### Summary

You searched for: Spectrum0=1/3,1/2,1/2,2/3

1

New Number: 4.36 |  AESZ: 109  |  Superseeker: 1434/7 18676572/7  |  Hash: bca2938ac7fa09f5bdc395cab75caf82

Degree: 4

$7^{2} \theta^4-2 3 7 x\left(1272\theta^4+2508\theta^3+1779\theta^2+525\theta+56\right)+2^{2} 3 x^{2}\left(43704\theta^4+38088\theta^3-25757\theta^2-20608\theta-3360\right)-2^{4} 3^{3} x^{3}\left(2736\theta^4-1512\theta^3-1672\theta^2-357\theta-14\right)-2^{6} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

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Coefficients of the holomorphic solution: 1, 48, 15840, 8148000, 5126536800, ...
--> OEIS
Normalized instanton numbers (n0=1): 1434/7, 14718, 18676572/7, 4988009280/7, 1646787631350/7, ... ; Common denominator:...

#### Discriminant

$-(432z^2+1080z-1)(-7+36z)^2$

#### Local exponents

$-\frac{ 5}{ 4}-\frac{ 13}{ 18}\sqrt{ 3}$$0$$s_1$$s_2$$-\frac{ 5}{ 4}+\frac{ 13}{ 18}\sqrt{ 3}$$\frac{ 7}{ 36}$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$1$$1$$\frac{ 1}{ 2}$
$1$$0$$1$$1$$1$$3$$\frac{ 1}{ 2}$
$2$$0$$2$$2$$2$$4$$\frac{ 2}{ 3}$

#### Note:

2

New Number: 4.44 |  AESZ: 232  |  Superseeker: 379/5 1364199/5  |  Hash: 8d5ff690c87757ed51a092dee764eede

Degree: 4

$5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

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Coefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ...
--> OEIS
Normalized instanton numbers (n0=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...

#### Discriminant

$-(27z+1)(512z-1)(-5+96z)^2$

#### Local exponents

$-\frac{ 1}{ 27}$$0$$\frac{ 1}{ 512}$$\frac{ 5}{ 96}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$
$1$$0$$1$$3$$\frac{ 1}{ 2}$
$2$$0$$2$$4$$\frac{ 2}{ 3}$

#### Note:

3

New Number: 4.45 |  AESZ: 233  |  Superseeker: 80 104976  |  Hash: 03f67459f6d678669f766c99281b1e79

Degree: 4

$\theta^4-2^{4} x\left(83\theta^4+94\theta^3+71\theta^2+24\theta+3\right)+2^{11} 3 x^{2}\left(101\theta^4+191\theta^3+174\theta^2+71\theta+10\right)-2^{16} 3^{2} x^{3}\left(203\theta^4+432\theta^3+333\theta^2+102\theta+11\right)+2^{23} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 9360, 2553600, 813027600, ...
--> OEIS
Normalized instanton numbers (n0=1): 80, 2794, 104976, 5367454, 508265072, ... ; Common denominator:...

#### Discriminant

$(512z-1)(432z-1)(-1+192z)^2$

#### Local exponents

$0$$\frac{ 1}{ 512}$$\frac{ 1}{ 432}$$\frac{ 1}{ 192}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$0$$1$$1$$1$$\frac{ 1}{ 2}$
$0$$1$$1$$3$$\frac{ 1}{ 2}$
$0$$2$$2$$4$$\frac{ 2}{ 3}$

#### Note:

4

New Number: 4.46 |  AESZ: 237  |  Superseeker: 208 1218192  |  Hash: 52c18dd4477f6548dd3b185e97b94c20

Degree: 4

$\theta^4-2^{4} x\left(46\theta^4+128\theta^3+91\theta^2+27\theta+3\right)-2^{9} 3 x^{2}\left(74\theta^4-16\theta^3-231\theta^2-127\theta-20\right)+2^{14} 3^{2} x^{3}\left(14\theta^4+216\theta^3+175\theta^2+51\theta+5\right)+2^{19} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 12240, 4972800, 2489533200, ...
--> OEIS
Normalized instanton numbers (n0=1): 208, 5874, 1218192, 220754467, 56417503216, ... ; Common denominator:...

#### Discriminant

$(864z-1)(64z-1)(1+96z)^2$

#### Local exponents

$-\frac{ 1}{ 96}$$0$$\frac{ 1}{ 864}$$\frac{ 1}{ 64}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$
$3$$0$$1$$1$$\frac{ 1}{ 2}$
$4$$0$$2$$2$$\frac{ 2}{ 3}$

#### Note:

This is operator "4.46" from ...

5

New Number: 4.48 |  AESZ: 241  |  Superseeker: 320 19748928  |  Hash: b4d16d8dd1eb7839630ecf8e8d242023

Degree: 4

$\theta^4-2^{4} x\left(152\theta^4+160\theta^3+110\theta^2+30\theta+3\right)+2^{10} 3 x^{2}\left(428\theta^4+176\theta^3-299\theta^2-170\theta-25\right)-2^{17} 3^{2} x^{3}\left(136\theta^4-216\theta^3-180\theta^2-51\theta-5\right)-2^{24} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 26640, 21907200, 22048765200, ...
--> OEIS
Normalized instanton numbers (n0=1): 320, 61084, 19748928, 9428973876, 5618509433280, ... ; Common denominator:...

#### Discriminant

$-(64z+1)(1728z-1)(-1+384z)^2$

#### Local exponents

$-\frac{ 1}{ 64}$$0$$\frac{ 1}{ 1728}$$\frac{ 1}{ 384}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$
$1$$0$$1$$3$$\frac{ 1}{ 2}$
$2$$0$$2$$4$$\frac{ 2}{ 3}$

#### Note:

6

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:

7

New Number: 4.53 |  AESZ: 264  |  Superseeker: 37216 464865119712  |  Hash: 625990ef22ba977bc3dd247ccc791780

Degree: 4

$\theta^4+2^{4} x\left(3392\theta^4-9344\theta^3-5764\theta^2-1092\theta-93\right)-2^{17} 3 x^{2}\left(1952\theta^4+15200\theta^3-7758\theta^2-2593\theta-323\right)-2^{26} 3^{2} 7 x^{3}\left(11584\theta^4-6912\theta^3-5364\theta^2-1632\theta-167\right)+2^{42} 3^{3} 7^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1488, 11258640, 139962144000, 2191135140810000, ...
--> OEIS
Normalized instanton numbers (n0=1): 37216, -75619080, 464865119712, -2749454414283384, 24030314100181942560, ... ; Common denominator:...

#### Discriminant

$(27648z-1)(4096z-1)(1+43008z)^2$

#### Local exponents

$-\frac{ 1}{ 43008}$$0$$\frac{ 1}{ 27648}$$\frac{ 1}{ 4096}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$
$3$$0$$1$$1$$\frac{ 1}{ 2}$
$4$$0$$2$$2$$\frac{ 2}{ 3}$

#### Note:

8

New Number: 4.54 |  AESZ: 265  |  Superseeker: 1056 138459552  |  Hash: fad89ac60b7ab4118edfed4cf6350d0c

Degree: 4

$\theta^4+2^{4} 3 x\left(96\theta^4-96\theta^3-60\theta^2-12\theta-1\right)+2^{13} 3 x^{2}\left(288\theta^4-144\theta^3+526\theta^2+206\theta+27\right)+2^{20} 3^{3} x^{3}\left(288\theta^4+864\theta^3+652\theta^2+204\theta+23\right)+2^{30} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, -30960, -11961600, 15342742800, ...
--> OEIS
Normalized instanton numbers (n0=1): 1056, -360672, 138459552, -50965971720, 20236543243104, ... ; Common denominator:...

#### Discriminant

$(1769472z^2+1)(1+2304z)^2$

#### Local exponents

$-\frac{ 1}{ 2304}$$0-\frac{ 1}{ 2304}\sqrt{ 3}I$$0$$s_1$$s_2$$0+\frac{ 1}{ 2304}\sqrt{ 3}I$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 3}$
$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{ 2}{ 3}$

#### Note:

9

New Number: 4.55 |  AESZ: 276  |  Superseeker: -188832 -101990911789344  |  Hash: 797e27181bf0a060708a3d221ec79699

Degree: 4

$\theta^4-2^{4} 3 x\left(18432\theta^4-4608\theta^3-1024\theta^2+1280\theta+221\right)+2^{17} 3^{4} x^{2}\left(25344\theta^4-2304\theta^3+11680\theta^2+1472\theta-33\right)-2^{28} 3^{8} x^{3}\left(18432\theta^4+13824\theta^3+11392\theta^2+3264\theta+359\right)+2^{46} 3^{12} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10608, 477012240, 30101658720000, 2213759644568010000, ...
--> OEIS
Normalized instanton numbers (n0=1): -188832, -3134817768, -101990911789344, -4414817659429205136, -223930278487379610386400, ... ; Common denominator:...

#### Discriminant

$(331776z-1)^2(110592z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 331776}$$\frac{ 1}{ 110592}$$\infty$
$0$$0$$0$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$
$0$$3$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$
$0$$4$$1$$\frac{ 2}{ 3}$

#### Note:

10

New Number: 4.57 |  AESZ: 278  |  Superseeker: 243 513936  |  Hash: b30f6ac0da69cf91ab39089e6bf1ac8c

Degree: 4

$\theta^4-3 x\left(279\theta^4+882\theta^3+641\theta^2+200\theta+24\right)-2 3^{5} x^{2}\left(72\theta^4-1710\theta^3-3665\theta^2-1864\theta-296\right)+2^{2} 3^{9} x^{3}\left(909\theta^4+3888\theta^3+3082\theta^2+918\theta+92\right)+2^{4} 3^{15} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 72, 18360, 6552000, 2767980600, ...
--> OEIS
Normalized instanton numbers (n0=1): 243, -3402, 513936, 2470824, 6888345300, ... ; Common denominator:...

#### Discriminant

$(729z-1)(432z-1)(1+162z)^2$

#### Local exponents

$-\frac{ 1}{ 162}$$0$$\frac{ 1}{ 729}$$\frac{ 1}{ 432}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$\frac{ 1}{ 2}$
$3$$0$$1$$1$$\frac{ 1}{ 2}$
$4$$0$$2$$2$$\frac{ 2}{ 3}$

#### Note:

11

New Number: 4.67 |  AESZ: 305  |  Superseeker: 1565472 28381748186959008  |  Hash: 4ce63e568901a8cef3f9c2f60b6ce2d2

Degree: 4

$\theta^4+2^{4} 3 x\left(81552\theta^4-94944\theta^3-53688\theta^2-6216\theta-379\right)+2^{20} 3 x^{2}\left(1091952\theta^4-2917008\theta^3+1388032\theta^2+225284\theta+19545\right)-2^{34} 3^{3} 7 x^{3}\left(207504\theta^4-221184\theta^3-157480\theta^2-52224\theta-5855\right)+2^{59} 3^{5} 7^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18192, 178183440, -132466290835200, -18938901463932265200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1565472, -155959736064, 28381748186959008, -6798945051352302862848, 1905341636283453444266170464, ... ; Common denominator:...

#### Discriminant

$(57982058496z^2-214272z+1)(1+2064384z)^2$

#### Local exponents

$-\frac{ 1}{ 2064384}$$0$$s_1$$s_2$$\frac{ 31}{ 16777216}-\frac{ 145}{ 150994944}\sqrt{ 15}I$$\frac{ 31}{ 16777216}+\frac{ 145}{ 150994944}\sqrt{ 15}I$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$0$$1$$1$$1$$1$$\frac{ 1}{ 2}$
$3$$0$$1$$1$$1$$1$$\frac{ 1}{ 2}$
$4$$0$$2$$2$$2$$2$$\frac{ 2}{ 3}$

#### Note:

12

New Number: 4.76 |  AESZ:  |  Superseeker: 6015 9668470011  |  Hash: f16cc33931b60f0c5d3a1a0239a01062

Degree: 4

$\theta^4-3 x\left(2871\theta^4+10926\theta^3+7069\theta^2+1606\theta+136\right)-2^{6} 3^{4} x^{2}\left(12573\theta^4+16677\theta^3-5762\theta^2-2938\theta-348\right)-2^{10} 3^{8} x^{3}\left(14085\theta^4+864\theta^3-29\theta^2+204\theta+44\right)-2^{17} 3^{12} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 408, 1616760, 10409448000, 82877787531000, ...
--> OEIS
Normalized instanton numbers (n0=1): 6015, 3451026, 9668470011, 32924097729576, 144270059475420597, ... ; Common denominator:...

#### Discriminant

$-(27z+1)(13824z-1)(1+2592z)^2$

#### Local exponents

$-\frac{ 1}{ 27}$$-\frac{ 1}{ 2592}$$0$$\frac{ 1}{ 13824}$$\infty$
$0$$0$$0$$0$$\frac{ 1}{ 3}$
$1$$1$$0$$1$$\frac{ 1}{ 2}$
$1$$3$$0$$1$$\frac{ 1}{ 2}$
$2$$4$$0$$2$$\frac{ 2}{ 3}$

#### Note:

B-Incarnation as Diagonal.

13

New Number: 1.5 |  AESZ: 5  |  Superseeker: 60 134292  |  Hash: a6c4fb927cb2a4bb1103c1c739a252b0

Degree: 1

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 3240, 672000, 169785000, ...
--> OEIS
Normalized instanton numbers (n0=1): 60, 1869, 134292, 14016600, 1806410976, ... ; Common denominator:...

#### Discriminant

$1-432z$

#### Local exponents

$0$$\frac{ 1}{ 432}$$\infty$
$0$$0$$\frac{ 1}{ 3}$
$0$$1$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 2}$
$0$$2$$\frac{ 2}{ 3}$

#### Note:

A-incarnation: X(2,2,3) in $P^6$.