Calabi-Yau differential operator database v.3.0

1

New Number: 2.10 | AESZ: 70 | Superseeker: 27 18089 | Hash: 3d2adae6eaf26a56c76b8b67d92cc5df

Degree: 2

$\theta^4-3 x(3\theta+1)(3\theta+2)(10\theta^2+10\theta+3)+3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Coefficients of the holomorphic solution: 1, 18, 1350, 156240, 22141350, ...
--> OEIS
Normalized instanton numbers (n₀=1): 27, 432, 18089, 997785, 68438142, ... ; Common denominator:...

Discriminant

$(243z-1)(27z-1)$

Local exponents

$0$ $\frac{ 1}{ 243}$ $\frac{ 1}{ 27}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $\frac{ 5}{ 3}$

\(0\)	\(\frac{ 1}{ 243}\)	\(\frac{ 1}{ 27}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 4}{ 3}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast c$.

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-156\)	\(72\)	\(18\)	\(9\)

2

New Number: 2.16 | AESZ: 65 | Superseeker: 240 19105840 | Hash: 13ba368bcbb10731ac8727b510731ff2

Degree: 2

$\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{9} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 240, 277200, 457416960, 904864680720, ...
--> OEIS
Normalized instanton numbers (n₀=1): 240, 57102, 19105840, 14810143935, 10017820614480, ... ; Common denominator:...

Discriminant

$(3456z-1)(1728z-1)$

Local exponents

$0$ $\frac{ 1}{ 3456}$ $\frac{ 1}{ 1728}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $1$ $\frac{ 5}{ 6}$
$0$ $1$ $1$ $\frac{ 7}{ 6}$
$0$ $2$ $2$ $\frac{ 11}{ 6}$

\(0\)	\(\frac{ 1}{ 3456}\)	\(\frac{ 1}{ 1728}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*d

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 240, 457056, 515857920, 947849668896, 1252227576810240, 1951472479155996672, 2805919645433093677056,...
Coefficients of the q-coordinate : 0, 1, -1488, 1737216, -1936036864, 2030351668656, -2106830943512064, 2118312344000340992,...

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

Explicit solution

$A_{n}=\dbinom{3n}{n}\dbinom{6n}{3n}\sum_{k=0}^{n}\dbinom{n}{k}\dbinom{2k}{k}\dbinom{2n-2k}{n-k}$

Maple LaTex

Characteristic classes:

$C_3$	$C_2 H$	$H^3$	$ \vert H \vert$
$-470$	$92$	$8$	$9$

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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$1.+2.277630552I$	$0$	$1.091364639I$	$.648450116$
$\frac{ 23}{ 6}$	$1$	$\frac{ 529}{ 288}$	$-1.091364639I$
$0$	$0$	$1$	$0$
$8$	$0$	$\frac{ 23}{ 6}$	$1.-2.277630552I$

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$\frac{ 37}{ 12}+940\lambda$	$-.52083333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.138815272I$	$.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889+2.182729279I$	$1.025632871-1.186265914I$
$\frac{ 23}{ 3}+\frac{ 1}{ 250000000}I$	$-\frac{ 11}{ 12}+\frac{ 3}{ 1000000000}I$	$\frac{ 529}{ 144}-\frac{ 1}{ 250000000}I$	$-.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889-2.182729279I$
$4+\frac{ 1}{ 500000000}I$	$-1+\frac{ 1}{ 1000000000}I$	$\frac{ 35}{ 12}-\frac{ 1}{ 500000000}I$	$-\frac{ 25}{ 48}-235\lambda$
$16+\frac{ 9}{ 1000000000}I$	$-3.999999988+.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I$	$\frac{ 23}{ 3}-\frac{ 1}{ 125000000}I$	$-\frac{ 13}{ 12}-940\lambda$

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Basis of the Doran-Morgan lattice

$-\frac{ 284703819}{ 125000000}I$	$\frac{ 31}{ 6}$	$1$	$1$
$-\frac{ 23}{ 6}$	$-4$	$-1$	$0$
$0$	$8$	$0$	$0$
$-8$	$0$	$0$	$0$

copy data

3

New Number: 2.2 | AESZ: 15 | Superseeker: 21 15894 | Hash: c8053e0e9c05ef468263fafd5e3fc764

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...

Discriminant

$-(27z+1)(216z-1)$

Local exponents

$-\frac{ 1}{ 27}$ $0$ $\frac{ 1}{ 216}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $\frac{ 5}{ 3}$

\(-\frac{ 1}{ 27}\)	\(0\)	\(\frac{ 1}{ 216}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 4}{ 3}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast a$.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-162\)	\(72\)	\(18\)	\(9\)

4

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

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

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

Note:

Hadamard product $A\ast b$

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

	Gopakumar-Vafa invariants
g=0	400, 5540, 164400, 7059880, 373030720, 22532353740, 1493352046000, 105953648564840,...
g=1	0, 0, 0, 1537, 882496, 214941640, 37001766880, 5388182343297,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-120\)	\(68\)	\(20\)	\(9\)

5

New Number: 4.42 | AESZ: 222 | Superseeker: 69/5 29081/5 | Hash: aad7a72e711c9c463396d319e0bf7603

Degree: 4

$5^{2} \theta^4-5 x\left(407\theta^4+1198\theta^3+909\theta^2+310\theta+40\right)-2^{7} x^{2}\left(2103\theta^4+6999\theta^3+8358\theta^2+4050\theta+680\right)-2^{12} x^{3}\left(1387\theta^4+3840\theta^3+3081\theta^2+960\theta+100\right)-2^{21} x^{4}\left((2\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 504, 36800, 3518200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 69/5, 1383/4, 29081/5, 346080, 72023607/5, ... ; Common denominator:...

Discriminant

$-(8192z^2+107z-1)(5+64z)^2$

Local exponents

$-\frac{ 5}{ 64}$ $-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}$ $0$ $s_1$ $s_2$ $-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$3$ $1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$4$ $2$ $0$ $2$ $2$ $2$ $\frac{ 1}{ 2}$

\(-\frac{ 5}{ 64}\)	\(-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}\)	\(0\)	\(s_1\)	\(s_2\)	\(-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(4\)	\(2\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-128\)	\(68\)	\(20\)	\(9\)

6

New Number: 5.12 | AESZ: 74 | Superseeker: -30 -14632 | Hash: e668180adb7c88d4e5fbab5eb7ee61c7

Degree: 5

$\theta^4-2 3 x\left(99\theta^4+36\theta^3+39\theta^2+21\theta+4\right)+2^{2} 3^{2} x^{2}\left(3807\theta^4+3564\theta^3+3798\theta^2+1683\theta+284\right)-2^{3} 3^{5} x^{3}\left(7857\theta^4+13608\theta^3+14562\theta^2+7317\theta+1444\right)+2^{4} 3^{9} x^{4}\left(2592\theta^4+7128\theta^3+8550\theta^2+4851\theta+1052\right)-2^{5} 3^{13} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 1152, 71520, 5101200, ...
--> OEIS
Normalized instanton numbers (n₀=1): -30, -516, -14632, -4227807/8, -22139868, ... ; Common denominator:...

Discriminant

$-(-1+54z)(162z-1)^2(108z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 162}$ $\frac{ 1}{ 108}$ $\frac{ 1}{ 54}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 2}{ 3}$
$0$ $1$ $\frac{ 1}{ 2}$ $1$ $\frac{ 5}{ 6}$
$0$ $3$ $\frac{ 1}{ 2}$ $1$ $\frac{ 7}{ 6}$
$0$ $4$ $1$ $2$ $\frac{ 4}{ 3}$

\(0\)	\(\frac{ 1}{ 162}\)	\(\frac{ 1}{ 108}\)	\(\frac{ 1}{ 54}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(\frac{ 5}{ 6}\)
\(0\)	\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(4\)	\(1\)	\(2\)	\(\frac{ 4}{ 3}\)

Note:

This is operator "5.12" from ...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(450\)	\(-36\)	\(72\)	\(9\)

7

New Number: 5.35 | AESZ: 218 | Superseeker: 138/7 42984/7 | Hash: a76111af659715caf2c4344eedd9d678

Degree: 5

$7^{2} \theta^4-2 3 7 x\left(192\theta^4+396\theta^3+303\theta^2+105\theta+14\right)+2^{2} 3 x^{2}\left(1188\theta^4+11736\theta^3+20431\theta^2+12152\theta+2436\right)+2^{2} 3^{3} x^{3}\left(532\theta^4+504\theta^3-3455\theta^2-3829\theta-1036\right)-2^{4} 3^{4} x^{4}(2\theta+1)(36\theta^3+306\theta^2+421\theta+156)-2^{6} 3^{4} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 612, 48000, 4580100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 138/7, 1506/7, 42984/7, 235596, 78950334/7, ... ; Common denominator:...

Discriminant

$-(1296z^3-864z^2+168z-1)(7+12z)^2$

Local exponents

$-\frac{ 7}{ 12}$ $0$ ≈$0.006145$ ≈$0.330261-0.128447I$ ≈$0.330261+0.128447I$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 2}{ 3}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 4}{ 3}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 7}{ 12}\)	\(0\)	≈\(0.006145\)	≈\(0.330261-0.128447I\)	≈\(0.330261+0.128447I\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 4}{ 3}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.35" from ...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-100\)	\(66\)	\(21\)	\(9\)

8

New Number: 5.51 | AESZ: 250 | Superseeker: 308/23 70799/23 | Hash: 9c19794a84073d1c6dfd11c8a7c9a740

Degree: 5

$23^{2} \theta^4-23 x\left(3271\theta^4+5078\theta^3+3896\theta^2+1357\theta+184\right)+x^{2}\left(1357863\theta^4+999924\theta^3-787393\theta^2-850862\theta-205712\right)-2^{3} x^{3}\left(775799\theta^4-272481\theta^3-218821\theta^2+176709\theta+100234\right)-2^{4} 61 x^{4}\left(1005\theta^4-15654\theta^3-36317\theta^2-27938\theta-7304\right)-2^{9} 61^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 324, 19304, 1388260, ...
--> OEIS
Normalized instanton numbers (n₀=1): 308/23, 3526/23, 70799/23, 2148684/23, 81402822/23, ... ; Common denominator:...

Discriminant

$-(512z^3+113z^2+121z-1)(-23+244z)^2$

Local exponents

≈$-0.114451-0.474453I$ ≈$-0.114451+0.474453I$ $0$ ≈$0.008199$ $\frac{ 23}{ 244}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 3}{ 4}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $1$
$2$ $2$ $0$ $2$ $4$ $\frac{ 5}{ 4}$

≈\(-0.114451-0.474453I\)	≈\(-0.114451+0.474453I\)	\(0\)	≈\(0.008199\)	\(\frac{ 23}{ 244}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(1\)
\(2\)	\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 5}{ 4}\)

Note:

This is operator "5.51" from ...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-74\)	\(62\)	\(23\)	\(9\)

9

New Number: 5.70 | AESZ: 287 | Superseeker: 361/21 120472/21 | Hash: 97932196c46a8712f6dcb11165d698be

Degree: 5

$3^{2} 7^{2} \theta^4-3 7 x\left(3289\theta^4+6098\theta^3+4645\theta^2+1596\theta+210\right)+2^{2} 5 x^{2}\left(7712\theta^4-46168\theta^3-106885\theta^2-67410\theta-13629\right)+2^{4} x^{3}\left(106636\theta^4+493416\theta^3+420211\theta^2+116361\theta+6090\right)-2^{8} 5 x^{4}(2\theta+1)(1916\theta^3+2622\theta^2+1077\theta+91)-2^{12} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 510, 38260, 3473470, ...
--> OEIS
Normalized instanton numbers (n₀=1): 361/21, 4780/21, 120472/21, 1537864/7, 216261320/21, ... ; Common denominator:...

Discriminant

$-(64z^3+800z^2+149z-1)(-21+80z)^2$

Local exponents

≈$-12.310784$ ≈$-0.195701$ $0$ ≈$0.006485$ $\frac{ 21}{ 80}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $1$
$2$ $2$ $0$ $2$ $4$ $\frac{ 3}{ 2}$

≈\(-12.310784\)	≈\(-0.195701\)	\(0\)	≈\(0.006485\)	\(\frac{ 21}{ 80}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(1\)
\(2\)	\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.70" from ...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-104\)	\(66\)	\(21\)	\(9\)

10

New Number: 8.26 | AESZ: 301 | Superseeker: 193/11 48570/11 | Hash: a91db18876a9dfbf42b88f8d64c55d85

Degree: 8

$11^{2} \theta^4-11 x\left(1517\theta^4+3136\theta^3+2393\theta^2+825\theta+110\right)-x^{2}\left(24266+106953\theta+202166\theta^2+207620\theta^3+90362\theta^4\right)-x^{3}\left(53130+217437\theta+415082\theta^2+507996\theta^3+245714\theta^4\right)-x^{4}\left(15226+183269\theta+564786\theta^2+785972\theta^3+407863\theta^4\right)-x^{5}\left(25160+279826\theta+728323\theta^2+790148\theta^3+434831\theta^4\right)-2^{3} x^{6}\left(36361\theta^4+70281\theta^3+73343\theta^2+37947\theta+7644\right)-2^{4} 5 x^{7}\left(1307\theta^4+3430\theta^3+3877\theta^2+2162\theta+488\right)-2^{9} 5^{2} x^{8}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 10, 466, 32392, 2727826, ...
--> OEIS
Normalized instanton numbers (n₀=1): 193/11, 1973/11, 48570/11, 1689283/11, 72444183/11, ... ; Common denominator:...

Discriminant

$-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2$

Local exponents

$-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}$ $-1$ $-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I$ $-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I$ $0$ $-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $0$ $1$
$1$ $\frac{ 1}{ 2}$ $1$ $1$ $0$ $1$ $1$
$1$ $\frac{ 1}{ 2}$ $3$ $3$ $0$ $1$ $1$
$2$ $1$ $4$ $4$ $0$ $2$ $1$

\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\)	\(-1\)	\(-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I\)	\(-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I\)	\(0\)	\(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)
\(1\)	\(\frac{ 1}{ 2}\)	\(3\)	\(3\)	\(0\)	\(1\)	\(1\)
\(2\)	\(1\)	\(4\)	\(4\)	\(0\)	\(2\)	\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.27.

\(4+468\lambda\)	\(-1.-.755979502I\)	\(\frac{ 1}{ 2}+78\lambda\)	\(-.71415832e-1-52\lambda\)
\(9\)	\(-2\)	\(\frac{ 3}{ 2}\)	\(-\frac{ 1}{ 2}-78\lambda\)
\(18\)	\(-6\)	\(4\)	\(-1.-.755979502I\)
\(54\)	\(-18\)	\(9\)	\(-2-468\lambda\)

\(1.+2.277630552I\)	\(0\)	\(1.091364639I\)	\(.648450116\)
\(\frac{ 23}{ 6}\)	\(1\)	\(\frac{ 529}{ 288}\)	\(-1.091364639I\)
\(0\)	\(0\)	\(1\)	\(0\)
\(8\)	\(0\)	\(\frac{ 23}{ 6}\)	\(1.-2.277630552I\)

\(\frac{ 37}{ 12}+940\lambda\)	\(-.52083333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.138815272I\)	\(.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889+2.182729279I\)	\(1.025632871-1.186265914I\)
\(\frac{ 23}{ 3}+\frac{ 1}{ 250000000}I\)	\(-\frac{ 11}{ 12}+\frac{ 3}{ 1000000000}I\)	\(\frac{ 529}{ 144}-\frac{ 1}{ 250000000}I\)	\(-.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889-2.182729279I\)
\(4+\frac{ 1}{ 500000000}I\)	\(-1+\frac{ 1}{ 1000000000}I\)	\(\frac{ 35}{ 12}-\frac{ 1}{ 500000000}I\)	\(-\frac{ 25}{ 48}-235\lambda\)
\(16+\frac{ 9}{ 1000000000}I\)	\(-3.999999988+.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I\)	\(\frac{ 23}{ 3}-\frac{ 1}{ 125000000}I\)	\(-\frac{ 13}{ 12}-940\lambda\)

\(4+324\lambda\)	\(-\frac{ 3}{ 2}-162\lambda\)	\(\frac{ 3}{ 4}+81\lambda\)	\(-\frac{ 222}{ 1223}-54\lambda\)
\(9\)	\(-\frac{ 7}{ 2}\)	\(\frac{ 9}{ 4}\)	\(-\frac{ 3}{ 4}-81\lambda\)
\(18\)	\(-9\)	\(\frac{ 11}{ 2}\)	\(-\frac{ 3}{ 2}-162\lambda\)
\(36\)	\(-18\)	\(9\)	\(-2-324\lambda\)

\(\frac{ 16}{ 3}+480\lambda\)	\(-\frac{ 13}{ 6}-240\lambda\)	\(\frac{ 299}{ 360}+92\lambda\)	\(-.167088493-52\lambda\)
\(\frac{ 46}{ 3}\)	\(-\frac{ 20}{ 3}\)	\(\frac{ 529}{ 180}\)	\(-\frac{ 299}{ 360}-92\lambda\)
\(40\)	\(-20\)	\(\frac{ 26}{ 3}\)	\(-\frac{ 13}{ 6}-240\lambda\)
\(80\)	\(-40\)	\(\frac{ 46}{ 3}\)	\(-\frac{ 10}{ 3}-480\lambda\)

\(1.+.755979502I\)	\(0\)	\(26\lambda\)	\(.31750278e-1\)
\(3\)	\(1\)	\(\frac{ 1}{ 2}\)	\(-26\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(18\)	\(0\)	\(3\)	\(1.-.755979502I\)

\(-\frac{ 377989751}{ 500000000}I\)	\(6\)	\(1\)	\(1\)
\(-3\)	\(-9\)	\(-1\)	\(0\)
\(0\)	\(18\)	\(0\)	\(0\)
\(-18\)	\(0\)	\(0\)	\(0\)

\(-\frac{ 284703819}{ 125000000}I\)	\(\frac{ 31}{ 6}\)	\(1\)	\(1\)
\(-\frac{ 23}{ 6}\)	\(-4\)	\(-1\)	\(0\)
\(0\)	\(8\)	\(0\)	\(0\)
\(-8\)	\(0\)	\(0\)	\(0\)

\(1+162\lambda\)	\(0\)	\(27\lambda\)	\(.34239575e-1\)
\(3\)	\(1\)	\(\frac{ 1}{ 2}\)	\(-27\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(18\)	\(0\)	\(3\)	\(1-162\lambda\)

\(-162\lambda\)	\(6\)	\(1\)	\(1\)
\(-3\)	\(-9\)	\(-1\)	\(0\)
\(0\)	\(18\)	\(0\)	\(0\)
\(-18\)	\(0\)	\(0\)	\(0\)

\(1+120\lambda\)	\(0\)	\(17\lambda\)	\(.16908432e-1\)
\(\frac{ 17}{ 6}\)	\(1\)	\(\frac{ 289}{ 720}\)	\(-17\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(20\)	\(0\)	\(\frac{ 17}{ 6}\)	\(1-120\lambda\)

\(-120\lambda\)	\(\frac{ 37}{ 6}\)	\(1\)	\(1\)
\(-\frac{ 17}{ 6}\)	\(-10\)	\(-1\)	\(0\)
\(0\)	\(20\)	\(0\)	\(0\)
\(-20\)	\(0\)	\(0\)	\(0\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

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:

Explicit solution

Characteristic classes:

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:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice