Calabi-Yau differential operator database v.3.0

31

New Number: 2.38 | AESZ: 61 | Superseeker: -41184 -5124430612320 | Hash: 191cd9ad5f43862072f3be6811803748

Degree: 2

$\theta^4-2^{4} 3^{2} x(6\theta+1)(6\theta+5)(72\theta^2+72\theta+31)+2^{12} 3^{8} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 22320, 2060205840, 248752033770240, 33839074380496104720, ...
--> OEIS
Normalized instanton numbers (n₀=1): -41184, 251271360, -5124430612320, 160031225395327320, -6251395923736354968480, ... ; Common denominator:...

Discriminant

$(186624z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 186624}$ $\infty$
$0$ $0$ $\frac{ 1}{ 6}$
$0$ $\frac{ 1}{ 6}$ $\frac{ 5}{ 6}$
$0$ $\frac{ 5}{ 6}$ $\frac{ 7}{ 6}$
$0$ $1$ $\frac{ 11}{ 6}$

\(0\)	\(\frac{ 1}{ 186624}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(\frac{ 1}{ 6}\)	\(\frac{ 5}{ 6}\)
\(0\)	\(\frac{ 5}{ 6}\)	\(\frac{ 7}{ 6}\)
\(0\)	\(1\)	\(\frac{ 11}{ 6}\)

Note:

This is operator "2.38" from ...

32

New Number: 2.39 | AESZ: ~80,~81 | Superseeker: -2450 -623291900 | Hash: a4500006693bca99ed7ce6d889944382

Degree: 2

$\theta^4-2 5 x\left(2500\theta^4+5000\theta^3+5875\theta^2+3375\theta+738\right)+2^{2} 5^{6} x^{2}(5\theta+4)(5\theta+6)(10\theta+9)(10\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 7380, 71382150, 753157832000, 8295076883047500, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2450, -1825075/2, -623291900, -559511912750, -584671005670010, ... ; Common denominator:...

Discriminant

$(12500z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 12500}$ $\infty$
$0$ $0$ $\frac{ 4}{ 5}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 9}{ 10}$
$0$ $1$ $\frac{ 11}{ 10}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 6}{ 5}$

\(0\)	\(\frac{ 1}{ 12500}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 4}{ 5}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 9}{ 10}\)
\(0\)	\(1\)	\(\frac{ 11}{ 10}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 6}{ 5}\)

Note:

Operator equivalent to $\hat{1}$ of AESZ

33

New Number: 2.3 | AESZ: 68 | Superseeker: 52 220220 | Hash: 13a48045ff0a42a9fcfbdb710baf1997

Degree: 2

$\theta^4-2^{2} x(4\theta+1)(4\theta+3)(7\theta^2+7\theta+2)-2^{7} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 4200, 1034880, 311711400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 52, 2814, 220220, 29135058, 4512922272, ... ; Common denominator:...

Discriminant

$-(64z+1)(512z-1)$

Local exponents

$-\frac{ 1}{ 64}$ $0$ $\frac{ 1}{ 512}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$1$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 5}{ 4}$
$2$ $0$ $2$ $\frac{ 7}{ 4}$

\(-\frac{ 1}{ 64}\)	\(0\)	\(\frac{ 1}{ 512}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 5}{ 4}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

C*a

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-228\)	\(72\)	\(12\)	\(8\)

34

New Number: 2.40 | AESZ: | Superseeker: -791200 -4288711075194400 | Hash: 43d26d7aa358d5634e12c133ddc42a01

Degree: 2

$\theta^4-2^{4} 5 x\left(80000\theta^4+160000\theta^3+186000\theta^2+106000\theta+22811\right)+2^{16} 5^{6} x^{2}(10\theta+7)(10\theta+9)(10\theta+11)(10\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 1824880, 4485741488400, 12079072308276832000, 33999719248816985649610000, ...
--> OEIS
Normalized instanton numbers (n₀=1): -791200, -41486886600, -4288711075194400, -585926703697412494000, -93381074165698184340671200, ... ; Common denominator:...

Discriminant

$(3200000z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 3200000}$ $\infty$
$0$ $0$ $\frac{ 7}{ 10}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 9}{ 10}$
$0$ $1$ $\frac{ 11}{ 10}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 13}{ 10}$

\(0\)	\(\frac{ 1}{ 3200000}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 7}{ 10}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 9}{ 10}\)
\(0\)	\(1\)	\(\frac{ 11}{ 10}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 13}{ 10}\)

Note:

Operator equivalent to $\hat{2}$ of AESZ.

35

New Number: 2.41 | AESZ: | Superseeker: -522 -9879192 | Hash: 73d9f98b2c49f1c35df531f020cf1721

Degree: 2

$\theta^4-2 3^{2} x\left(324\theta^4+648\theta^3+765\theta^2+441\theta+97\right)+2^{2} 3^{10} x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 1746, 3951990, 9740271348, 25043989159350, ...
--> OEIS
Normalized instanton numbers (n₀=1): -522, -105291/2, -9879192, -2420127936, -689420749716, ... ; Common denominator:...

Discriminant

$(2916z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 2916}$ $\infty$
$0$ $0$ $\frac{ 5}{ 6}$
$0$ $-\frac{ 1}{ 2}$ $1$
$0$ $1$ $1$
$0$ $\frac{ 3}{ 2}$ $\frac{ 7}{ 6}$

\(0\)	\(\frac{ 1}{ 2916}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 5}{ 6}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(1\)
\(0\)	\(1\)	\(1\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 7}{ 6}\)

Note:

Operator equivalent to $\hat{4}$

36

New Number: 2.42 | AESZ: ~98 | Superseeker: -288 -2339616 | Hash: acfee9d4b5fefd1a945cfa6b1bc61373

Degree: 2

$\theta^4-2^{2} 3 x\left(288\theta^4+576\theta^3+682\theta^2+394\theta+87\right)+2^{4} 3^{2} x^{2}(12\theta+11)^2(12\theta+13)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 1044, 1403100, 2051002800, 3126485684700, ...
--> OEIS
Normalized instanton numbers (n₀=1): -288, -19260, -2339616, -369882612, -67925445408, ... ; Common denominator:...

Discriminant

$(1728z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 1728}$ $\infty$
$0$ $0$ $\frac{ 11}{ 12}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 12}$
$0$ $1$ $\frac{ 13}{ 12}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 13}{ 12}$

\(0\)	\(\frac{ 1}{ 1728}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 11}{ 12}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 12}\)
\(0\)	\(1\)	\(\frac{ 13}{ 12}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 13}{ 12}\)

Note:

Operator equivalent to $\hat{5}$

37

New Number: 2.43 | AESZ: ~77, ~78,~97 | Superseeker: -736 -26911072 | Hash: 3d2cd06eccf32145816b35cb63878900

Degree: 2

$\theta^4-2^{4} x\left(512\theta^4+1024\theta^3+1208\theta^2+696\theta+153\right)+2^{12} x^{2}(8\theta+7)^2(8\theta+9)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 2448, 7779600, 26927622400, 97242114301200, ...
--> OEIS
Normalized instanton numbers (n₀=1): -736, -104512, -26911072, -9061573696, -3547993303456, ... ; Common denominator:...

Discriminant

$(4096z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 4096}$ $\infty$
$0$ $0$ $\frac{ 7}{ 8}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 7}{ 8}$
$0$ $1$ $\frac{ 9}{ 8}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 9}{ 8}$

\(0\)	\(\frac{ 1}{ 4096}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 7}{ 8}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 7}{ 8}\)
\(0\)	\(1\)	\(\frac{ 9}{ 8}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 9}{ 8}\)

Note:

Operator equivalent to $\hat{6}$

38

New Number: 2.44 | AESZ: | Superseeker: -57760 -3869123234080 | Hash: db68f352287fb91ca91e65eb38318ac4

Degree: 2

$\theta^4-2^{4} x\left(32768\theta^4+65536\theta^3+76544\theta^2+43776\theta+9495\right)+2^{26} x^{2}(4\theta+3)(4\theta+5)(8\theta+7)(8\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 151920, 30692221200, 6779721385465600, 1564471951791288368400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -57760, -354010600, -3869123234080, -56296618019665040, -953499788550226132960, ... ; Common denominator:...

Discriminant

$(262144z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 262144}$ $\infty$
$0$ $0$ $\frac{ 3}{ 4}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 7}{ 8}$
$0$ $1$ $\frac{ 9}{ 8}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 4}$

\(0\)	\(\frac{ 1}{ 262144}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 7}{ 8}\)
\(0\)	\(1\)	\(\frac{ 9}{ 8}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{7}$

39

New Number: 2.45 | AESZ: ~82 | Superseeker: -10080 -24400330080 | Hash: 11afa89027677e0616228cad62a9f990

Degree: 2

$\theta^4-2^{2} 3^{2} x\left(2592\theta^4+5184\theta^3+6066\theta^2+3474\theta+755\right)+2^{4} 3^{10} x^{2}(4\theta+3)(4\theta+5)(12\theta+11)(12\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 27180, 978471900, 38487760088400, 1581137831289447900, ...
--> OEIS
Normalized instanton numbers (n₀=1): -10080, -11338740, -24400330080, -69157402598340, -228492096441648480, ... ; Common denominator:...

Discriminant

$(46656z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 46656}$ $\infty$
$0$ $0$ $\frac{ 3}{ 4}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 12}$
$0$ $1$ $\frac{ 13}{ 12}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 4}$

\(0\)	\(\frac{ 1}{ 46656}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 12}\)
\(0\)	\(1\)	\(\frac{ 13}{ 12}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{8}$

40

New Number: 2.46 | AESZ: | Superseeker: -2710944 -302270555492914464 | Hash: a06fc8c91c1e4c766fdb1e79370bef7a

Degree: 2

$\theta^4-2^{4} 3^{2} x\left(165888\theta^4+331776\theta^3+386496\theta^2+220608\theta+47711\right)+2^{22} 3^{10} x^{2}(4\theta+3)(4\theta+5)(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6870384, 63135105483024, 634962415293388429056, 6673257595142837863377354000, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2710944, -717640301160, -302270555492914464, -171507700573958028578832, -113303073680022744870130144224, ... ; Common denominator:...

Discriminant

$(11943936z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 11943936}$ $\infty$
$0$ $0$ $\frac{ 3}{ 4}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 6}$
$0$ $1$ $\frac{ 7}{ 6}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 4}$

\(0\)	\(\frac{ 1}{ 11943936}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 5}{ 6}\)
\(0\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{9}$

41

New Number: 2.47 | AESZ: | Superseeker: -3488 -1142687008 | Hash: 413005461e43cfa75125577c2d4c2fde

Degree: 2

$\theta^4-2^{4} x\left(2048\theta^4+4096\theta^3+4800\theta^2+2752\theta+599\right)+2^{24} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 9584, 121274640, 1675847866112, 24182028281658640, ...
--> OEIS
Normalized instanton numbers (n₀=1): -3488, -1406056, -1142687008, -1211614451216, -1500013956719584, ... ; Common denominator:...

Discriminant

$(16384z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 16384}$ $\infty$
$0$ $0$ $\frac{ 3}{ 4}$
$0$ $-\frac{ 1}{ 2}$ $1$
$0$ $1$ $1$
$0$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 4}$

Note:

Operator equivalent to $\hat{10}$

42

New Number: 2.48 | AESZ: ~94 | Superseeker: -1344 -109320512 | Hash: 892e497a83d12667b7f189a3d743fb7c

Degree: 2

$\theta^4-2^{2} 3 x\left(1152\theta^4+2304\theta^3+2710\theta^2+1558\theta+341\right)+2^{4} 3^{2} x^{2}(24\theta+19)(24\theta+23)(24\theta+25)(24\theta+29)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4092, 21900060, 127808119824, 778493560064220, ...
--> OEIS
Normalized instanton numbers (n₀=1): -1344, -278040, -109320512, -56290146024, -33748229589312, ... ; Common denominator:...

Discriminant

$(6912z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 6912}$ $\infty$
$0$ $0$ $\frac{ 19}{ 24}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 23}{ 24}$
$0$ $1$ $\frac{ 25}{ 24}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 29}{ 24}$

Note:

Operator equivalent to $\hat{11}$

43

New Number: 2.49 | AESZ: | Superseeker: -26400 -230398034080 | Hash: ffdc338b55d1f4e1f989f4359b06df6c

Degree: 2

$\theta^4-2^{4} 3 x\left(4608\theta^4+9216\theta^3+10744\theta^2+6136\theta+1325\right)+2^{12} 3^{2} x^{2}(24\theta+17)(24\theta+23)(24\theta+25)(24\theta+31)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 63600, 5412963600, 504140776339200, 49063316029156400400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -26400, -52511160, -230398034080, -1287524740195200, -8504689433002312800, ... ; Common denominator:...

Discriminant

$(110592z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 110592}$ $\infty$
$0$ $0$ $\frac{ 17}{ 24}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 23}{ 24}$
$0$ $1$ $\frac{ 25}{ 24}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 31}{ 24}$

Note:

Operator equivalent to $\hat{12}$

44

New Number: 2.4 | AESZ: 62 | Superseeker: 372 71562236 | Hash: 07a3fd7577f878056e765831c6820f3d

Degree: 2

$\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(7\theta^2+7\theta+2)-2^{7} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 120, 138600, 228708480, 463140798120, ...
--> OEIS
Normalized instanton numbers (n₀=1): 372, 136182, 71562236, 63364481358, 65860679690400, ... ; Common denominator:...

Discriminant

$-(432z+1)(3456z-1)$

Local exponents

$-\frac{ 1}{ 432}$ $0$ $\frac{ 1}{ 3456}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 6}$
$1$ $0$ $1$ $\frac{ 5}{ 6}$
$1$ $0$ $1$ $\frac{ 7}{ 6}$
$2$ $0$ $2$ $\frac{ 11}{ 6}$

Note:

Hadamard product D*a

45

New Number: 2.50 | AESZ: | Superseeker: -201888 -40177844666400 | Hash: 5309f0b5a4362f22faafad07a0eb1bb8

Degree: 2

$\theta^4-2^{4} 3^{2} x\left(10368\theta^4+20736\theta^3+24048\theta^2+13680\theta+2927\right)+2^{20} 3^{10} x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 421488, 241251334416, 151434902650832640, 99396938275247309913360, ...
--> OEIS
Normalized instanton numbers (n₀=1): -201888, -1567499400, -40177844666400, -988883543512335600, -35724019937142805037280, ... ; Common denominator:...

Discriminant

$(746496z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 746496}$ $\infty$
$0$ $0$ $\frac{ 2}{ 3}$
$0$ $-\frac{ 1}{ 2}$ $1$
$0$ $1$ $1$
$0$ $\frac{ 3}{ 2}$ $\frac{ 4}{ 3}$

Note:

Operator equivalent to $\hat{13}$ of AESZ

46

New Number: 2.51 | AESZ: ~88,~89 | Superseeker: -5472 -6444589536 | Hash: 02d09c6c320ab036e45834cf0d3951e7

Degree: 2

$\theta^4-2^{4} 3 x\left(1152\theta^4+2304\theta^3+2704\theta^2+1552\theta+339\right)+2^{16} 3^{2} x^{2}(6\theta+5)^2(6\theta+7)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 16272, 347859216, 8115450239232, 197661638029770000, ...
--> OEIS
Normalized instanton numbers (n₀=1): -5472, -4476528, -6444589536, -12228845295024, -27012506850929952, ... ; Common denominator:...

