### Summary

You searched for: sol=108

1

New Number: 2.60 |  AESZ: 18  |  Superseeker: 4 364  |  Hash: bb479f8a4185bf4a943dba2d433e13e5

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 4, 108, 3280, 126700, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 39, 364, 6800, 662416/5, ... ; Common denominator:...

#### Discriminant

$-(16z+1)(64z-1)$

#### Local exponents

$-\frac{ 1}{ 16}$$0$$\frac{ 1}{ 64}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$1$$\frac{ 3}{ 4}$
$1$$0$$1$$\frac{ 5}{ 4}$
$2$$0$$2$$\frac{ 3}{ 2}$

#### Note:

A-Incarnation: (1,1) and (2,2) intersection in $P^3 \times P^3$

2

New Number: 3.11 |  AESZ:  |  Superseeker: 37 15270  |  Hash: e7db0935aa1b331d8fb696a009d2d7bb

Degree: 3

$\theta^4-x\left(865\theta^4+1730\theta^3+1501\theta^2+636\theta+108\right)+2^{5} 3^{2} x^{2}(\theta+1)^2(866\theta^2+1732\theta+709)-2^{8} 3^{4} 17^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

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Coefficients of the holomorphic solution: 1, 108, 19908, 4278240, 990152100, ...
--> OEIS
Normalized instanton numbers (n0=1): 37, -570, 15270, -529994, 21300463, ... ; Common denominator:...

#### Discriminant

$-(289z-1)(-1+288z)^2$

#### Local exponents

$0$$\frac{ 1}{ 289}$$\frac{ 1}{ 288}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 2}$$1$
$0$$1$$\frac{ 1}{ 2}$$2$
$0$$2$$1$$\frac{ 5}{ 2}$

#### Note:

Operator equivalent to AESZ 144=c \ast c\$

3

New Number: 12.4 |  AESZ:  |  Superseeker: 4 -228/5  |  Hash: c24070a1d4a449404cd7b46398fa6d6e

Degree: 12

$5^{2} \theta^4-2^{2} 5^{2} x\left(16\theta^4+32\theta^3+31\theta^2+15\theta+3\right)+2^{4} 5 x^{2}\left(736\theta^4+2368\theta^3+3848\theta^2+2960\theta+915\right)-2^{10} 5 x^{3}\left(304\theta^4+1176\theta^3+2337\theta^2+2313\theta+891\right)+2^{12} 3 x^{4}\left(2608\theta^4+10688\theta^3+21652\theta^2+23580\theta+9945\right)-2^{16} 3 x^{5}\left(2784\theta^4+11616\theta^3+21812\theta^2+22396\theta+9191\right)+2^{21} 3 x^{6}\left(1232\theta^4+5232\theta^3+9332\theta^2+7968\theta+2649\right)-2^{25} 3^{2} x^{7}\left(304\theta^4+1312\theta^3+2472\theta^2+1992\theta+559\right)+2^{30} 3 x^{8}\left(280\theta^4+1216\theta^3+2491\theta^2+2337\theta+827\right)-2^{32} x^{9}\left(1664\theta^4+7200\theta^3+13692\theta^2+11988\theta+3951\right)+2^{38} x^{10}\left(164\theta^4+832\theta^3+1751\theta^2+1731\theta+663\right)-2^{40} x^{11}\left(160\theta^4+928\theta^3+2072\theta^2+2072\theta+777\right)+2^{44} x^{12}\left((2\theta+3)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 108, 688, 3564, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, -29/5, -228/5, 3724/5, -31856/5, ... ; Common denominator:...

#### Discriminant

$(16z-1)^2(256z^2-16z+1)^2(4096z^3-768z^2-5)^2$

#### Local exponents

≈$-0.013312-0.074322I$ ≈$-0.013312+0.074322I$$0$$\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 3}I$$\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 3}I$$\frac{ 1}{ 16}$ ≈$0.214124$$\infty$
$0$$0$$0$$0$$0$$0$$0$$\frac{ 3}{ 2}$
$1$$1$$0$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$1$$\frac{ 3}{ 2}$
$3$$3$$0$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$3$$\frac{ 3}{ 2}$
$4$$4$$0$$1$$1$$1$$4$$\frac{ 3}{ 2}$

#### Note:

This is operator "12.4" from ...

4

New Number: 12.3 |  AESZ:  |  Superseeker: -12/5 444/5  |  Hash: 45726409a4c817f929c9e6e49b33a941

Degree: 12

$5^{2} \theta^4+2^{2} 5 x\left(4\theta^4+56\theta^3+53\theta^2+25\theta+5\right)-2^{4} x^{2}\left(976\theta^4+6208\theta^3+9016\theta^2+6360\theta+1985\right)+2^{8} x^{3}\left(832\theta^4-2304\theta^3-11276\theta^2-12780\theta-5495\right)+2^{13} x^{4}\left(176\theta^4+4672\theta^3+16244\theta^2+19860\theta+9145\right)-2^{16} x^{5}\left(1824\theta^4+8448\theta^3+1052\theta^2-6884\theta-5771\right)+2^{21} x^{6}\left(432\theta^4+192\theta^3-3816\theta^2-9540\theta-5869\right)+2^{24} x^{7}\left(704\theta^4+10048\theta^3+21804\theta^2+22348\theta+7847\right)-2^{29} x^{8}\left(472\theta^4+2176\theta^3+7884\theta^2+11644\theta+5965\right)+2^{32} x^{9}\left(336\theta^4+672\theta^3+1144\theta^2+2904\theta+2145\right)+2^{36} x^{10}\left(368\theta^4+1216\theta^3+1304\theta^2-240\theta-697\right)-2^{44} x^{11}(2\theta+3)(4\theta^3+28\theta^2+51\theta+28)-2^{46} x^{12}\left((2\theta+3)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 108, -912, 21484, ...
--> OEIS
Normalized instanton numbers (n0=1): -12/5, 103/5, 444/5, 1148/5, -6704, ... ; Common denominator:...

#### Discriminant

$-(-1-16z+256z^2)(16z+1)^2(16z-1)^2(8192z^3+768z^2-32z+5)^2$

#### Local exponents

≈$-0.148005$$-\frac{ 1}{ 16}$$\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}$$0$ ≈$0.027128-0.058206I$ ≈$0.027128+0.058206I$$\frac{ 1}{ 16}$$\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$\frac{ 3}{ 2}$
$1$$0$$1$$0$$1$$1$$\frac{ 1}{ 2}$$1$$\frac{ 3}{ 2}$
$3$$1$$1$$0$$3$$3$$\frac{ 1}{ 2}$$1$$\frac{ 3}{ 2}$
$4$$1$$2$$0$$4$$4$$1$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "12.3" from ...

5

New Number: 9.5 |  AESZ:  |  Superseeker: 17/3 4127/9  |  Hash: 98a7e046a956f1c9ec13973072ab8283

Degree: 9

$3^{2} \theta^4-3 x\left(152\theta^4+316\theta^3+245\theta^2+87\theta+12\right)-x^{2}\left(5808+25608\theta+43193\theta^2+31076\theta^3+8807\theta^4\right)-2 x^{3}\left(10633\theta^4+106320\theta^3+235087\theta^2+185292\theta+52896\right)+2^{2} x^{4}\left(65651\theta^4+19144\theta^3-434467\theta^2-508704\theta-175376\right)+2^{3} x^{5}\left(151497\theta^4+645060\theta^3+272053\theta^2-269230\theta-183720\right)-2^{8} x^{6}\left(3386\theta^4-52470\theta^3-83275\theta^2-46299\theta-7926\right)-2^{10} x^{7}\left(11425\theta^4+14072\theta^3-3794\theta^2-13632\theta-5575\right)-2^{15} x^{8}(590\theta^2+1126\theta+597)(\theta+1)^2-2^{20} 3^{2} x^{9}(\theta+1)^2(\theta+2)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 108, 3496, 137548, ...
--> OEIS
Normalized instanton numbers (n0=1): 17/3, 257/6, 4127/9, 23827/3, 496999/3, ... ; Common denominator:...

#### Discriminant

$-(9z+1)(2z+1)(z+1)(128z^2+64z-1)(-3-2z+64z^2)^2$

#### Local exponents

$-1$$-\frac{ 1}{ 4}-\frac{ 3}{ 16}\sqrt{ 2}$$-\frac{ 1}{ 2}$$\frac{ 1}{ 64}-\frac{ 1}{ 64}\sqrt{ 193}$$-\frac{ 1}{ 9}$$0$$-\frac{ 1}{ 4}+\frac{ 3}{ 16}\sqrt{ 2}$$\frac{ 1}{ 64}+\frac{ 1}{ 64}\sqrt{ 193}$$\infty$
$0$$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$1$$0$$1$$1$$1$
$1$$1$$1$$3$$1$$0$$1$$3$$2$
$2$$2$$2$$4$$2$$0$$2$$4$$2$

#### Note:

This is operator "9.5" from ...