}\left(44423\theta^4+264028\theta^3+597368\theta^2+599643\theta+221430\right)-2 3^{2} 5^{2} x^{5}(\theta+2)(\theta+1)(533\theta^2+1694\theta+1290)-3^{3} 5^{3} x^{6}(3\theta+5)(3\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 26, 344, 5650, ...
--> OEIS
Normalized instanton numbers (n₀=1): 58/43, 211/43, 1024/43, 7544/43, 64880/43, ... ; Common denominator:...

Discriminant

\(-(5z+1)(27z-1)(15z+43)^2(z+1)^2\)

Local exponents

\(-\frac{ 43}{ 15}\)	\(-1\)	\(-\frac{ 1}{ 5}\)	\(0\)	\(\frac{ 1}{ 27}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(1\)	\(\frac{ 4}{ 3}\)
\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(1\)	\(\frac{ 5}{ 3}\)
\(4\)	\(1\)	\(2\)	\(0\)	\(2\)	\(2\)

Note:

This is operator "6.26" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.27 |  AESZ:  |  Superseeker: 6/17 33/17  |  Hash: af5aea32756746d4fc4931e4da73756b  

Degree: 6

\(17^{6} \theta^4-17^{5} x\left(427\theta^4+854\theta^3+814\theta^2+387\theta+74\right)+17^{4} x^{2}\left(47239\theta^4+188956\theta^3+300763\theta^2+223614\theta+64536\right)-2 3 17^{3} x^{3}\left(237751\theta^4+1426506\theta^3+3169919\theta^2+3090480\theta+1104868\right)-2^{2} 3^{2} 17^{2} x^{4}\left(1549605\theta^4+12396840\theta^3+35038211\theta^2+40978124\theta+16802716\right)+2^{3} 3^{3} 7 17 139 x^{5}(\theta+4)(\theta+1)(3737\theta^2+18685\theta+21310)-2^{5} 3^{4} 7^{2} 139^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 74/17, 7788/289, 1036400/4913, 164905648/83521, ...
--> OEIS
Normalized instanton numbers (n₀=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...

Discriminant

\(-(28z+17)(278z-17)(8757z^2-2805z+289)(6z-17)^2\)

Local exponents

\(-\frac{ 17}{ 28}\)	\(0\)	\(\frac{ 17}{ 278}\)	\(\frac{ 935}{ 5838}-\frac{ 289}{ 5838}\sqrt{ 3}I\)	\(\frac{ 935}{ 5838}+\frac{ 289}{ 5838}\sqrt{ 3}I\)	\(\frac{ 17}{ 6}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(2\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(4\)
\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(1\)	\(5\)

Note:

This is operator "6.27" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.28 |  AESZ:  |  Superseeker: 32/3 14279/9  |  Hash: 62617eacb39580484b6f6cca4374260e  

Degree: 6

\(3^{6} \theta^4-2 3^{5} x\left(93\theta^4+186\theta^3+122\theta^2+29\theta+1\right)-2^{2} 3^{4} x^{2}\left(5958\theta^4+23832\theta^3+36111\theta^2+24558\theta+6497\right)-3^{3} x^{3}\left(999379\theta^4+5996274\theta^3+13111103\theta^2+12350076\theta+4316124\right)-2^{2} 3^{2} 11 x^{4}\left(455691\theta^4+3645528\theta^3+10306397\theta^2+12061364\theta+4978244\right)-2^{2} 3^{2} 5 11^{2} 19 x^{5}(\theta+4)(\theta+1)(1431\theta^2+7155\theta+7978)-2^{6} 5^{2} 11^{3} 19^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2/3, 1732/9, 213524/27, 37218544/81, ...
--> OEIS
Normalized instanton numbers (n₀=1): 32/3, 284/3, 14279/9, 118940/3, 1226784, ... ; Common denominator:...

Discriminant

\(-(16z+3)(19z+3)(5225z^2+795z-9)(3+22z)^2\)

Local exponents

\(-\frac{ 3}{ 16}\)	\(-\frac{ 159}{ 2090}-\frac{ 81}{ 2090}\sqrt{ 5}\)	\(-\frac{ 3}{ 19}\)	\(-\frac{ 3}{ 22}\)	\(0\)	\(-\frac{ 159}{ 2090}+\frac{ 81}{ 2090}\sqrt{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(1\)	\(0\)	\(0\)	\(1\)	\(2\)
\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(4\)
\(2\)	\(2\)	\(2\)	\(1\)	\(0\)	\(2\)	\(5\)

Note:

This is operator "6.28" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.41 |  AESZ:  |  Superseeker: 161/13 26946/13  |  Hash: a18253e410f284ecdac465808ec8a6e1  

Degree: 6

\(13^{6} \theta^4-13^{5} x\left(1382\theta^4+2764\theta^3+2109\theta^2+727\theta+96\right)-13^{4} x^{2}\left(104743\theta^4+418972\theta^3+637899\theta^2+437854\theta+116928\right)-2^{2} 13^{3} x^{3}\left(746084\theta^4+4476504\theta^3+9750459\theta^2+9107109\theta+3146850\right)-2^{5} 7 13^{2} x^{4}\left(180214\theta^4+1441712\theta^3+4063657\theta^2+4720932\theta+1930533\right)-2^{9} 3 5 7^{2} 13 x^{5}(\theta+4)(\theta+1)(688\theta^2+3440\theta+3823)-2^{13} 3^{2} 5^{2} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 96/13, 49776/169, 35502696/2197, 30531314880/28561, ...
--> OEIS
Normalized instanton numbers (n₀=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...

Discriminant

\(-(-169+18720z+22400z^2)(8z+13)^2(21z+13)^2\)

Local exponents

\(-\frac{ 13}{ 8}\)	\(-\frac{ 117}{ 280}-\frac{ 169}{ 560}\sqrt{ 2}\)	\(-\frac{ 13}{ 21}\)	\(0\)	\(-\frac{ 117}{ 280}+\frac{ 169}{ 560}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(0\)	\(1\)	\(0\)	\(0\)	\(1\)	\(2\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(4\)
\(1\)	\(2\)	\(1\)	\(0\)	\(2\)	\(5\)

Note:

This is operator "6.41" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.2 |  AESZ:  |  Superseeker: -8 -1552/3  |  Hash: fd7b14f2d0f2a78723588771a9b1a984  

Degree: 6

\(\theta^4-x\left(280\theta^4+560\theta^3+686\theta^2+406\theta+93\right)+3 x^{2}\left(9296\theta^4+37184\theta^3+66322\theta^2+58276\theta+20863\right)-2 x^{3}\left(594560\theta^4+3567360\theta^3+8664912\theta^2+9941616\theta+4484205\right)+x^{4}\left(21204736\theta^4+169637888\theta^3+520783424\theta^2+726030592\theta+387696585\right)-2^{3} 3^{2} 5^{2} x^{5}(4\theta+9)(4\theta+11)(4144\theta^2+20720\theta+28335)+2^{4} 3^{4} 5^{4} x^{6}(4\theta+9)(4\theta+11)(4\theta+13)(4\theta+15)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 93, 15717/2, 1345795/2, 473123715/8, ...
--> OEIS
Normalized instanton numbers (n₀=1): -8, -44, -1552/3, -8044, -138528, ... ; Common denominator:...

Discriminant

\((100z-1)^2(4z-1)^2(36z-1)^2\)

Local exponents

\(0\)	\(\frac{ 1}{ 100}\)	\(\frac{ 1}{ 36}\)	\(\frac{ 1}{ 4}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 9}{ 4}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 4}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 13}{ 4}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 15}{ 4}\)

Note:

This is operator "6.2" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.30 |  AESZ:  |  Superseeker: 4 436  |  Hash: bc45bbf252bff0ad05b31f8e076f64cb  

Degree: 6

\(\theta^4+2^{2} x(\theta^2+\theta+1)(18\theta^2+18\theta+5)+2^{4} x^{2}\left(39\theta^4+156\theta^3+337\theta^2+362\theta+135\right)-2^{6} x^{3}\left(1124\theta^4+6744\theta^3+14434\theta^2+12954\theta+4329\right)-2^{8} 3 7 x^{4}\left(445\theta^4+3560\theta^3+10034\theta^2+11656\theta+4779\right)-2^{10} 3^{2} 7^{2} x^{5}(\theta+4)(\theta+1)(62\theta^2+310\theta+345)-2^{12} 3^{4} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -20, 480, -11264, 285712, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...

Discriminant

\(-(-1+36z)(12z+1)^2(28z+1)^3\)

Local exponents

\(-\frac{ 1}{ 12}\)	\(-\frac{ 1}{ 28}\)	\(0\)	\(\frac{ 1}{ 36}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(1\)	\(2\)
\(\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 4}\)	\(0\)	\(1\)	\(4\)
\(1\)	\(\frac{ 1}{ 4}\)	\(0\)	\(2\)	\(5\)

Note:

This is operator "6.30" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.31 |  AESZ:  |  Superseeker: 2/3 13/3  |  Hash: fcd8db2a3ad7e58151e501b5872652df  

Degree: 6

\(3^{6} \theta^4+2 3^{5} x\left(7\theta^2+7\theta+2\right)-2^{2} 3^{4} x^{2}\left(465\theta^4+1860\theta^3+3069\theta^2+2418\theta+752\right)-3^{3} x^{3}(\theta+2)(\theta+1)(19327\theta^2+57981\theta+52674)+2^{5} 3^{2} x^{4}(17298\theta^2+69192\theta+54655)(\theta+2)^2+2^{4} 3^{2} 11 31 251 x^{5}(\theta+1)(\theta+2)(\theta+3)(\theta+4)-2^{3} 11^{2} 251^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4/3, 196/9, -604/27, 83956/81, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2/3, 5/3, 13/3, 59/3, 119, ... ; Common denominator:...

Discriminant

\(-(11z-3)(22z+3)(1004z^2+66z-9)(251z^2-33z-9)\)

Local exponents

\(-\frac{ 3}{ 22}\)	\(\frac{ 33}{ 502}-\frac{ 45}{ 502}\sqrt{ 5}\)	\(-\frac{ 33}{ 1004}-\frac{ 45}{ 1004}\sqrt{ 5}\)	\(0\)	\(-\frac{ 33}{ 1004}+\frac{ 45}{ 1004}\sqrt{ 5}\)	\(\frac{ 33}{ 502}+\frac{ 45}{ 502}\sqrt{ 5}\)	\(\frac{ 3}{ 11}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(2\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(4\)
\(2\)	\(2\)	\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(5\)

Note:

This is operator "6.31" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.39 |  AESZ:  |  Superseeker: 8 3784/3  |  Hash: 6429f42cbe18bee944ac13edab1fbbcc  

Degree: 6

\(\theta^4+2^{2} x\left(49\theta^4+98\theta^3+86\theta^2+37\theta+6\right)+2^{5} x^{2}\left(593\theta^4+2372\theta^3+3521\theta^2+2298\theta+504\right)+2^{10} 3 x^{3}\left(332\theta^4+1992\theta^3+4194\theta^2+3618\theta+945\right)+2^{14} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)+2^{18} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{21} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, 648, -11520, -123480, ...
--> OEIS
Normalized instanton numbers (n₀=1): 8, 39/2, 3784/3, 51036, 1659840, ... ; Common denominator:...

Discriminant

\((24z+1)(110592z^3+6912z^2+108z+1)(1+32z)^2\)

Local exponents

≈\(-0.045368\)	\(-\frac{ 1}{ 24}\)	\(-\frac{ 1}{ 32}\)	≈\(-0.008566-0.011222I\)	≈\(-0.008566+0.011222I\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(0\)	\(\frac{ 5}{ 2}\)
\(1\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(0\)	\(\frac{ 7}{ 2}\)
\(2\)	\(2\)	\(1\)	\(2\)	\(2\)	\(0\)	\(\frac{ 11}{ 2}\)

Note:

This is operator "6.39" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.33 |  AESZ:  |  Superseeker: 352 26115552  |  Hash: 0677bb20f37d2fa88bafbc665d5157c1  

Degree: 6

\(\theta^4-2^{4} x\left(96\theta^4+192\theta^3+404\theta^2+308\theta+85\right)+2^{12} x^{2}\left(112\theta^4+448\theta^3+416\theta^2-64\theta-159\right)+2^{20} x^{3}\left(192\theta^4+1152\theta^3+3448\theta^2+5160\theta+3101\right)-2^{28} x^{4}\left(272\theta^4+2176\theta^3+6880\theta^2+10112\theta+5757\right)-2^{38} 3 x^{5}\left(8\theta^4+80\theta^3+315\theta^2+575\theta+407\right)+2^{48} 3^{2} x^{6}\left((\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1360, 1516304, 1522167040, 1444349938960, ...
--> OEIS
Normalized instanton numbers (n₀=1): 352, 60664, 26115552, 16623590600, 13165993300256, ... ; Common denominator:...

Discriminant

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

Local exponents

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

Note:

This is operator "6.33" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.34 |  AESZ:  |  Superseeker: 4/3 -124/81  |  Hash: 1153f8807d42d96ede28f7a8d06c144b  

Degree: 6

\(3^{2} \theta^4-2^{2} 3 x\left(8\theta^4+16\theta^3+27\theta^2+19\theta+5\right)-2^{4} x^{2}\left(272\theta^4+1088\theta^3+1984\theta^2+1792\theta+621\right)+2^{8} x^{3}\left(192\theta^4+1152\theta^3+3448\theta^2+5160\theta+3101\right)+2^{12} x^{4}\left(112\theta^4+896\theta^3+2432\theta^2+2560\theta+753\right)-2^{16} x^{5}\left(96\theta^4+960\theta^3+3860\theta^2+7300\theta+5389\right)+2^{24} x^{6}\left((\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 20/3, 332/3, 13360/27, 966020/81, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...

Discriminant

\((16z-1)^2(16z-3)^2(16z+1)^2\)

Local exponents

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

Note:

This is operator "6.34" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.35 |  AESZ:  |  Superseeker:  |  Hash: de26083962cade55a4938b4011d0008e  

Degree: 6

\(\theta^4-3 x\left(63\theta^4+234\theta^3+247\theta^2+130\theta+28\right)+2 3^{4} x^{2}\left(9\theta^4+522\theta^3+1207\theta^2+1058\theta+356\right)+2^{2} 3^{7} x^{3}\left(135\theta^4+270\theta^3-730\theta^2-1395\theta-696\right)-2^{3} 3^{10} x^{4}\left(63\theta^4+774\theta^3+1372\theta^2+817\theta+88\right)-2^{4} 3^{13} x^{5}\left(72\theta^4+72\theta^3-325\theta^2-629\theta-308\right)+2^{5} 3^{16} x^{6}(3\theta+5)(3\theta+4)(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 84, 7452, 692688, 66448116, ...
--> OEIS
Normalized instanton numbers (n₀=1): 21, -1617/4, 7941, -986355/4, 8179455, ... ; Common denominator:...

Discriminant

\((54z-1)(27z-1)(54z+1)^2(108z-1)^2\)

Local exponents

\(-\frac{ 1}{ 54}\)	\(0\)	\(\frac{ 1}{ 108}\)	\(\frac{ 1}{ 54}\)	\(\frac{ 1}{ 27}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 4}{ 3}\)
\(1\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(4\)	\(0\)	\(\frac{ 3}{ 2}\)	\(2\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

This is operator "6.35" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.36 |  AESZ:  |  Superseeker: 10/7 508/7  |  Hash: b890cacbc73012eb6554263c3ea04707  

Degree: 6

\(7^{2} \theta^4-2 7 x\left(60\theta^4+24\theta^3-9\theta^2-21\theta-7\right)-2^{2} x^{2}\left(6492\theta^4+30192\theta^3+46665\theta^2+30786\theta+7777\right)+2^{4} x^{3}\left(3632\theta^4-27552\theta^3-133920\theta^2-173880\theta-76083\right)+2^{9} x^{4}\left(1776\theta^4+10272\theta^3+15264\theta^2+7608\theta+121\right)-2^{14} x^{5}\left(48\theta^4-480\theta^3-2016\theta^2-2568\theta-1091\right)-2^{19} x^{6}\left((2\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2, 38, 204, 7462, ...
--> OEIS
Normalized instanton numbers (n₀=1): 10/7, 100/7, 508/7, 808, 59910/7, ... ; Common denominator:...

Discriminant

\(-(16z+1)(32z-1)(4z+1)^2(32z-7)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)	\(-\frac{ 1}{ 16}\)	\(0\)	\(\frac{ 1}{ 32}\)	\(\frac{ 7}{ 32}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(\frac{ 3}{ 2}\)
\(\frac{ 3}{ 2}\)	\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "6.36" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.37 |  AESZ:  |  Superseeker: 80 249872  |  Hash: 0c2998041752cbd976fcc2e18f2072ad  

Degree: 6

\(\theta^4-2^{4} x\left(6\theta^4+96\theta^3+99\theta^2+51\theta+11\right)-2^{9} x^{2}\left(222\theta^4+48\theta^3-873\theta^2-897\theta-328\right)+2^{14} x^{3}\left(454\theta^4+6168\theta^3+4887\theta^2+891\theta-651\right)+2^{19} x^{4}\left(6492\theta^4+8760\theta^3-1557\theta^2-6945\theta-2438\right)-2^{28} 7 x^{5}\left(60\theta^4+336\theta^3+693\theta^2+642\theta+227\right)-2^{33} 7^{2} x^{6}\left((2\theta+3)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 176, 35792, 7805184, 1768710928, ...
--> OEIS
Normalized instanton numbers (n₀=1): 80, -4222, 249872, -22251117, 2195810928, ... ; Common denominator:...

Discriminant

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

Local exponents

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

Note:

This is operator "6.37" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

New Number: 6.38 |  AESZ:  |  Superseeker: 2 952  |  Hash: ab13475ec61ba4278f6e59d858b5c527  

Degree: 6

\(\theta^4-2 x\left(84\theta^4+264\theta^3+299\theta^2+167\theta+37\right)+2^{2} x^{2}\left(260\theta^4+10640\theta^3+22443\theta^2+18950\theta+6071\right)+2^{7} x^{3}\left(4550\theta^4+16140\theta^3+7327\theta^2-8178\theta-6485\right)+2^{12} x^{4}\left(935\theta^4-8660\theta^3-28587\theta^2-29234\theta-10036\right)-2^{18} 3 x^{5}\left(414\theta^4+2385\theta^3+5123\theta^2+4909\theta+1773\right)-2^{22} 3^{2} x^{6}(3\theta+5)^2(3\theta+4)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 74, 6354, 585020, 55958290, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -172, 952, -45148, 17303644/25, ... ; Common denominator:...

Discriminant

\(-(-1+16z+256z^2)(32z+1)^2(108z-1)^2\)

Local exponents

\(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)	\(-\frac{ 1}{ 32}\)	\(0\)	\(\frac{ 1}{ 108}\)	\(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 4}{ 3}\)
\(1\)	\(1\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(1\)	\(\frac{ 4}{ 3}\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 3}\)
\(2\)	\(4\)	\(0\)	\(\frac{ 3}{ 2}\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

This is operator "6.38" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex