### Summary

You searched for: degz=3

1-30  31-34

1

New Number: 3.10 |  AESZ: ~103  |  Superseeker: 10 664  |  Hash: 9239615e8ac132ca232c13367a39ae3b

Degree: 3

$\theta^4-2 x\left(86\theta^4+172\theta^3+143\theta^2+57\theta+9\right)+2^{2} 3^{2} x^{2}(\theta+1)^2(236\theta^2+472\theta+187)-2^{4} 3^{4} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 630, 28980, 1593270, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 24, 664, 9088, 234388, ... ; Common denominator:...

#### Discriminant

$-(100z-1)(-1+36z)^2$

#### Local exponents

$0$$\frac{ 1}{ 100}$$\frac{ 1}{ 36}$$\infty$
$0$$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 103 =$c \ast c$.

2

New Number: 3.12 |  AESZ:  |  Superseeker: 252 1162036  |  Hash: baa148eb1a5a05a0d9aca4c78be26905

Degree: 3

$\theta^4-2^{2} 3^{2} x\left(132\theta^4+216\theta^3+165\theta^2+57\theta+7\right)+2^{4} 3^{6} x^{2}(4\theta+3)(160\theta^3+408\theta^2+316\theta+57)-2^{8} 3^{10} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 252, 202500, 212132880, 251548748100, ...
--> OEIS
Normalized instanton numbers (n0=1): 252, -19512, 1162036, -91851948, 24209298720, ... ; Common denominator:...

#### Discriminant

$-(1296z-1)(-1+1728z)^2$

#### Local exponents

$0$$\frac{ 1}{ 1728}$$\frac{ 1}{ 1296}$$\infty$
$0$$0$$0$$\frac{ 1}{ 4}$
$0$$\frac{ 1}{ 2}$$1$$\frac{ 3}{ 4}$
$0$$1$$1$$\frac{ 7}{ 4}$
$0$$\frac{ 3}{ 2}$$2$$\frac{ 9}{ 4}$

#### Note:

Operator equivalent to AESZ 154

3

New Number: 3.13 |  AESZ:  |  Superseeker: 352 15001120/3  |  Hash: b5a6f76d274395537de2c3169fdac9bf

Degree: 3

$\theta^4-2^{2} x\left(688\theta^4+1232\theta^3+902\theta^2+286\theta+33\right)+2^{4} 3^{2} x^{2}(4\theta+3)(3776\theta^3+10096\theta^2+8268\theta+1515)-2^{10} 3^{4} 5^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 132, 62748, 43686384, 37830871260, ...
--> OEIS
Normalized instanton numbers (n0=1): 352, 18676, 15001120/3, 1489325052, 586526654304, ... ; Common denominator:...

#### Discriminant

$-(1600z-1)(-1+576z)^2$

#### Local exponents

$0$$\frac{ 1}{ 1600}$$\frac{ 1}{ 576}$$\infty$
$0$$0$$0$$\frac{ 1}{ 4}$
$0$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 4}$
$0$$1$$1$$\frac{ 7}{ 4}$
$0$$2$$\frac{ 3}{ 2}$$\frac{ 9}{ 4}$

#### Note:

Operator equivalent to AESZ 229

4

New Number: 3.14 |  AESZ:  |  Superseeker: 444 19050964  |  Hash: dc96aa2da269d989ee90c49dab6a9c5a

Degree: 3

$\theta^4-2^{2} x\left(452\theta^4+920\theta^3+633\theta^2+173\theta+17\right)-2^{4} x^{2}(4\theta+3)(3808\theta^3+10504\theta^2+8884\theta+1635)-2^{8} 11^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 68, 42220, 38866320, 43812369900, ...
--> OEIS
Normalized instanton numbers (n0=1): 444, 57104, 19050964, 9432910668, 5781274591408, ... ; Common denominator:...

#### Discriminant

$-(1936z-1)(1+64z)^2$

#### Local exponents

$-\frac{ 1}{ 64}$$0$$\frac{ 1}{ 1936}$$\infty$
$0$$0$$0$$\frac{ 1}{ 4}$
$\frac{ 1}{ 2}$$0$$1$$\frac{ 3}{ 4}$
$1$$0$$1$$\frac{ 7}{ 4}$
$\frac{ 3}{ 2}$$0$$2$$\frac{ 9}{ 4}$

#### Note:

This is operator Pi = 3.14 (approx.), equivalent to AESZ 238.

5

New Number: 3.15 |  AESZ:  |  Superseeker: -32 -16288  |  Hash: e21c92d8f9a2222be40fdc71ea51ee35

Degree: 3

$\theta^4+2^{3} x\left(21\theta^4+42\theta^3+30\theta^2+9\theta+1\right)-2^{6} x^{2}(\theta+1)^2(96\theta^2+192\theta+77)+2^{9} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 720, -68480, 8123920, ...
--> OEIS
Normalized instanton numbers (n0=1): -32, 468, -16288, 1681645/2, -53608288, ... ; Common denominator:...

#### Discriminant

$(200z+1)(-1+16z)^2$

#### Local exponents

$-\frac{ 1}{ 200}$$0$$\frac{ 1}{ 16}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$1$$0$$\frac{ 1}{ 6}$$1$
$1$$0$$\frac{ 5}{ 6}$$2$
$2$$0$$1$$\frac{ 5}{ 2}$

#### Note:

Operator equivalent to AESZ 328

6

New Number: 3.16 |  AESZ: 386  |  Superseeker: 10 18328  |  Hash: 7d032616d3bd41272e22a4d23747d7a0

Degree: 3

$\theta^4-2 x\left(422\theta^4+844\theta^3+751\theta^2+329\theta+57\right)+2^{2} 3^{4} x^{2}(\theta+1)^2(716\theta^2+1432\theta+579)-2^{4} 3^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 114, 22518, 5236980, 1321024950, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -872, 18328, -432528, 13706388, ... ; Common denominator:...

#### Discriminant

$-(196z-1)(-1+324z)^2$

#### Local exponents

$0$$\frac{ 1}{ 324}$$\frac{ 1}{ 196}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$0$$1$$1$
$0$$1$$1$$2$
$0$$1$$2$$\frac{ 5}{ 2}$

7

New Number: 3.17 |  AESZ: 387  |  Superseeker: 68 125636/3  |  Hash: 06864aab02693f4b84eb494138bb3428

Degree: 3

$\theta^4-2^{2} x\left(228\theta^4+456\theta^3+385\theta^2+157\theta+26\right)+2^{11} x^{2}(\theta+1)^2(132\theta^2+264\theta+109)-2^{18} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 104, 18600, 3925760, 906368680, ...
--> OEIS
Normalized instanton numbers (n0=1): 68, 204, 125636/3, 841384, 123715360, ... ; Common denominator:...

#### Discriminant

$-(400z-1)(-1+256z)^2$

#### Local exponents

$0$$\frac{ 1}{ 400}$$\frac{ 1}{ 256}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$0$$1$
$0$$1$$1$$2$
$0$$2$$1$$\frac{ 5}{ 2}$

#### Note:

This is operator "3.17" from ...

8

New Number: 3.18 |  AESZ: 388  |  Superseeker: 266 11433160/3  |  Hash: 7e11db69c1b7bd8781e54a5eadb0e307

Degree: 3

$\theta^4-2 x\left(582\theta^4+1164\theta^3+815\theta^2+233\theta+25\right)+2^{2} x^{2}(\theta+1)^2(2316\theta^2+4632\theta+1907)-2^{4} 17^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 50, 17142, 9383540, 6301530550, ...
--> OEIS
Normalized instanton numbers (n0=1): 266, 19320, 11433160/3, 1106069392, 397606861972, ... ; Common denominator:...

#### Discriminant

$-(1156z-1)(4z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 1156}$$\frac{ 1}{ 4}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$0$$1$
$0$$1$$1$$2$
$0$$2$$1$$\frac{ 5}{ 2}$

#### Note:

This is operator "3.18" from ...

9

New Number: 3.1 |  AESZ: 34  |  Superseeker: 1 28/3  |  Hash: e5461c5f5ae4d929328f66b8955a31f5

Degree: 3

$\theta^4-x\left(35\theta^4+70\theta^3+63\theta^2+28\theta+5\right)+x^{2}(\theta+1)^2(259\theta^2+518\theta+285)-3^{2} 5^{2} x^{3}(\theta+1)^2(\theta+2)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...

#### Discriminant

$-(z-1)(25z-1)(9z-1)$

#### Local exponents

$0$$\frac{ 1}{ 25}$$\frac{ 1}{ 9}$$1$$\infty$
$0$$0$$0$$0$$1$
$0$$1$$1$$1$$1$
$0$$1$$1$$1$$2$
$0$$2$$2$$2$$2$

10

New Number: 3.20 |  AESZ: 390  |  Superseeker: 19 4455  |  Hash: cd8ca8746f3610e70893770a090533f9

Degree: 3

$\theta^4-x\left(561\theta^4+1122\theta^3+975\theta^2+414\theta+70\right)+2^{2} 7^{2} x^{2}(\theta+1)^2(534\theta^2+1068\theta+433)-2^{2} 7^{4} 13^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 70, 8442, 1192660, 182057050, ...
--> OEIS
Normalized instanton numbers (n0=1): 19, -276, 4455, -104648, 2969383, ... ; Common denominator:...

#### Discriminant

$-(169z-1)(-1+196z)^2$

#### Local exponents

$0$$\frac{ 1}{ 196}$$\frac{ 1}{ 169}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$\frac{ 1}{ 6}$$1$$1$
$0$$\frac{ 5}{ 6}$$1$$2$
$0$$1$$2$$\frac{ 5}{ 2}$

#### Note:

This is operator "3.20" from ...

11

New Number: 3.22 |  AESZ: 392  |  Superseeker: 166 1016100  |  Hash: 5862be5cc4d3ec1686e6b9a6ec08f7e7

Degree: 3

$\theta^4-2 x\left(230\theta^4+496\theta^3+323\theta^2+75\theta+6\right)-2^{2} 3 x^{2}(6\theta+5)(1866\theta^3+5341\theta^2+4760\theta+1084)-2^{4} 3^{2} 13^{2} x^{3}(6\theta+5)(6\theta+11)(3\theta+1)(3\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 5760, 1664544, 681014880, ...
--> OEIS
Normalized instanton numbers (n0=1): 166, 8076, 1016100, 189329096, 43879949258, ... ; Common denominator:...

#### Discriminant

$-(676z-1)(1+108z)^2$

#### Local exponents

$-\frac{ 1}{ 108}$$0$$\frac{ 1}{ 676}$$\infty$
$0$$0$$0$$\frac{ 1}{ 3}$
$\frac{ 1}{ 3}$$0$$1$$\frac{ 5}{ 6}$
$1$$0$$1$$\frac{ 11}{ 6}$
$\frac{ 4}{ 3}$$0$$2$$\frac{ 7}{ 3}$

#### Note:

This is operator "3.22" from ...

12

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

Degree: 3

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

Maple   LaTex

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}$

Operator equivalent to AESZ 144=c \ast c$Show more... or download as plain text | PDF | Maple | LaTex 13 New Number: 3.19 | AESZ: 389 | Superseeker: 66 69048 | Hash: c5cca5b7bfc61c4e8b38fab025244078 Degree: 3 $\theta^4-2 x\left(742\theta^4+1484\theta^3+1295\theta^2+553\theta+95\right)+2^{2} 5^{3} x^{2}(\theta+1)^2(1468\theta^2+2936\theta+1211)-2^{4} 5^{6} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$ Maple LaTex Coefficients of the holomorphic solution: 1, 190, 61170, 22892500, 9212271250, ... --> OEIS Normalized instanton numbers (n0=1): 66, -1780, 69048, -3847892, 244783420, ... ; Common denominator:... #### Discriminant $-(484z-1)(-1+500z)^2$ #### Local exponents $0$$\frac{ 1}{ 500}$$\frac{ 1}{ 484}$$\infty$ $0$$0$$0$$\frac{ 1}{ 2}$ $0$$0$$1$$1$ $0$$1$$1$$2$ $0$$1$$2$$\frac{ 5}{ 2}$ #### Note: This is operator "3.19" from ... Show more... or download as plain text | PDF | Maple | LaTex 14 New Number: 3.21 | AESZ: 391 | Superseeker: 964 85888580/3 | Hash: 907f1fbd0b6f7c89689fb136ee18482a Degree: 3 $\theta^4-2^{2} x\left(3460\theta^4+5768\theta^3+4385\theta^2+1501\theta+186\right)+2^{10} 3^{2} x^{2}(4\theta+3)(1732\theta^3+4475\theta^2+3531\theta+645)-2^{14} 3^{4} 17^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$ Maple LaTex Coefficients of the holomorphic solution: 1, 744, 1731240, 5192436480, 17479541356200, ... --> OEIS Normalized instanton numbers (n0=1): 964, -111140, 85888580/3, -9197858184, 3544241969952, ... ; Common denominator:... #### Discriminant $-(4624z-1)(-1+4608z)^2$ #### Local exponents $0$$\frac{ 1}{ 4624}$$\frac{ 1}{ 4608}$$\infty$ $0$$0$$0$$\frac{ 1}{ 4}$ $0$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 4}$ $0$$1$$1$$\frac{ 7}{ 4}$ $0$$2$$\frac{ 3}{ 2}$$\frac{ 9}{ 4}$ #### Note: This is operator "3.21" from ... Show more... or download as plain text | PDF | Maple | LaTex 15 New Number: 3.23 | AESZ: 393 | Superseeker: -128 -263808 | Hash: c49c1e5d127755611021be0fc2c55d06 Degree: 3 $\theta^4+2^{5} x\left(79\theta^4+140\theta^3+112\theta^2+42\theta+6\right)+2^{8} 3 x^{2}(6\theta+5)(462\theta^3+1255\theta^2+1052\theta+235)+2^{13} 3^{2} 5^{2} x^{3}(6\theta+5)(6\theta+11)(3\theta+1)(3\theta+7)$ Maple LaTex Coefficients of the holomorphic solution: 1, -192, 89136, -51502080, 32954034960, ... --> OEIS Normalized instanton numbers (n0=1): -128, -5148, -263808, -22378134, -2164448640, ... ; Common denominator:... #### Discriminant $(800z+1)(1+864z)^2$ #### Local exponents $-\frac{ 1}{ 800}$$-\frac{ 1}{ 864}$$0$$\infty$ $0$$0$$0$$\frac{ 1}{ 3}$ $1$$\frac{ 1}{ 3}$$0$$\frac{ 5}{ 6}$ $1$$1$$0$$\frac{ 11}{ 6}$ $2$$\frac{ 4}{ 3}$$0$$\frac{ 7}{ 3}$ #### Note: This is operator "3.23" from ... Show more... or download as plain text | PDF | Maple | LaTex 16 New Number: 3.24 | AESZ: | Superseeker: -2 -108 | Hash: 3c89cc2017daa2eba88c016b8ae5865c Degree: 3 $\theta^4+2 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} x^{2}(2\theta+1)(2\theta+3)(47\theta^2+94\theta+51)+2^{4} 7 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$ Maple LaTex Coefficients of the holomorphic solution: 1, -2, 54, -980, 26950, ... --> OEIS Normalized instanton numbers (n0=1): -2, 17, -108, 1498, -19630, ... ; Common denominator:... #### Discriminant $(16z-1)(112z^2-40z-1)$ #### Local exponents $\frac{ 5}{ 28}-\frac{ 1}{ 7}\sqrt{ 2}$$0$$\frac{ 1}{ 16}$$\frac{ 5}{ 28}+\frac{ 1}{ 7}\sqrt{ 2}$$\infty$ $0$$0$$0$$0$$\frac{ 1}{ 2}$ $1$$0$$1$$1$$\frac{ 3}{ 2}$ $1$$0$$1$$1$$\frac{ 3}{ 2}$ $2$$0$$2$$2$$\frac{ 5}{ 2}$ #### Note: This is operator$\tilde{C_9}$Show more... or download as plain text | PDF | Maple | LaTex 17 New Number: 3.25 | AESZ: | Superseeker: -2 -308/3 | Hash: 287da3a26b0da679d81da411b46958d1 Degree: 3 $\theta^4+2 x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{2} x^{2}(2\theta+1)(2\theta+3)(29\theta^2+58\theta+33)+2^{4} 3 5 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$ Maple LaTex Coefficients of the holomorphic solution: 1, -6, 90, -2100, 59850, ... --> OEIS Normalized instanton numbers (n0=1): -2, 12, -308/3, 1058, -71158/5, ... ; Common denominator:... #### Discriminant $(48z+1)(80z^2+8z+1)$ #### Local exponents $-\frac{ 1}{ 20}-\frac{ 1}{ 10}I$$-\frac{ 1}{ 20}+\frac{ 1}{ 10}I$$-\frac{ 1}{ 48}$$0$$\infty$ $0$$0$$0$$0$$\frac{ 1}{ 2}$ $1$$1$$1$$0$$\frac{ 3}{ 2}$ $1$$1$$1$$0$$\frac{ 3}{ 2}$ $2$$2$$2$$0$$\frac{ 5}{ 2}$ #### Note: This is operator$\tilde{C_17}$Show more... or download as plain text | PDF | Maple | LaTex 18 New Number: 3.26 | AESZ: 407 | Superseeker: 2 440 | Hash: c46d32ba4b3738ba34fe1e6c16e6f242 Degree: 3 $\theta^4+2 x\left(132\theta^4+264\theta^3+293\theta^2+161\theta+35\right)+2^{2} 5^{2} x^{2}(\theta+1)^2(228\theta^2+456\theta+335)+2^{6} 5^{4} x^{3}(\theta+1)(\theta+2)(4\theta+5)(4\theta+7)$ Maple LaTex Coefficients of the holomorphic solution: 1, -70, 5650, -484900, 43071250, ... --> OEIS Normalized instanton numbers (n0=1): 2, -44, 440, -4844, 46268, ... ; Common denominator:... #### Discriminant $(64z+1)(1+100z)^2$ #### Local exponents $-\frac{ 1}{ 64}$$-\frac{ 1}{ 100}$$0$$\infty$ $0$$0$$0$$1$ $1$$-\frac{ 1}{ 2}$$0$$\frac{ 5}{ 4}$ $1$$1$$0$$\frac{ 7}{ 4}$ $2$$\frac{ 3}{ 2}$$0$$2$ #### Note: This is operator "3.26" from ... Show more... or download as plain text | PDF | Maple | LaTex 19 New Number: 3.27 | AESZ: 408 | Superseeker: -60 -61780 | Hash: 32ab77c73baf49023973ad11e5d0852e Degree: 3 $\theta^4-2^{2} x(2\theta+1)(46\theta^3+53\theta^2+45\theta+11)-2^{4} x^{2}(8\theta+7)(64\theta^3+312\theta^2+440\theta+135)+2^{8} 3^{2} x^{3}(8\theta+3)(8\theta+7)(8\theta+15)(8\theta+19)$ Maple LaTex Coefficients of the holomorphic solution: 1, 44, 6060, 972720, 182017260, ... --> OEIS Normalized instanton numbers (n0=1): -60, 975, -61780, 4166460, -1853578608/5, ... ; Common denominator:... #### Discriminant $(144z+1)(-1+256z)^2$ #### Local exponents $-\frac{ 1}{ 144}$$0$$\frac{ 1}{ 