Discriminant

$(27648z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 27648}$ $\infty$
$0$ $0$ $\frac{ 5}{ 6}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 6}$
$0$ $1$ $\frac{ 7}{ 6}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 7}{ 6}$

Note:

Operator equivalent to $\widehat{14}$
B-Incarnations:
Double octics: D.O.267, D.O.275

47

New Number: 2.52 | AESZ: 16 | Superseeker: 4 644/3 | Hash: 05af0662662bfbec63e3186c4f363313

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{8} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 168, 5120, 190120, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4, 20, 644/3, 3072, 52512, ... ; Common denominator:...

Discriminant

$(64z-1)(16z-1)$

Local exponents

$0$ $\frac{ 1}{ 64}$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $I \ast \alpha$
A-Incarnation: diagonal subfamily of 1,1,1,1-intersection in $P^1 \times P^1 \times P^1 \times \P^1$
B-Incarnations:
Fibre products: 62211- x 632--1, S62211

48

New Number: 2.53 | AESZ: 29 | Superseeker: 14 10424/3 | Hash: 92e8a038051b3fb8e0cc6ad6a52b8bfb

Degree: 2

$\theta^4-2 x(2\theta+1)^2(17\theta^2+17\theta+5)+2^{2} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 438, 28900, 2310070, ...
--> OEIS
Normalized instanton numbers (n₀=1): 14, 303/2, 10424/3, 113664, 4579068, ... ; Common denominator:...

Discriminant

$1-136z+16z^2$

Local exponents

$0$ $\frac{ 17}{ 4}-3\sqrt{ 2}$ $\frac{ 17}{ 4}+3\sqrt{ 2}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $I \ast \gamma$

49

New Number: 2.54 | AESZ: 41 | Superseeker: 2 -104 | Hash: a9ddeed4299f59fb9ac9f6f248383b8f

Degree: 2

$\theta^4-2 x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{2} 3^{4} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 60, -19530, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -7, -104, -588, 3300, ... ; Common denominator:...

Discriminant

$1-56z+1296z^2$

Local exponents

$0$ $\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I$ $\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $I \ast \delta$

50

New Number: 2.55 | AESZ: 42 | Superseeker: 8 1000 | Hash: c389d3bc0e31801bc4b7b3e186702bc9

Degree: 2

$\theta^4-2^{3} x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 240, 10880, 597520, ...
--> OEIS
Normalized instanton numbers (n₀=1): 8, 63, 1000, 44369/2, 606168, ... ; Common denominator:...

Discriminant

$1-96z+256z^2$

Local exponents

$0$ $\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}$ $\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $I \ast \epsilon$

51

New Number: 2.56 | AESZ: 185 | Superseeker: 6 608 | Hash: 80506439e4d4fdc41f5b16e246a69fbf

Degree: 2

$\theta^4-2 3 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} 3^{3} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 162, 6180, 284130, ...
--> OEIS
Normalized instanton numbers (n₀=1): 6, 93/2, 608, 11754, 275352, ... ; Common denominator:...

Discriminant

$1-72z-432z^2$

Local exponents

$-\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}$ $0$ $-\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$
$1$ $0$ $1$ $1$
$2$ $0$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $I \ast \zeta$

52

New Number: 2.57 | AESZ: 184 | Superseeker: 2 -8 | Hash: ee8bb517b329e58eeb4352dc3cdc3f81

Degree: 2

$\theta^4-2 x(2\theta+1)^2(11\theta^2+11\theta+5)+2^{2} 5^{3} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 210, 5500, 159250, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, 4, -8, -194, -2820, ... ; Common denominator:...

Discriminant

$1-88z+2000z^2$

Local exponents

$0$ $\frac{ 11}{ 500}-\frac{ 1}{ 250}I$ $\frac{ 11}{ 500}+\frac{ 1}{ 250}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $I \ast \eta$

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 2, 34, -214, -12382, -352498, -6554486, -92778754,...
Coefficients of the q-coordinate : 0, 1, -22, 359, -4892, 61955, -725338, 8256993,...

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

No topological data

Monodromy (with respect to Frobenius basis)

$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+.969204490I$	$-\frac{ 1}{ 12}+20\lambda$	$-\frac{ 1}{ 18}+\frac{ 40}{ 3}\lambda$	$.2449129e-2+\frac{ 10}{ 3}\lambda$
$\frac{ 20}{ 3}$	$\frac{ 5}{ 3}$	$\frac{ 4}{ 9}$	$\frac{ 1}{ 18}-\frac{ 40}{ 3}\lambda$
$-10$	$-1$	$\frac{ 1}{ 3}$	$-\frac{ 1}{ 12}+20\lambda$
$100$	$10$	$\frac{ 20}{ 3}$	$1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-.969204490I$

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$1.8333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+.969204490I$	$-\frac{ 1}{ 12}-20\lambda$	$\frac{ 1}{ 18}+\frac{ 40}{ 3}\lambda$	$.2449129e-2-\frac{ 10}{ 3}\lambda$
$\frac{ 20}{ 3}$	$\frac{ 1}{ 3}$	$\frac{ 4}{ 9}$	$-\frac{ 1}{ 18}-\frac{ 40}{ 3}\lambda$
$10$	$-1$	$\frac{ 5}{ 3}$	$-\frac{ 1}{ 12}-20\lambda$
$100$	$-10$	$\frac{ 20}{ 3}$	$.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.969204490I$

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Basis of the Doran-Morgan lattice

$\frac{ 5}{ 6}-\frac{ 96920449}{ 100000000}I$	$\frac{ 85}{ 3}$	$\frac{ 11}{ 10}$	$1$
$-\frac{ 20}{ 3}$	$-60$	$-1$	$0$
$10$	$100$	$0$	$0$
$-100$	$0$	$0$	$0$

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53

New Number: 2.58 | AESZ: 46 | Superseeker: -6 -104 | Hash: 2226ec115674e71c483ba2c0350e8adf

Degree: 2

$\theta^4-2 3 x(2\theta+1)^2(9\theta^2+9\theta+5)+2^{2} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 1782, 129900, 10463670, ...
--> OEIS
Normalized instanton numbers (n₀=1): -6, -6, -104, 36, -4812, ... ; Common denominator:...

Discriminant

$(108z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 108}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 6}$ $1$
$0$ $\frac{ 5}{ 6}$ $1$
$0$ $1$ $\frac{ 3}{ 2}$

Note:

Hadamard product $I \ast \iota$

54

New Number: 2.59 | AESZ: 47 | Superseeker: -384 -164736 | Hash: 792da990d2d2e5263bb789ad37b00d44

Degree: 2

$\theta^4-2^{4} 3 x(2\theta+1)^2(18\theta^2+18\theta+13)+2^{10} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 624, 685584, 883925760, 1229988226320, ...
--> OEIS
Normalized instanton numbers (n₀=1): -384, -1356, -164736, 96211836, -3267254400, ... ; Common denominator:...

Discriminant

$(1728z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 1728}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $-\frac{ 1}{ 6}$ $1$
$0$ $1$ $1$
$0$ $\frac{ 7}{ 6}$ $\frac{ 3}{ 2}$

Note:

Hadamard product $I \ast \kappa$

55

New Number: 2.5 | AESZ: 25 | Superseeker: 20 8220 | Hash: 93279abcbeeade30c29508de7784e582

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(11\theta^2+11\theta+3)-2^{4} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 684, 58800, 6129900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 20, 277, 8220, 352994, 18651536, ... ; Common denominator:...

Discriminant

$1-176z-256z^2$

Local exponents

$-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}$ $0$ $-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 3}{ 2}$
$2$ $0$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $A\ast b$

A-incarnation: X(1,2,2) in G(2,5)

56

New Number: 2.60 | AESZ: 18 | Superseeker: 4 364 | Hash: bb479f8a4185bf4a943dba2d433e13e5

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{4} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4, 108, 3280, 126700, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4, 39, 364, 6800, 662416/5, ... ; Common denominator:...

Discriminant

$-(16z+1)(64z-1)$

Local exponents

$-\frac{ 1}{ 16}$ $0$ $\frac{ 1}{ 64}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 5}{ 4}$
$2$ $0$ $2$ $\frac{ 3}{ 2}$

Note:

A-Incarnation: (1,1) and (2,2) intersection in $P^3 \times P^3$

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 4, 316, 9832, 435516, 16560404, 683129368, 27488583896,...
Coefficients of the q-coordinate : 0, 1, -12, -90, 848, -14079, -313608, -8135374,...

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

Characteristic classes:

$C_3$	$C_2 H$	$H^3$	$ \vert H \vert$
$-128$	$88$	$40$	$14$

Monodromy (with respect to Frobenius basis)

$5.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+1.240581747I$	$-2.1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.620290874I$	$.83055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556+.237778168I$	$-.215484184-.13439635535307517084282460136674259681093394077448747152619589977220956719817767653758542141230068337129840546697038724373576309794988610478359908883826879271070615034168564920273348519362186788154897I$
$\frac{ 46}{ 3}$	$-\frac{ 20}{ 3}$	$\frac{ 529}{ 180}$	$-.83055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556-.237778168I$
$40$	$-20$	$\frac{ 26}{ 3}$	$-2.1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.620290874I$
$80$	$-40$	$\frac{ 46}{ 3}$	$-\frac{ 10}{ 3}-256\lambda$

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$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$1.+.620290874I$	$0$	$.56859997e-1I$	$.9619019e-2$
$\frac{ 11}{ 3}$	$1$	$\frac{ 121}{ 360}$	$-.56859997e-1I$
$0$	$0$	$1$	$0$
$40$	$0$	$\frac{ 11}{ 3}$	$1.-.620290874I$

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Basis of the Doran-Morgan lattice

$-\frac{ 310145437}{ 500000000}I$	$\frac{ 31}{ 3}$	$1$	$1$
$-\frac{ 11}{ 3}$	$-20$	$-1$	$0$
$0$	$40$	$0$	$0$
$-40$	$0$	$0$	$0$

copy data

57

New Number: 2.61 | AESZ: 26 | Superseeker: 10 1724 | Hash: f3fc09474973b19b8bdb783e3322eb65

Degree: 2

$\theta^4-2 x(2\theta+1)^2(13\theta^2+13\theta+4)-2^{2} 3 x^{2}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 288, 15200, 968800, ...
--> OEIS
Normalized instanton numbers (n₀=1): 10, 191/2, 1724, 45680, 1478214, ... ; Common denominator:...

Discriminant

$-(4z+1)(108z-1)$

Local exponents

$-\frac{ 1}{ 4}$ $0$ $\frac{ 1}{ 108}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $\frac{ 3}{ 2}$

Note:

A-incarnation: $X(1,1,1,1,2) \subset Grass(2,6)$

58

New Number: 2.62 | AESZ: 28 | Superseeker: 5 312 | Hash: 06dd455cafc5097e4f671d385984c1a2

Degree: 2

$\theta^4-x\left(65\theta^4+130\theta^3+105\theta^2+40\theta+6\right)+2^{2} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 126, 3948, 149310, ...
--> OEIS
Normalized instanton numbers (n₀=1): 5, 28, 312, 4808, 91048, ... ; Common denominator:...

Discriminant

$(64z-1)(z-1)$

Local exponents

$0$ $\frac{ 1}{ 64}$ $1$ $\infty$
$0$ $0$ $0$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 5}{ 4}$

Note:

A-incarnation: $X(1, 1, 1, 1, 1, 1) \subset Grass(3, 6)$

59

New Number: 2.63 | AESZ: 84 | Superseeker: -4 -44 | Hash: 908b978c0c447d3643c3018c40e7f5d1

Degree: 2

$\theta^4-2^{2} x\left(32\theta^4+64\theta^3+63\theta^2+31\theta+6\right)+2^{8} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 936, 43008, 2145960, ...
--> OEIS
Normalized instanton numbers (n₀=1): -4, -11, -44, -156, -288, ... ; Common denominator:...

Discriminant

$(64z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 64}$ $\infty$
$0$ $0$ $\frac{ 3}{ 4}$
$0$ $0$ $1$
$0$ $1$ $1$
$0$ $1$ $\frac{ 5}{ 4}$

Note:

This is operator "2.63" from ...

60

New Number: 2.64 | AESZ: 182 | Superseeker: 1 7 | Hash: 89ba4729efa82413b33fe6928ff8d2c9

Degree: 2

$\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...

Discriminant

$(27z-1)(16z-1)$

Local exponents

$0$ $\frac{ 1}{ 27}$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $\frac{ 5}{ 6}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 7}{ 6}$

Note:

This is operator "2.64" from ...

\(\frac{ 25}{ 48}+62\lambda\)	\(\frac{ 23}{ 32}+31\lambda\)	\(-\frac{ 23}{ 1152}+\frac{ 31}{ 12}\lambda\)	\(.598529843\)
\(-\frac{ 1}{ 24}\)	\(\frac{ 47}{ 48}\)	\(-\frac{ 1}{ 576}\)	\(-\frac{ 23}{ 1152}-\frac{ 31}{ 12}\lambda\)
\(-\frac{ 1}{ 2}\)	\(\frac{ 3}{ 4}\)	\(\frac{ 47}{ 48}\)	\(\frac{ 23}{ 32}-31\lambda\)
\(-1\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 24}\)	\(\frac{ 25}{ 48}-62\lambda\)

\(1.024864490\)	\(-.910226992I\)	\(-.22515962e-1\)	\(0\)
\(0\)	\(-1.024864490\)	\(0\)	\(-.22515962e-1\)
\(\sqrt{ 5}\)	\(0\)	\(-1.024864490\)	\(.910226992I\)
\(0\)	\(\sqrt{ 5}\)	\(0\)	\(1.024864490\)

\(cy[DM_basis]\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)

\(4.+2.209786237I\)	\(-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119I\)	\(1+152\lambda\)	\(-.171535199-114\lambda\)
\(8\)	\(-3\)	\(\frac{ 8}{ 3}\)	\(-1-152\lambda\)
\(12\)	\(-6\)	\(5\)	\(-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119I\)
\(24\)	\(-12\)	\(8\)	\(-2.-2.209786237I\)

\(cy[DM_basis]\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)

\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(0\)	\(1\)	\(-1\)
\(0\)	\(0\)	\(0\)	\(1\)

\(\frac{ 23}{ 48}-62\lambda\)	\(\frac{ 1}{ 24}\)	\(\frac{ 1}{ 2}\)	\(1\)
\(\frac{ 1}{ 24}\)	\(0\)	\(-1\)	\(0\)
\(\frac{ 1}{ 2}\)	\(-1\)	\(0\)	\(0\)
\(1\)	\(0\)	\(0\)	\(0\)

\(1.+1.104893119I\)	\(0\)	\(57\lambda\)	\(\frac{ 276}{ 2713}\)
\(3\)	\(1\)	\(\frac{ 3}{ 4}\)	\(-57\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(12\)	\(0\)	\(3\)	\(1.-1.104893119I\)

\(-\frac{ 1104893119}{ 1000000000}I\)	\(5\)	\(1\)	\(1\)
\(-3\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(\frac{ 35}{ 24}\)	\(-580\lambda\)	\(-\frac{ 649}{ 576}\)	\(0\)
\(0\)	\(-\frac{ 35}{ 24}\)	\(0\)	\(-\frac{ 649}{ 576}\)
\(1\)	\(0\)	\(-\frac{ 35}{ 24}\)	\(580\lambda\)
\(0\)	\(1\)	\(0\)	\(\frac{ 35}{ 24}\)

\(\frac{ 7}{ 8}\)	\(-108\lambda\)	\(\frac{ 5}{ 64}\)	\(0\)
\(0\)	\(-\frac{ 7}{ 8}\)	\(0\)	\(\frac{ 5}{ 64}\)
\(3\)	\(0\)	\(-\frac{ 7}{ 8}\)	\(108\lambda\)
\(0\)	\(3\)	\(0\)	\(\frac{ 7}{ 8}\)

\(\frac{ 1}{ 2}\sqrt{ 3}\)	\(-.470039198I\)	\(\frac{ 1}{ 24}\sqrt{ 3}\)	\(0\)
\(0\)	\(-\frac{ 1}{ 2}\sqrt{ 3}\)	\(0\)	\(\frac{ 1}{ 24}\sqrt{ 3}\)
\(2\sqrt{ 3}\)	\(0\)	\(-\frac{ 1}{ 2}\sqrt{ 3}\)	\(.470039198I\)
\(0\)	\(2\sqrt{ 3}\)	\(0\)	\(\frac{ 1}{ 2}\sqrt{ 3}\)

\(\frac{ 2}{ 3}\sqrt{ 2}\)	\(-.657917825I\)	\(\frac{ 1}{ 36}\sqrt{ 2}\)	\(0\)
\(0\)	\(-\frac{ 2}{ 3}\sqrt{ 2}\)	\(0\)	\(\frac{ 1}{ 36}\sqrt{ 2}\)
\(2\sqrt{ 2}\)	\(0\)	\(-\frac{ 2}{ 3}\sqrt{ 2}\)	\(.657917825I\)
\(0\)	\(2\sqrt{ 2}\)	\(0\)	\(\frac{ 2}{ 3}\sqrt{ 2}\)

\(1.355287997\)	\(-2.055993202I\)	\(-.591710883\)	\(0\)
\(0\)	\(-1.355287997\)	\(0\)	\(-.591710883\)
\(\sqrt{ 2}\)	\(0\)	\(-1.355287997\)	\(2.055993202I\)
\(0\)	\(\sqrt{ 2}\)	\(0\)	\(1.355287997\)

\(\frac{ 5}{ 8}\sqrt{ 3}\)	\(-1.175097994I\)	\(-.99232078e-1\)	\(0\)
\(0\)	\(-1.082531755\)	\(0\)	\(-.99232078e-1\)
\(\sqrt{ 3}\)	\(0\)	\(-1.082531755\)	\(1.175097994I\)
\(0\)	\(\sqrt{ 3}\)	\(0\)	\(\frac{ 5}{ 8}\sqrt{ 3}\)

\(\frac{ 47}{ 24}\)	\(-4.710333822I\)	\(-\frac{ 1633}{ 576}\)	\(0\)
\(0\)	\(-\frac{ 47}{ 24}\)	\(0\)	\(-\frac{ 1633}{ 576}\)
\(1\)	\(0\)	\(-\frac{ 47}{ 24}\)	\(4.710333822I\)
\(0\)	\(1\)	\(0\)	\(\frac{ 47}{ 24}\)

\(\frac{ 11}{ 12}\)	\(-152\lambda\)	\(\frac{ 23}{ 288}\)	\(0\)
\(0\)	\(-\frac{ 11}{ 12}\)	\(0\)	\(\frac{ 23}{ 288}\)
\(2\)	\(0\)	\(-\frac{ 11}{ 12}\)	\(152\lambda\)
\(0\)	\(2\)	\(0\)	\(\frac{ 11}{ 12}\)

\(0\)	\(\frac{ 1}{ 6912}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 19}{ 24}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 23}{ 24}\)
\(0\)	\(1\)	\(\frac{ 25}{ 24}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 29}{ 24}\)

\(.918558654\)	\(-.664735808I\)	\(.63788795e-1\)	\(0\)
\(0\)	\(-\frac{ 3}{ 8}\sqrt{ 2}\sqrt{ 3}\)	\(0\)	\(.63788795e-1\)
\(\sqrt{ 6}\)	\(0\)	\(-\frac{ 3}{ 8}\sqrt{ 2}\sqrt{ 3}\)	\(.664735808I\)
\(0\)	\(\sqrt{ 6}\)	\(0\)	\(.918558654\)

\(0\)	\(\frac{ 1}{ 110592}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 17}{ 24}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 23}{ 24}\)
\(0\)	\(1\)	\(\frac{ 25}{ 24}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 31}{ 24}\)

\(1.001734607\)	\(-1.096529708I\)	\(-.2455232e-2\)	\(0\)
\(0\)	\(-1.001734607\)	\(0\)	\(-.2455232e-2\)
\(\sqrt{ 2}\)	\(0\)	\(-1.001734607\)	\(1.096529708I\)
\(0\)	\(\sqrt{ 2}\)	\(0\)	\(1.001734607\)

\(4.+3.547288434I\)	\(-\frac{ 3}{ 2}-366\lambda\)	\(1.7500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+2.069251586I\)	\(.298604603-366\lambda\)
\(7\)	\(-\frac{ 5}{ 2}\)	\(\frac{ 49}{ 12}\)	\(-1.7500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-2.069251586I\)
\(6\)	\(-3\)	\(\frac{ 9}{ 2}\)	\(-\frac{ 3}{ 2}-366\lambda\)
\(12\)	\(-6\)	\(7\)	\(-2.-3.547288434I\)

\(1+366\lambda\)	\(0\)	\(183\lambda\)	\(.524302301\)
\(3\)	\(1\)	\(\frac{ 3}{ 2}\)	\(-183\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(6\)	\(0\)	\(3\)	\(1-366\lambda\)

