### Summary

You searched for: sol=240

1

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}$

#### Note:

2

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 $I \ast \epsilon$

3

New Number: 4.49 |  AESZ: 254  |  Superseeker: -5408 -22147077792  |  Hash: 2539c1ff260271c9f7de53e267e2e8cf

Degree: 4

$\theta^4-2^{4} x\left(2608\theta^4-544\theta^3-200\theta^2+72\theta+15\right)+2^{15} 3 x^{2}\left(6128\theta^4-208\theta^3+2328\theta^2+452\theta+25\right)-2^{24} 3^{2} 5 x^{3}\left(4592\theta^4+3456\theta^3+2632\theta^2+816\theta+95\right)+2^{38} 3^{3} 5^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 314640, 627244800, 1516001533200, ...
--> OEIS
Normalized instanton numbers (n0=1): -5408, -8033784, -22147077792, -80392290665536, -341267541912723040, ... ; Common denominator:...

#### Discriminant

$(6912z-1)(4096z-1)(-1+15360z)^2$

#### Local exponents

$0$$\frac{ 1}{ 15360}$$\frac{ 1}{ 6912}$$\frac{ 1}{ 4096}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$0$$1$$1$$1$$\frac{ 1}{ 2}$
$0$$3$$1$$1$$\frac{ 1}{ 2}$
$0$$4$$2$$2$$\frac{ 2}{ 3}$

#### Note:

4

New Number: 4.4 |  AESZ:  |  Superseeker: -48 -32368  |  Hash: a0903e578f379289d79849a566639775

Degree: 4

$\theta^4-2^{4} x\left(48\theta^4+96\theta^3+115\theta^2+67\theta+15\right)+2^{9} x^{2}\left(304\theta^4+1216\theta^3+1890\theta^2+1348\theta+375\right)-2^{14} x^{3}(48\theta^2+144\theta+145)(2\theta+3)^2+2^{22} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 69840, 22068480, 7268490000, ...
--> OEIS
Normalized instanton numbers (n0=1): -48, -910, -32368, -1409193, -71439120, ... ; Common denominator:...

#### Discriminant

$(1-384z+4096z^2)^2$

#### Local exponents

$0$$s_1$$s_2$$\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}$$\frac{ 3}{ 64}+\frac{ 1}{ 32}\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 $d \ast e \tilde A \ast \epsilon$

5

New Number: 5.114 |  AESZ: 412  |  Superseeker: -1312 -127846048  |  Hash: 4a9870395db313fa368bbafcfc6a7435

Degree: 5

$\theta^4-2^{4} x\left(560\theta^4-32\theta^3+56\theta^2+72\theta+15\right)+2^{15} x^{2}\left(896\theta^4+272\theta^3+604\theta^2+196\theta+21\right)-2^{24} 3^{2} x^{3}\left(288\theta^4+352\theta^3+364\theta^2+164\theta+29\right)+2^{35} 3^{3} x^{4}(2\theta+1)(16\theta^3+32\theta^2+28\theta+9)-2^{46} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 118032, 72810240, 50454043920, ...
--> OEIS
Normalized instanton numbers (n0=1): -1312, -301048, -127846048, -70845744192, -45645879602784, ... ; Common denominator:...

#### Discriminant

$-(-1+768z)(3072z-1)^2(1024z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 3072}$$\frac{ 1}{ 1024}$$\frac{ 1}{ 768}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 2}$$1$$1$
$0$$3$$\frac{ 1}{ 2}$$1$$1$
$0$$4$$1$$2$$\frac{ 3}{ 2}$

#### Note:

B-Incarnation as double octic D.O.256

6

New Number: 5.19 |  AESZ: 180  |  Superseeker: -624 -43406256  |  Hash: c174fb2dfd87730e48b4ae8b57ac66df

Degree: 5

$\theta^4-2^{4} 3 x\left(198\theta^4+72\theta^3+69\theta^2+33\theta+5\right)+2^{9} 3^{2} x^{2}\left(7614\theta^4+7128\theta^3+6813\theta^2+2529\theta+340\right)-2^{14} 3^{5} x^{3}\left(15714\theta^4+27216\theta^3+26343\theta^2+11151\theta+1685\right)+2^{19} 3^{9} x^{4}(3\theta+1)(3\theta+2)(576\theta^2+1008\theta+605)-2^{27} 3^{13} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 173520, 170016000, 193451504400, ...
--> OEIS
Normalized instanton numbers (n0=1): -624, -137190, -43406256, -18281817141, -9083828410320, ... ; Common denominator:...

#### Discriminant

$-(-1+864z)(2592z-1)^2(1728z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 2592}$$\frac{ 1}{ 1728}$$\frac{ 1}{ 864}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 1}{ 2}$$1$$\frac{ 2}{ 3}$
$0$$3$$\frac{ 1}{ 2}$$1$$\frac{ 4}{ 3}$
$0$$4$$1$$2$$\frac{ 5}{ 3}$

#### Note:

This is operator "5.19" from ...

7

New Number: 5.94 |  AESZ: 334  |  Superseeker: 7/3 -4843/81  |  Hash: 1ab1dce2847b14dd89a8f8f48ddc7214

Degree: 5

$3^{2} \theta^4-3 x\left(166\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+x^{2}\left(11155\theta^4+42652\theta^3+60463\theta^2+36876\theta+8172\right)-3^{2} x^{3}\left(4705\theta^4+23418\theta^3+42217\theta^2+31152\theta+7932\right)+2^{2} 3 x^{4}\left(3514\theta^4+16403\theta^3+25581\theta^2+16442\theta+3744\right)-2^{2} 5 x^{5}(5\theta+3)(5\theta+4)(5\theta+6)(5\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 240, -9450, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/3, -79/12, -4843/81, -1058/3, 3620/3, ... ; Common denominator:...

#### Discriminant

$-(3125z^3-1167z^2+54z-1)(2z-3)^2$

#### Local exponents

$0$ ≈$0.025215-0.018839I$ ≈$0.025215+0.018839I$ ≈$0.32301$$\frac{ 3}{ 2}$$\infty$
$0$$0$$0$$0$$0$$\frac{ 3}{ 5}$
$0$$1$$1$$1$$1$$\frac{ 4}{ 5}$
$0$$1$$1$$1$$3$$\frac{ 6}{ 5}$
$0$$2$$2$$2$$4$$\frac{ 7}{ 5}$

#### Note:

This is operator "5.94" from ...

8

New Number: 13.5 |  AESZ:  |  Superseeker: 224 4999008  |  Hash: 6d924b9c12ee7379761d409ee75e42ab

Degree: 13

$\theta^4-2^{4} x\left(80\theta^4+160\theta^3+152\theta^2+72\theta+15\right)+2^{14} x^{2}\left(24\theta^4+240\theta^3+355\theta^2+230\theta+69\right)+2^{20} x^{3}\left(416\theta^4-2400\theta^3-6216\theta^2-4824\theta-1773\right)-2^{28} x^{4}\left(1840\theta^4-544\theta^3-15328\theta^2-15056\theta-6525\right)+2^{38} 3 x^{5}\left(236\theta^4+1040\theta^3-1629\theta^2-2248\theta-1208\right)+2^{47} 3 x^{6}\left(8\theta^4-1512\theta^3+192\theta^2+951\theta+786\right)-2^{53} 3 x^{7}\left(1568\theta^4-7952\theta^3-4278\theta^2-740\theta+1981\right)+2^{60} 3 x^{8}\left(6976\theta^4-6656\theta^3-9268\theta^2-7912\theta-55\right)-2^{70} x^{9}\left(6680\theta^4+8856\theta^3+8397\theta^2+3060\theta+1017\right)+2^{76} x^{10}\left(22672\theta^4+71840\theta^3+113068\theta^2+90072\theta+30483\right)-2^{84} x^{11}\left(12912\theta^4+62592\theta^3+128336\theta^2+126736\theta+49707\right)+2^{93} 7 x^{12}(2\theta+3)(164\theta^3+810\theta^2+1434\theta+891)-2^{102} 7^{2} x^{13}(\theta+2)^2(2\theta+3)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 44304, 7503616, 1459723536, ...
--> OEIS
Normalized instanton numbers (n0=1): 224, -22712, 4999008, -855952448, 199163179936, ... ; Common denominator:...

#### Discriminant

$-(65536z^2-256z+1)^2(117440512z^3-196608z^2+1)^2(256z-1)^3$

#### Local exponents

≈$-0.00161$$0$ ≈$0.001642-0.00161I$ ≈$0.001642+0.00161I$$\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 3}I$$\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 3}I$$\frac{ 1}{ 256}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$\frac{ 3}{ 2}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$0$$2$
$3$$0$$3$$3$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$0$$2$
$4$$0$$4$$4$$1$$1$$0$$\frac{ 5}{ 2}$

#### Note:

This is operator "13.5" from ...

9

New Number: 8.50 |  AESZ:  |  Superseeker: 2/23 27/23  |  Hash: 68499833fa99ef8841a3d64e042d4a6e

Degree: 8

$23^{2} \theta^4-2 23 x\theta^2(136\theta^2+2\theta+1)-2^{2} x^{2}\left(7589\theta^4+54926\theta^3+89975\theta^2+69828\theta+21160\right)+x^{3}\left(573259\theta^4+2342274\theta^3+3791849\theta^2+3070914\theta+1010160\right)-2 5 x^{4}\left(122351\theta^4+62266\theta^3-795547\theta^2-1404486\theta-669744\right)-2^{3} 3 5^{2} x^{5}(\theta+1)(16105\theta^3+133047\theta^2+320040\theta+245740)+2^{4} 3^{2} 5^{3} x^{6}(\theta+1)(\theta+2)(3107\theta^2+16911\theta+22834)-2^{4} 3^{4} 5^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(133\theta+404)+2^{5} 3^{6} 5^{5} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 10, 0, 270, ...
--> OEIS
Normalized instanton numbers (n0=1): 2/23, 18/23, 27/23, 136/23, 395/23, ... ; Common denominator:...

#### Discriminant

$(3z-1)(2z-1)(10z-1)(6z+1)(25z^2-5z-1)(-23+90z)^2$

#### Local exponents

$-\frac{ 1}{ 6}$$\frac{ 1}{ 10}-\frac{ 1}{ 10}\sqrt{ 5}$$0$$\frac{ 1}{ 10}$$\frac{ 23}{ 90}$$\frac{ 1}{ 10}+\frac{ 1}{ 10}\sqrt{ 5}$$\frac{ 1}{ 3}$$\frac{ 1}{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$0$$1$$1$$1$$1$$1$$2$
$1$$1$$0$$1$$3$$1$$1$$1$$3$
$2$$2$$0$$2$$4$$2$$2$$2$$4$

#### Note:

This is operator "8.50" from ...

10

New Number: 8.73 |  AESZ:  |  Superseeker: 161/13 26946/13  |  Hash: 13db5d8c98a3d4f31589970217896191

Degree: 8

$13^{2} \theta^4-13 x\theta(614\theta^3+1804\theta^2+1149\theta+247)-x^{2}\left(775399\theta^4+2692636\theta^3+3693483\theta^2+2450110\theta+648960\right)-2^{2} x^{3}\left(5408420\theta^4+24616488\theta^3+45163287\theta^2+38795913\theta+12838410\right)-2^{5} x^{4}\left(9763642\theta^4+55386224\theta^3+123097843\theta^2+124066416\theta+46600563\right)-2^{9} 3 x^{5}(\theta+1)(1717504\theta^3+9940776\theta^2+20063523\theta+13933966)-2^{13} 3^{2} x^{6}(\theta+1)(\theta+2)(178975\theta^2+874119\theta+1112486)-2^{19} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(857\theta+2533)-2^{23} 3^{6} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 240, 10440, 679104, ...
--> OEIS
Normalized instanton numbers (n0=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...

#### Discriminant

$-(-1+96z+896z^2)(9z+1)^2(96z+13)^2(8z+1)^2$

#### Local exponents

$-\frac{ 13}{ 96}$$-\frac{ 1}{ 8}$$-\frac{ 3}{ 56}-\frac{ 5}{ 112}\sqrt{ 2}$$-\frac{ 1}{ 9}$$0$$-\frac{ 3}{ 56}+\frac{ 5}{ 112}\sqrt{ 2}$$\infty$
$0$$0$$0$$0$$0$$0$$1$
$1$$0$$1$$0$$0$$1$$2$
$3$$1$$1$$1$$0$$1$$3$
$4$$1$$2$$1$$0$$2$$4$

#### Note:

This is operator "8.73" from ...

11

New Number: 1.14 |  AESZ: 14  |  Superseeker: 1248 683015008  |  Hash: 03af56f4ae0cea2c4b219620b08dc49b

Degree: 1

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 498960, 1633632000, 6558930378000, ...
--> OEIS
Normalized instanton numbers (n0=1): 1248, 597192, 683015008, 1149904141056, 2394928461766560, ... ; Common denominator:...

#### Discriminant

$1-6912z$

#### Local exponents

$0$$\frac{ 1}{ 6912}$$\infty$
$0$$0$$\frac{ 1}{ 6}$
$0$$1$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 2}$
$0$$2$$\frac{ 5}{ 6}$

#### Note:

A-incarnation: X(2,6) in P^5(1,1,1,1,1,3)