Summary

You searched for: sol=336

1

New Number: 3.28 |  AESZ: 410  |  Superseeker: 7 1057/3  |  Hash: accbbff67291992dfbc89e78f5a3c897

Degree: 3

$\theta^4-x\left(145\theta^4+242\theta^3+199\theta^2+78\theta+12\right)+2^{3} x^{2}(2\theta+1)(4\theta+3)(97\theta^2+182\theta+114)-2^{4} 3^{4} x^{3}(2\theta+1)(2\theta+3)(4\theta+3)(4\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 336, 12880, 592200, ...
--> OEIS
Normalized instanton numbers (n0=1): 7, 22, 1057/3, 5460, 108241, ... ; Common denominator:...

Discriminant

$-(81z-1)(-1+32z)^2$

Local exponents

$0$$\frac{ 1}{ 81}$$\frac{ 1}{ 32}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 3}{ 4}$$\frac{ 3}{ 4}$
$0$$1$$1$$\frac{ 3}{ 2}$
$0$$2$$\frac{ 7}{ 4}$$\frac{ 7}{ 4}$

Note:

This is operator "3.28" from ...

2

New Number: 3.9 |  AESZ: ~101  |  Superseeker: 13 2650  |  Hash: a6878d847acf199583e8168a33967174

Degree: 3

$\theta^4-x\left(113\theta^4+226\theta^3+173\theta^2+60\theta+8\right)-2^{3} x^{2}(\theta+1)^2(119\theta^2+238\theta+92)-2^{2} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 336, 19880, 1420720, ...
--> OEIS
Normalized instanton numbers (n0=1): 13, 128, 2650, 79400, 2921395, ... ; Common denominator:...

Discriminant

$-(121z-1)(4z+1)^2$

Local exponents

$-\frac{ 1}{ 4}$$0$$\frac{ 1}{ 121}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$\frac{ 1}{ 2}$$0$$1$$1$
$\frac{ 1}{ 2}$$0$$1$$2$
$1$$0$$2$$\frac{ 5}{ 2}$

Operator equivalent to $AESZ 101=$b \ast b$. Show more... or download as plain text | PDF | Maple | LaTex 3 New Number: 4.2 | AESZ: ~44 | Superseeker: -76 -92996 | Hash: 79f5f70bb79e740c1cd7e835ff99a64c Degree: 4 $\theta^4-2^{2} x\left(272\theta^4+544\theta^3+649\theta^2+377\theta+84\right)+2^{6} 3 x^{2}\left(1544\theta^4+6176\theta^3+9307\theta^2+6262\theta+1588\right)-2^{8} x^{3}(272\theta^2+816\theta+819)(2\theta+3)^2+2^{14} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)$ Maple LaTex Coefficients of the holomorphic solution: 1, 336, 142728, 65762368, 31568339880, ... --> OEIS Normalized instanton numbers (n0=1): -76, -2002, -92996, -5555506, -384650592, ... ; Common denominator:... Discriminant $(1-544z+256z^2)^2$ Local exponents $0$$s_1$$s_2$$\frac{ 17}{ 16}-\frac{ 3}{ 4}\sqrt{ 2}$$\frac{ 17}{ 16}+\frac{ 3}{ 4}\sqrt{ 2}$$\infty$ $0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$0$$0$$\frac{ 3}{ 2}$ $0$$0$$0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$2$ $0$$1$$1$$1$$1$$2$ $0$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 5}{ 2}$ Note: YY-Operator equivalent to AESZ 44=$ A \ast \gamma\$

4

New Number: 16.14 |  AESZ:  |  Superseeker: 256 1223936  |  Hash: d10cd1b312c30ab12f758790dc9274ac

Degree: 16

$\theta^4+2^{4} x\left(56\theta^4-104\theta^3-134\theta^2-82\theta-21\right)+2^{11} x^{2}\left(35\theta^4-436\theta^3-347\theta^2-119\theta+42\right)-2^{15} x^{3}\left(1966\theta^4+60\theta^3+16732\theta^2+19722\theta+9459\right)-2^{20} x^{4}\left(3584\theta^4+27304\theta^3+185836\theta^2+233924\theta+91509\right)-2^{27} x^{5}\left(12022\theta^4+11932\theta^3+55862\theta^2+66188\theta+7683\right)+2^{31} x^{6}\left(226300\theta^4+1586208\theta^3+4219376\theta^2+5722536\theta+3385737\right)+2^{36} x^{7}\left(438788\theta^4+2589688\theta^3+6773816\theta^2+9975396\theta+6761583\right)-2^{43} x^{8}\left(422486\theta^4+4780100\theta^3+19717558\theta^2+36354718\theta+25567071\right)-2^{49} x^{9}\left(303952\theta^4+3230064\theta^3+12848329\theta^2+23301081\theta+16479450\right)+2^{53} x^{10}\left(557664\theta^4+10324416\theta^3+63062300\theta^2+159895724\theta+146177745\right)+2^{58} x^{11}\left(989920\theta^4+15846592\theta^3+90575768\theta^2+223282616\theta+202862541\right)+2^{64} x^{12}\left(483232\theta^4+6857664\theta^3+35423928\theta^2+80004312\theta+67210461\right)+2^{71} x^{13}\left(63968\theta^4+880384\theta^3+4440756\theta^2+9817108\theta+8063427\right)+2^{79} x^{14}\left(2924\theta^4+38096\theta^3+187141\theta^2+410905\theta+340155\right)+2^{82} 3 x^{15}\left(880\theta^4+11424\theta^3+55992\theta^2+122760\theta+101547\right)+2^{88} 3^{2} x^{16}\left((2\theta+7)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 336, 90384, 22565120, 5339450640, ...
--> OEIS
Normalized instanton numbers (n0=1): 256, -9340, 1223936, -91401864, 19822164736, ... ; Common denominator:...

Discriminant



No data for singularities

Note:

This is operator "16.14" from ...