\(-366\lambda\)	\(4\)	\(1\)	\(1\)
\(-3\)	\(-3\)	\(-1\)	\(0\)
\(0\)	\(6\)	\(0\)	\(0\)
\(-6\)	\(0\)	\(0\)	\(0\)

\(0\)	\(\frac{ 1}{ 746496}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(1\)
\(0\)	\(1\)	\(1\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 4}{ 3}\)

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:

Explicit solution

Characteristic classes:

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

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:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

\(\frac{ 23}{ 24}\)	\(-Iarctan(\frac{ 809}{ 331})\)	\(\frac{ 47}{ 576}\)	\(0\)
\(0\)	\(-\frac{ 23}{ 24}\)	\(0\)	\(\frac{ 47}{ 576}\)
\(1\)	\(0\)	\(-\frac{ 23}{ 24}\)	\(Iarctan(\frac{ 809}{ 331})\)
\(0\)	\(1\)	\(0\)	\(\frac{ 23}{ 24}\)

\(\frac{ 7}{ 6}\)	\(I(-\frac{ 7}{ 8}-\frac{ 1}{ 8}ln(2)^(\frac{ 1}{ 2})-\frac{ 1}{ 4}/ln(2)^(\frac{ 1}{ 2}))\)	\(-\frac{ 13}{ 72}\)	\(0\)
\(0\)	\(-\frac{ 7}{ 6}\)	\(0\)	\(-\frac{ 13}{ 72}\)
\(2\)	\(0\)	\(-\frac{ 7}{ 6}\)	\(I(\frac{ 7}{ 8}+\frac{ 1}{ 8}ln(2)^(\frac{ 1}{ 2})+\frac{ 1}{ 4}/ln(2)^(\frac{ 1}{ 2}))\)
\(0\)	\(2\)	\(0\)	\(\frac{ 7}{ 6}\)

\(1.+.620290874I\)	\(0\)	\(\frac{ 32}{ 3}\lambda\)	\(.8015849e-2\)
\(4\)	\(1\)	\(\frac{ 1}{ 3}\)	\(-\frac{ 32}{ 3}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(48\)	\(0\)	\(4\)	\(1.-.620290874I\)

\(5+512\lambda\)	\(-1.-.620290874I\)	\(\frac{ 1}{ 3}+\frac{ 128}{ 3}\lambda\)	\(-\frac{ 1}{ 7}7^{ \frac{ 5}{ 8})exp(-\frac{ 9}{ 4}}Zeta(5)^(\frac{ 1}{ 4})-\frac{ 64}{ 3}\lambda\)
\(16\)	\(-3\)	\(\frac{ 4}{ 3}\)	\(-\frac{ 1}{ 3}-\frac{ 128}{ 3}\lambda\)
\(48\)	\(-12\)	\(5\)	\(-1.-.620290874I\)
\(192\)	\(-48\)	\(16\)	\(-3-512\lambda\)

\(-\frac{ 310145437}{ 500000000}I\)	\(12\)	\(1\)	\(1\)
\(-4\)	\(-24\)	\(-1\)	\(0\)
\(0\)	\(48\)	\(0\)	\(0\)
\(-48\)	\(0\)	\(0\)	\(0\)

	Gopakumar-Vafa invariants
g=0	336, 3636, 83392, 2727936, 109897632, 5057935376, 255380668896, 13802556520272,...
g=1	0, 0, 0, 66, 121056, 29099400, 4233172704, 496392888006,...
g=2	,...

\(1+116\lambda\)	\(0\)	\(\frac{ 29}{ 2}\lambda\)	\(\frac{ 79}{ 6000}\)
\(3\)	\(1\)	\(\frac{ 3}{ 8}\)	\(-\frac{ 29}{ 2}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(24\)	\(0\)	\(3\)	\(1-116\lambda\)

\(21.+14.053465106I\)	\(-8.-5.621386042I\)	\(\frac{ 5}{ 2}+\frac{ 725}{ 2}\lambda\)	\(-.337500198-\frac{ 580}{ 3}\lambda\)
\(75\)	\(-29\)	\(\frac{ 75}{ 8}\)	\(-\frac{ 5}{ 2}-\frac{ 725}{ 2}\lambda\)
\(240\)	\(-96\)	\(31\)	\(-8.-5.621386042I\)
\(600+\frac{ 1}{ 1000000000}I\)	\(-240\)	\(75\)	\(-19.-14.053465106I\)

\(-116\lambda\)	\(7\)	\(1\)	\(1\)
\(-3\)	\(-12\)	\(-1\)	\(0\)
\(0\)	\(24\)	\(0\)	\(0\)
\(-24\)	\(0\)	\(0\)	\(0\)

\(.872284041I\)	\(-\frac{ 1}{ 6}+30\lambda\)	\(-\frac{ 1}{ 12}+15\lambda\)	\(-\frac{ 1}{ 243}\sqrt{ 3}ln(2)^2/(-8I\lambdaPi^3)^(\frac{ 1}{ 6})+5\lambda\)
\(6\)	\(2\)	\(\frac{ 1}{ 2}\)	\(\frac{ 1}{ 12}-15\lambda\)
\(-12\)	\(-2\)	\(0\)	\(-\frac{ 1}{ 6}+30\lambda\)
\(72\)	\(12\)	\(6\)	\(2.-.872284041I\)