Calabi-Yau differential operator database v.3.0

1

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

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

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

Note:

This is operator "6.17" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

2

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

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

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

Note:

This is operator "6.18" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

3

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

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

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

Note:

This is operator "6.19" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

4

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

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

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

Note:

This is operator "6.20" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

5

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

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

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

Note:

This is operator "6.21" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

6

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

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

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

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

7

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

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

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

Note:

This is operator "6.23" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

8

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

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

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

Note:

This is operator "6.24" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

9

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

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

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

Note:

This is operator "6.25" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

10

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

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

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

Note:

This is operator "6.27" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

11

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

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

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

Note:

This is operator "6.28" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

12

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

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

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

Note:

This is operator "6.41" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

13

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

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

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

Note:

This is operator "6.30" from ...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

14

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

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

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

Note:

This is operator "6.31" from ...

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice