Calabi-Yau differential operator database v.3.0

61

New Number: 5.33 | AESZ: 216 | Superseeker: 9 14201/3 | Hash: af7027bf24acce4fd0ed5b09e575e2a5

Degree: 5

$\theta^4-3 x\theta(2+11\theta+18\theta^2+27\theta^3)-2 3^{3} x^{2}\left(72\theta^4+414\theta^3+603\theta^2+330\theta+64\right)+2^{2} 3^{5} x^{3}\left(93\theta^4-720\theta^2-708\theta-184\right)+2^{3} 3^{7} x^{4}(2\theta+1)(54\theta^3+405\theta^2+544\theta+200)-2^{4} 3^{10} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, 216, 7200, 567000, ...
--> OEIS
Normalized instanton numbers (n₀=1): 9, 225, 14201/3, 154800, 6298596, ... ; Common denominator:...

Discriminant

$-(27z+1)(108z-1)(36z+1)(-1+18z)^2$

Local exponents

$-\frac{ 1}{ 27}$ $-\frac{ 1}{ 36}$ $0$ $\frac{ 1}{ 108}$ $\frac{ 1}{ 18}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $\frac{ 2}{ 3}$
$1$ $1$ $0$ $1$ $3$ $\frac{ 4}{ 3}$
$2$ $2$ $0$ $2$ $4$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 27}\)	\(-\frac{ 1}{ 36}\)	\(0\)	\(\frac{ 1}{ 108}\)	\(\frac{ 1}{ 18}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(\frac{ 4}{ 3}\)
\(2\)	\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.33" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-52\)	\(48\)	\(18\)	\(7\)

62

New Number: 5.34 | AESZ: 217 | Superseeker: 17/7 5095/21 | Hash: e8743aeac19deca699ff90aaef6b8ea7

Degree: 5

$7^{2} \theta^4+7 x\theta(-14-73\theta-118\theta^2+13\theta^3)-2^{3} 3 x^{2}\left(3378\theta^4+13446\theta^3+18869\theta^2+11158\theta+2352\right)-2^{4} 3^{3} x^{3}\left(3628\theta^4+17920\theta^3+31668\theta^2+22596\theta+5383\right)-2^{8} 3^{3} x^{4}(2\theta+1)(572\theta^3+2370\theta^2+2896\theta+1095)-2^{10} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, 72, 720, 37800, ...
--> OEIS
Normalized instanton numbers (n₀=1): 17/7, 254/7, 5095/21, 29600/7, 491991/7, ... ; Common denominator:...

Discriminant

$-(16z+1)(27z+1)(48z-1)(7+24z)^2$

Local exponents

$-\frac{ 7}{ 24}$ $-\frac{ 1}{ 16}$ $-\frac{ 1}{ 27}$ $0$ $\frac{ 1}{ 48}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $0$ $1$ $\frac{ 5}{ 6}$
$3$ $1$ $1$ $0$ $1$ $\frac{ 7}{ 6}$
$4$ $2$ $2$ $0$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 7}{ 24}\)	\(-\frac{ 1}{ 16}\)	\(-\frac{ 1}{ 27}\)	\(0\)	\(\frac{ 1}{ 48}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(\frac{ 5}{ 6}\)
\(3\)	\(1\)	\(1\)	\(0\)	\(1\)	\(\frac{ 7}{ 6}\)
\(4\)	\(2\)	\(2\)	\(0\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.34" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-112\)	\(84\)	\(42\)	\(14\)

63

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 ...

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

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

64

New Number: 5.36 | AESZ: 219 | Superseeker: 166/5 360988/15 | Hash: b7068bb339f61ebd7c591b7be3fe5893

Degree: 5

$5^{2} \theta^4-2 5 x\left(464\theta^4+1036\theta^3+763\theta^2+245\theta+30\right)-2^{2} 3^{2} x^{2}\left(7064\theta^4+22472\theta^3+26699\theta^2+13200\theta+2340\right)-2^{4} 3^{4} x^{3}\left(3440\theta^4+13320\theta^3+18784\theta^2+10665\theta+2070\right)-2^{6} 3^{8} x^{4}(19\theta^2+59\theta+45)(2\theta+1)^2-2^{8} 3^{9} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 972, 109200, 14949900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 166/5, 638, 360988/15, 7222128/5, 524377242/5, ... ; Common denominator:...

Discriminant

$-(16z+1)(3888z^2+216z-1)(5+36z)^2$

Local exponents

$-\frac{ 5}{ 36}$ $-\frac{ 1}{ 16}$ $-\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 3}$ $0$ $-\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 3}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $0$ $1$ $\frac{ 1}{ 2}$
$3$ $1$ $1$ $0$ $1$ $\frac{ 3}{ 2}$
$4$ $2$ $2$ $0$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 5}{ 36}\)	\(-\frac{ 1}{ 16}\)	\(-\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 3}\)	\(0\)	\(-\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 3}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(1\)	\(1\)	\(0\)	\(1\)	\(\frac{ 3}{ 2}\)
\(4\)	\(2\)	\(2\)	\(0\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.36" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-80\)	\(54\)	\(15\)	\(7\)

65

New Number: 5.37 | AESZ: 221 | Superseeker: 492/5 872164/5 | Hash: b7ce7a734c057660ce3d6341a7572078

Degree: 5

$5^{2} \theta^4-2^{2} 5 x\left(404\theta^4+1096\theta^3+773\theta^2+225\theta+25\right)-2^{4} x^{2}\left(66896\theta^4+137408\theta^3+101096\theta^2+52800\theta+11625\right)-2^{8} 3 5 x^{3}(2\theta+1)(5672\theta^3+9500\theta^2+8422\theta+2689)-2^{15} 3^{2} x^{4}(2\theta+1)(1208\theta^3+2892\theta^2+2842\theta+969)-2^{20} 3^{3} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 20, 2988, 618320, 156299500, ...
--> OEIS
Normalized instanton numbers (n₀=1): 492/5, 10376/5, 872164/5, 91316176/5, 12181916784/5, ... ; Common denominator:...

Discriminant

$-(-1+432z)(16z+1)^2(192z+5)^2$

Local exponents

$-\frac{ 1}{ 16}$ $-\frac{ 5}{ 192}$ $0$ $\frac{ 1}{ 432}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$\frac{ 1}{ 4}$ $1$ $0$ $1$ $\frac{ 5}{ 6}$
$\frac{ 3}{ 4}$ $3$ $0$ $1$ $\frac{ 7}{ 6}$
$1$ $4$ $0$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 16}\)	\(-\frac{ 5}{ 192}\)	\(0\)	\(\frac{ 1}{ 432}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 4}\)	\(1\)	\(0\)	\(1\)	\(\frac{ 5}{ 6}\)
\(\frac{ 3}{ 4}\)	\(3\)	\(0\)	\(1\)	\(\frac{ 7}{ 6}\)
\(1\)	\(4\)	\(0\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.37" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-32\)	\(40\)	\(10\)	\(5\)

66

New Number: 5.38 | AESZ: 223 | Superseeker: 18 64744/3 | Hash: e3ab25cffe4a0968b175bd9e98c96427

Degree: 5

$\theta^4+2 3 x\theta(48\theta^3-12\theta^2-7\theta-1)+2^{2} 3^{3} x^{2}\left(392\theta^4+488\theta^3+775\theta^2+376\theta+64\right)+2^{4} 3^{5} x^{3}\left(1184\theta^4+3288\theta^3+3512\theta^2+1635\theta+278\right)+2^{6} 3^{8} x^{4}(169\theta^2+361\theta+238)(2\theta+1)^2+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, -432, 7200, 1587600, ...
--> OEIS
Normalized instanton numbers (n₀=1): 18, -873, 64744/3, -229968, -1628892, ... ; Common denominator:...

Discriminant

$(36z+1)(13824z^2+36z+1)(1+108z)^2$

Local exponents

$-\frac{ 1}{ 36}$ $-\frac{ 1}{ 108}$ $-\frac{ 1}{ 768}-\frac{ 5}{ 2304}\sqrt{ 15}I$ $-\frac{ 1}{ 768}+\frac{ 5}{ 2304}\sqrt{ 15}I$ $0$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $1$ $0$ $\frac{ 1}{ 2}$
$1$ $3$ $1$ $1$ $0$ $\frac{ 3}{ 2}$
$2$ $4$ $2$ $2$ $0$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 36}\)	\(-\frac{ 1}{ 108}\)	\(-\frac{ 1}{ 768}-\frac{ 5}{ 2304}\sqrt{ 15}I\)	\(-\frac{ 1}{ 768}+\frac{ 5}{ 2304}\sqrt{ 15}I\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(3\)	\(1\)	\(1\)	\(0\)	\(\frac{ 3}{ 2}\)
\(2\)	\(4\)	\(2\)	\(2\)	\(0\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.38" from ...

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

67

New Number: 5.39 | AESZ: 224 | Superseeker: 59/5 22503/5 | Hash: ba17e8cb074bba75e7a27206be530698

Degree: 5

$5^{2} \theta^4-5 x\left(1057\theta^4+1058\theta^3+819\theta^2+290\theta+40\right)+2^{5} x^{2}\left(10123\theta^4+11419\theta^3+5838\theta^2+1510\theta+180\right)-2^{8} x^{3}\left(30981\theta^4+46560\theta^3+48211\theta^2+25500\theta+5100\right)+2^{14} 11 x^{4}(2\theta+1)(234\theta^3+591\theta^2+581\theta+202)-2^{20} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 312, 19520, 1475320, ...
--> OEIS
Normalized instanton numbers (n₀=1): 59/5, 186, 22503/5, 718052/5, 29091017/5, ... ; Common denominator:...

Discriminant

$-(128z-1)(128z^2-13z+1)(-5+176z)^2$

Local exponents

$0$ $\frac{ 1}{ 128}$ $\frac{ 5}{ 176}$ $\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I$ $\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $3$ $1$ $1$ $1$
$0$ $2$ $4$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 128}\)	\(\frac{ 5}{ 176}\)	\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)	\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(3\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(4\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.39" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-72\)	\(56\)	\(20\)	\(8\)

68

New Number: 5.3 | AESZ: 20 | Superseeker: 3 245/3 | Hash: a9a698dc5c79ffda497a7897390408b0

Degree: 5

$\theta^4-3 x\left(48\theta^4+60\theta^3+53\theta^2+23\theta+4\right)+3^{2} x^{2}\left(873\theta^4+1980\theta^3+2319\theta^2+1344\theta+304\right)-2 3^{4} x^{3}\left(1269\theta^4+3888\theta^3+5259\theta^2+3348\theta+800\right)+2^{2} 3^{6} x^{4}\left(891\theta^4+3240\theta^3+4653\theta^2+2952\theta+688\right)-2^{3} 3^{11} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 252, 6600, 198540, ...
--> OEIS
Normalized instanton numbers (n₀=1): 3, 33/2, 245/3, 879, 11829, ... ; Common denominator:...

Discriminant

$-(54z-1)(27z-1)^2(18z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 54}$ $\frac{ 1}{ 27}$ $\frac{ 1}{ 18}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 2}{ 3}$
$0$ $1$ $\frac{ 1}{ 3}$ $1$ $1$
$0$ $1$ $\frac{ 2}{ 3}$ $3$ $1$
$0$ $2$ $1$ $4$ $\frac{ 4}{ 3}$

\(0\)	\(\frac{ 1}{ 54}\)	\(\frac{ 1}{ 27}\)	\(\frac{ 1}{ 18}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(\frac{ 1}{ 3}\)	\(1\)	\(1\)
\(0\)	\(1\)	\(\frac{ 2}{ 3}\)	\(3\)	\(1\)
\(0\)	\(2\)	\(1\)	\(4\)	\(\frac{ 4}{ 3}\)

Note:

A-Incarnation: (3,0),(0,3),(1,1) intersection in $P^3 \times \P^3$.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-18\)	\(72\)	\(54\)	\(15\)

69

New Number: 5.40 | AESZ: 226 | Superseeker: 62/5 4060/3 | Hash: 92f95cd33ac4bf18c2d05ce3040c5203

Degree: 5

$5^{2} \theta^4-2 5 x\left(328\theta^4+692\theta^3+551\theta^2+205\theta+30\right)+2^{2} 3 x^{2}\left(5352\theta^4+25416\theta^3+38387\theta^2+23020\theta+4860\right)-2^{4} 3^{3} x^{3}\left(352\theta^4+4520\theta^3+12108\theta^2+10205\theta+2630\right)-2^{6} 3^{3} x^{4}(2\theta+1)(586\theta^3+3039\theta^2+3947\theta+1527)-2^{8} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 396, 19920, 1241100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 62/5, 55, 4060/3, 28790, 861786, ... ; Common denominator:...

Discriminant

$-(16z-1)(108z-1)(12z-1)(5+12z)^2$

Local exponents

$-\frac{ 5}{ 12}$ $0$ $\frac{ 1}{ 108}$ $\frac{ 1}{ 16}$ $\frac{ 1}{ 12}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 5}{ 6}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 7}{ 6}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 5}{ 12}\)	\(0\)	\(\frac{ 1}{ 108}\)	\(\frac{ 1}{ 16}\)	\(\frac{ 1}{ 12}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 5}{ 6}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 7}{ 6}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.40" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-76\)	\(72\)	\(30\)	\(11\)

70

New Number: 5.41 | AESZ: 230 | Superseeker: 291 7935104 | Hash: ac762b013587176079179af09a110ab6

Degree: 5

$\theta^4+3 x\left(945\theta^4-162\theta^3-49\theta^2+32\theta+8\right)+2 3^{4} x^{2}\left(17928\theta^4+2970\theta^3+10187\theta^2+3376\theta+408\right)+2^{2} 3^{7} x^{3}\left(156285\theta^4+200016\theta^3+193630\theta^2+84378\theta+13964\right)+2^{4} 3^{10} 19 x^{4}(4743\theta^2+8199\theta+4922)(2\theta+1)^2+2^{9} 3^{15} 19^{2} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, -24, -648, 494400, -82643400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 291, -38832, 7935104, -2098976940, 651305429796, ... ; Common denominator:...

Discriminant

$(432z+1)(93312z^2+351z+1)(1+1026z)^2$

Local exponents

$-\frac{ 1}{ 432}$ $-\frac{ 13}{ 6912}-\frac{ 7}{ 6912}\sqrt{ 7}I$ $-\frac{ 13}{ 6912}+\frac{ 7}{ 6912}\sqrt{ 7}I$ $-\frac{ 1}{ 1026}$ $0$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $1$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $3$ $0$ $\frac{ 3}{ 2}$
$2$ $2$ $2$ $4$ $0$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 432}\)	\(-\frac{ 13}{ 6912}-\frac{ 7}{ 6912}\sqrt{ 7}I\)	\(-\frac{ 13}{ 6912}+\frac{ 7}{ 6912}\sqrt{ 7}I\)	\(-\frac{ 1}{ 1026}\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(1\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(1\)	\(3\)	\(0\)	\(\frac{ 3}{ 2}\)
\(2\)	\(2\)	\(2\)	\(4\)	\(0\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.41" from ...

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

71

New Number: 5.42 | AESZ: 231 | Superseeker: 460/3 894404/3 | Hash: 6f793238336123adfdcd7ee17d64e5ec

Degree: 5

$3^{2} \theta^4-2^{2} 3 x\left(28\theta^4+1016\theta^3+739\theta^2+231\theta+30\right)-2^{9} x^{2}\left(1168\theta^4-968\theta^3-9518\theta^2-5325\theta-1005\right)+2^{16} x^{3}\left(988\theta^4+8208\theta^3-743\theta^2-4230\theta-1245\right)+2^{24} 5 x^{4}(2\theta+1)^2(9\theta^2-279\theta-277)-2^{33} 5^{2} x^{5}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 40, 3240, 313600, 39327400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 460/3, -16828/3, 894404/3, -42271624/3, 2076730720/3, ... ; Common denominator:...

Discriminant

$-(256z-1)(32768z^2-208z+1)(3+640z)^2$

Local exponents

$-\frac{ 3}{ 640}$ $0$ $\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I$ $\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 1}{ 2}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 3}{ 2}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 3}{ 640}\)	\(0\)	\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)	\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.42" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(160\)	\(48\)	\(24\)	\(8\)

72

New Number: 5.43 | AESZ: 234 | Superseeker: 18/7 5676/7 | Hash: 3e70b30959c0c3bd799b435b9c842186

Degree: 5

$7^{2} \theta^4-2 7 x\theta(192\theta^3+60\theta^2+37\theta+7)-2^{2} x^{2}\left(17608\theta^4+115144\theta^3+166715\theta^2+94556\theta+18816\right)+2^{4} 3^{2} x^{3}\left(20288\theta^4+57288\theta^3+27524\theta^2-7455\theta-5026\right)-2^{6} 3^{5} x^{4}(2\theta+1)(458\theta^3-657\theta^2-1799\theta-846)-2^{12} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 0, 96, 1440, 90720, ...
--> OEIS
Normalized instanton numbers (n₀=1): 18/7, 515/7, 5676/7, 133796/7, 2929726/7, ... ; Common denominator:...

Discriminant

$-(64z-1)(36z+1)(4z+1)(-7+108z)^2$

Local exponents

$-\frac{ 1}{ 4}$ $-\frac{ 1}{ 36}$ $0$ $\frac{ 1}{ 64}$ $\frac{ 7}{ 108}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $1$
$2$ $2$ $0$ $2$ $4$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 4}\)	\(-\frac{ 1}{ 36}\)	\(0\)	\(\frac{ 1}{ 64}\)	\(\frac{ 7}{ 108}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(1\)
\(2\)	\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.43" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-88\)	\(64\)	\(28\)	\(10\)

73

New Number: 5.44 | AESZ: 240 | Superseeker: 231/13 38037/13 | Hash: 8f46cd6968b3b676e251a9d8635637fc

Degree: 5

$13^{2} \theta^4-13 x\left(1449\theta^4+4050\theta^3+3143\theta^2+1118\theta+156\right)-2^{4} x^{2}\left(22760\theta^4-27112\theta^3-121046\theta^2-82316\theta-17589\right)+2^{8} x^{3}\left(3824\theta^4+39936\theta^3-34292\theta^2-63492\theta-19539\right)-2^{16} 3 x^{4}(2\theta+1)(40\theta^3+684\theta^2+1013\theta+399)-2^{20} 3^{2} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 468, 28560, 2135700, ...
--> OEIS
Normalized instanton numbers (n₀=1): 231/13, 826/13, 38037/13, 786076/13, 32662752/13, ... ; Common denominator:...

Discriminant

$-(128z-1)(128z^2-13z+1)(13+192z)^2$

Local exponents

$-\frac{ 13}{ 192}$ $0$ $\frac{ 1}{ 128}$ $\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I$ $\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 3}{ 4}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 5}{ 4}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 3}{ 2}$

\(-\frac{ 13}{ 192}\)	\(0\)	\(\frac{ 1}{ 128}\)	\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)	\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(3\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 5}{ 4}\)
\(4\)	\(0\)	\(2\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.44" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-72\)	\(68\)	\(26\)	\(10\)

74

New Number: 5.45 | AESZ: 242 | Superseeker: -18 1568/3 | Hash: 562c18d54c0080ebb0bb01b14a8241ce

Degree: 5

$\theta^4+2 3 x\left(72\theta^4+108\theta^3+91\theta^2+37\theta+6\right)+2^{2} 3^{3} x^{2}\left(648\theta^4+1800\theta^3+2211\theta^2+1248\theta+260\right)+2^{4} 3^{5} x^{3}\left(1344\theta^4+4968\theta^3+7320\theta^2+4749\theta+1072\right)+2^{6} 3^{7} x^{4}(2\theta+1)(630\theta^3+2241\theta^2+2617\theta+971)+2^{8} 3^{10} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -36, 2484, -208080, 19221300, ...
--> OEIS
Normalized instanton numbers (n₀=1): -18, 99/2, 1568/3, 22698, -165960, ... ; Common denominator:...

Discriminant

$(1+144z)(36z+1)^2(108z+1)^2$

Local exponents

$-\frac{ 1}{ 36}$ $-\frac{ 1}{ 108}$ $-\frac{ 1}{ 144}$ $0$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $\frac{ 1}{ 2}$ $1$ $0$ $\frac{ 5}{ 6}$
$3$ $\frac{ 1}{ 2}$ $1$ $0$ $\frac{ 7}{ 6}$
$4$ $1$ $2$ $0$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 36}\)	\(-\frac{ 1}{ 108}\)	\(-\frac{ 1}{ 144}\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(\frac{ 5}{ 6}\)
\(3\)	\(\frac{ 1}{ 2}\)	\(1\)	\(0\)	\(\frac{ 7}{ 6}\)
\(4\)	\(1\)	\(2\)	\(0\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "5.45" from ...

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

75

New Number: 5.46 | AESZ: 243 | Superseeker: -42 -41706 | Hash: 93c30005b5a976a2b7c5206d5e679a45

Degree: 5

$\theta^4+x\left(295\theta^4+572\theta^3+424\theta^2+138\theta+17\right)+2 x^{2}\left(843\theta^4+744\theta^3-473\theta^2-481\theta-101\right)+2 x^{3}\left(1129\theta^4-516\theta^3-725\theta^2-159\theta+4\right)-3 x^{4}\left(173\theta^4+352\theta^3+290\theta^2+114\theta+18\right)-3^{2} x^{5}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -17, 1549, -215585, 36505501, ...
--> OEIS
Normalized instanton numbers (n₀=1): -42, 875, -41706, 2954224, -257813864, ... ; Common denominator:...

Discriminant

$-(z^3+57z^2-289z-1)(3z+1)^2$

Local exponents

≈$-61.684843$ $-\frac{ 1}{ 3}$ ≈$-0.003458$ $0$ ≈$4.688301$ $\infty$
$0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $1$ $0$ $1$ $1$
$1$ $3$ $1$ $0$ $1$ $1$
$2$ $4$ $2$ $0$ $2$ $1$

≈\(-61.684843\)	\(-\frac{ 1}{ 3}\)	≈\(-0.003458\)	\(0\)	≈\(4.688301\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(1\)	\(0\)	\(1\)	\(1\)
\(1\)	\(3\)	\(1\)	\(0\)	\(1\)	\(1\)
\(2\)	\(4\)	\(2\)	\(0\)	\(2\)	\(1\)

Note:

A-incarnation: $7 \times 7$ linear Pfaffian in $P^7$.
There is a second MUM point at infinity, associated to
the 7 fold linear section of $G(2,7)$ AESZ 27/5.7

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

76

New Number: 5.47 | AESZ: 246 | Superseeker: -4/5 -108/5 | Hash: f51a0c39f9179dc6a561b9afb6f9d85f

Degree: 5

$5^{2} \theta^4-2^{2} 5 x\left(12\theta^4+48\theta^3+49\theta^2+25\theta+5\right)-2^{4} x^{2}\left(544\theta^4+1792\theta^3+2444\theta^2+1580\theta+405\right)+2^{9} x^{3}\left(112\theta^4+960\theta^3+2306\theta^2+2130\theta+685\right)+2^{12} x^{4}\left(144\theta^4+768\theta^3+1308\theta^2+924\theta+235\right)+2^{20} x^{5}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4, 44, 400, 5356, ...
--> OEIS
Normalized instanton numbers (n₀=1): -4/5, 22/5, -108/5, 694/5, -1040, ... ; Common denominator:...

Discriminant

$(1+16z)(16z+5)^2(16z-1)^2$

Local exponents

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

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

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 247/5.48

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

77

New Number: 5.48 | AESZ: 247 | Superseeker: 608 22293216 | Hash: 6c0503129f3500c26cf001c1908a17f7

Degree: 5

$\theta^4+2^{4} x\left(144\theta^4-192\theta^3-132\theta^2-36\theta-5\right)+2^{13} x^{2}\left(112\theta^4-512\theta^3+98\theta^2+50\theta+13\right)-2^{20} x^{3}\left(544\theta^4+384\theta^3+332\theta^2+108\theta+21\right)-2^{30} 5 x^{4}\left(12\theta^4-23\theta^2-23\theta-7\right)+2^{40} 5^{2} x^{5}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 80, 11024, 1850624, 343952656, ...
--> OEIS
Normalized instanton numbers (n₀=1): 608, -85544, 22293216, -7629059800, 3042437418016, ... ; Common denominator:...

Discriminant

$(1+256z)(1280z+1)^2(256z-1)^2$

Local exponents

$-\frac{ 1}{ 256}$ $-\frac{ 1}{ 1280}$ $0$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $0$ $1$
$1$ $1$ $0$ $\frac{ 1}{ 2}$ $1$
$1$ $3$ $0$ $\frac{ 1}{ 2}$ $1$
$2$ $4$ $0$ $1$ $1$

\(-\frac{ 1}{ 256}\)	\(-\frac{ 1}{ 1280}\)	\(0\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(\frac{ 1}{ 2}\)	\(1\)
\(1\)	\(3\)	\(0\)	\(\frac{ 1}{ 2}\)	\(1\)
\(2\)	\(4\)	\(0\)	\(1\)	\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operaor AESZ 246/ 5.47

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

78

New Number: 5.49 | AESZ: 248 | Superseeker: 7/3 148 | Hash: 0c9ccff1cb4f5096e455a9026799ed5a

Degree: 5

$3^{2} \theta^4-3 x\left(106\theta^4+146\theta^3+115\theta^2+42\theta+6\right)-x^{2}\left(4511\theta^4+24314\theta^3+37829\theta^2+23598\theta+5286\right)+2^{2} x^{3}\left(10457\theta^4+32184\theta^3+24449\theta^2+3627\theta-1317\right)-2^{2} 11 x^{4}\left(1596\theta^4+2040\theta^3-101\theta^2-1085\theta-386\right)-2^{4} 11^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 2, 54, 1028, 29110, ...
--> OEIS
Normalized instanton numbers (n₀=1): 7/3, 551/24, 148, 8241/4, 86854/3, ... ; Common denominator:...

Discriminant

$-(16z+1)(16z^2+44z-1)(-3+11z)^2$

Local exponents

$-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}$ $-\frac{ 1}{ 16}$ $0$ $-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}$ $\frac{ 3}{ 11}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 3}{ 4}$
$1$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $3$ $1$
$2$ $2$ $0$ $2$ $4$ $\frac{ 5}{ 4}$

\(-\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\)	\(-\frac{ 1}{ 16}\)	\(0\)	\(-\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\)	\(\frac{ 3}{ 11}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(3\)	\(1\)
\(2\)	\(2\)	\(0\)	\(2\)	\(4\)	\(\frac{ 5}{ 4}\)

Note:

This is operator "5.49" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-92\)	\(84\)	\(48\)	\(15\)

79

New Number: 5.4 | AESZ: 21 | Superseeker: 8/5 152/5 | Hash: 42a2bc0f0ee2a405ede956176c95721f

Degree: 5

$5^{2} \theta^4-2^{2} 5 x\left(36\theta^4+84\theta^3+72\theta^2+30\theta+5\right)-2^{4} x^{2}\left(181\theta^4+268\theta^3+71\theta^2-70\theta-35\right)+2^{8} x^{3}(\theta+1)(37\theta^3+248\theta^2+375\theta+165)+2^{10} x^{4}\left(39\theta^4+198\theta^3+331\theta^2+232\theta+59\right)+2^{15} x^{5}\left((\theta+1)^4\right)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4, 44, 688, 13036, ...
--> OEIS
Normalized instanton numbers (n₀=1): 8/5, 57/10, 152/5, 253, 11552/5, ... ; Common denominator:...

Discriminant

$(4z+1)(32z-1)(4z-1)(8z+5)^2$

Local exponents

$-\frac{ 5}{ 8}$ $-\frac{ 1}{ 4}$ $0$ $\frac{ 1}{ 32}$ $\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $1$
$1$ $1$ $0$ $1$ $1$ $1$
$3$ $1$ $0$ $1$ $1$ $1$
$4$ $2$ $0$ $2$ $2$ $1$

\(-\frac{ 5}{ 8}\)	\(-\frac{ 1}{ 4}\)	\(0\)	\(\frac{ 1}{ 32}\)	\(\frac{ 1}{ 4}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(3\)	\(1\)	\(0\)	\(1\)	\(1\)	\(1\)
\(4\)	\(2\)	\(0\)	\(2\)	\(2\)	\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 71/5.11

A-Incarnation: (2,0),(02),(1,1),(1,1),(1,1) intersection in $P^4 \times P^4$

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

Calabi-Yau differential operator database v.3

Summary

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:

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:

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