256}$$\infty$ $0$$0$$0$$\frac{ 3}{ 8}$ $1$$0$$\frac{ 1}{ 4}$$\frac{ 7}{ 8}$ $1$$0$$1$$\frac{ 15}{ 8}$ $2$$0$$\frac{ 5}{ 4}$$\frac{ 19}{ 8}$ #### Note: This is operator "3.27" from ... Show more... or download as plain text | PDF | Maple | LaTex 20 New Number: 3.28 | AESZ: 410 | Superseeker: 7 1057/3 | Hash: accbbff67291992dfbc89e78f5a3c897 Degree: 3 $\theta^4-x\left(145\theta^4+242\theta^3+199\theta^2+78\theta+12\right)+2^{3} x^{2}(2\theta+1)(4\theta+3)(97\theta^2+182\theta+114)-2^{4} 3^{4} x^{3}(2\theta+1)(2\theta+3)(4\theta+3)(4\theta+7)$ Maple LaTex Coefficients of the holomorphic solution: 1, 12, 336, 12880, 592200, ... --> OEIS Normalized instanton numbers (n0=1): 7, 22, 1057/3, 5460, 108241, ... ; Common denominator:... #### Discriminant $-(81z-1)(-1+32z)^2$ #### Local exponents $0$$\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 ... Show more... or download as plain text | PDF | Maple | LaTex 21 New Number: 3.29 | AESZ: 411 | Superseeker: 3 237 | Hash: 767c4e8d5a7bc53fbbd0d49797e65358 Degree: 3 $\theta^4-x\left(16+98\theta+235\theta^2+274\theta^3+145\theta^4\right)+2^{3} x^{2}(2\theta+1)(4\theta+5)(97\theta^2+190\theta+120)-2^{4} 3^{4} x^{3}(4\theta+5)(2\theta+3)(2\theta+1)(4\theta+9)$ Maple LaTex Coefficients of the holomorphic solution: 1, 16, 468, 17520, 774060, ... --> OEIS Normalized instanton numbers (n0=1): 3, 36, 237, 4638, 72330, ... ; 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{ 1}{ 4}$$\frac{ 5}{ 4}$ $0$$1$$1$$\frac{ 3}{ 2}$ $0$$2$$\frac{ 5}{ 4}$$\frac{ 9}{ 4}$ #### Note: This is operator "3.29" from ... Show more... or download as plain text | PDF | Maple | LaTex 22 New Number: 3.2 | AESZ: 227 | Superseeker: -900 8364884 | Hash: 2e00a51fe0c232d13a452380f44c79da Degree: 3 $\theta^4+2^{2} 3^{2} x\left(132\theta^4+264\theta^3+201\theta^2+69\theta+10\right)+2^{9} 3^{6} x^{2}\left(20\theta^4+80\theta^3+107\theta^2+54\theta+10\right)+2^{12} 3^{10} x^{3}(2\theta+5)^2(2\theta+1)^2$ Maple LaTex Coefficients of the holomorphic solution: 1, -360, 314280, -348076800, 431342188200, ... --> OEIS Normalized instanton numbers (n0=1): -900, -27387, 8364884, 2066389488, -208833104160, ... ; Common denominator:... #### Discriminant $(1296z+1)(1+1728z)^2$ #### Local exponents $-\frac{ 1}{ 1296}$$-\frac{ 1}{ 1728}$$0$$\infty$ $0$$0$$0$$\frac{ 1}{ 2}$ $1$$\frac{ 1}{ 2}$$0$$\frac{ 1}{ 2}$ $1$$\frac{ 1}{ 2}$$0$$\frac{ 5}{ 2}$ $2$$1$$0$$\frac{ 5}{ 2}$ Show more... or download as plain text | PDF | Maple | LaTex 23 New Number: 3.30 | AESZ: 422 | Superseeker: 124 2152276/9 | Hash: b37ac82ae57415849cb59beac4cd6adf Degree: 3 $\theta^4+2^{2} x\left(380\theta^4+760\theta^3+907\theta^2+527\theta+117\right)+2^{4} 3 x^{2}(8\theta+7)(8\theta+9)(184\theta^2+368\theta+183)-2^{8} 3^{2} x^{3}(8\theta+7)(8\theta+9)(8\theta+15)(8\theta+17)$ Maple LaTex Coefficients of the holomorphic solution: 1, -468, 280260, -182276400, 123566444100, ... --> OEIS Normalized instanton numbers (n0=1): 124, -3752, 2152276/9, -18042588, 1647569184, ... ; Common denominator:... #### Discriminant $-(16z-1)(1+768z)^2$ #### Local exponents $-\frac{ 1}{ 768}$$0$$\frac{ 1}{ 16}$$\infty$ $0$$0$$0$$\frac{ 7}{ 8}$ $-\frac{ 1}{ 2}$$0$$1$$\frac{ 9}{ 8}$ $1$$0$$1$$\frac{ 15}{ 8}$ $\frac{ 3}{ 2}$$0$$2$$\frac{ 17}{ 8}$ #### Note: This is operator "3.30" from ... Show more... or download as plain text | PDF | Maple | LaTex 24 New Number: 3.31 | AESZ: | Superseeker: 4 284 | Hash: 660b0951ad934fc17fda7eb9b1750649 Degree: 3 $\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{5} x^{2}(2\theta+1)(2\theta+3)(7\theta^2+14\theta+8)-2^{4} 11 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$ Maple LaTex Coefficients of the holomorphic solution: 1, 8, 168, 5360, 210280, ... --> OEIS Normalized instanton numbers (n0=1): 4, 27, 284, 4368, 80968, ... ; Common denominator:... #### Discriminant $1-80z+896z^2-2816z^3$ No data for singularities #### Note: This is operator "3.31" from ... Show more... or download as plain text | PDF | Maple | LaTex 25 New Number: 3.32 | AESZ: | Superseeker: 128 382592 | Hash: 9b39b616939718654c472dbfb37cdd4e Degree: 3 $\theta^4-2^{4} x(6\theta^2+6\theta-1)(2\theta+1)^2-2^{10} x^{2}(60\theta^2+120\theta+97)(\theta+1)^2-2^{21} x^{3}(\theta+1)^2(\theta+2)^2$ Maple LaTex Coefficients of the holomorphic solution: 1, -16, 4624, 678656, 238896400, ... --> OEIS Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:... #### Discriminant $-(512z-1)(1+64z)^2$ #### Local exponents $-\frac{ 1}{ 64}$$0$$\frac{ 1}{ 512}$$\infty$ $0$$0$$0$$1$ $-\frac{ 1}{ 2}$$0$$1$$1$ $1$$0$$1$$2$ $\frac{ 3}{ 2}$$0$$2$$2$ #### Note: Operator equivalent to AESZ 220 B-Incarnation: Double octic:D.O.244 Show more... or download as plain text | PDF | Maple | LaTex 26 New Number: 3.33 | AESZ: | Superseeker: 4 1580/9 | Hash: da01a7b2dfcebe6e332be6c29ed2a8e5 Degree: 3 $\theta^4+2^{2} x\left(36\theta^4+72\theta^3+85\theta^2+49\theta+11\right)+2^{4} x^{2}(8\theta^2+16\theta+11)(48\theta^2+96\theta+49)+2^{8} x^{3}(4\theta+7)^2(4\theta+5)^2$ Maple LaTex Coefficients of the holomorphic solution: 1, -44, 2244, -122576, 6952516, ... --> OEIS Normalized instanton numbers (n0=1): 4, -25, 1580/9, -1580, 17120, ... ; Common denominator:... #### Discriminant $(16z+1)(1+64z)^2$ #### Local exponents $-\frac{ 1}{ 16}$$-\frac{ 1}{ 64}$$0$$\infty$ $0$$0$$0$$\frac{ 5}{ 4}$ $1$$-\frac{ 1}{ 2}$$0$$\frac{ 5}{ 4}$ $1$$1$$0$$\frac{ 7}{ 4}$ $2$$\frac{ 3}{ 2}$$0$$\frac{ 7}{ 4}$ #### Note: Operator equivalent to AESZ 353 Show more... or download as plain text | PDF | Maple | LaTex 27 New Number: 3.34 | AESZ: | Superseeker: 16 1744 | Hash: 931a876bfe4d4aa192c6e18e74047640 Degree: 3 $\theta^4-2^{4} x\left(25\theta^4+50\theta^3+43\theta^2+18\theta+3\right)+2^{11} x^{2}(26\theta^2+52\theta+21)(\theta+1)^2-2^{16} 3^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$ Maple LaTex Coefficients of the holomorphic solution: 1, 48, 3984, 387840, 40818960, ... --> OEIS Normalized instanton numbers (n0=1): 16, -110, 1744, -29526, 644016, ... ; Common denominator:... #### Discriminant $-(144z-1)(-1+128z)^2$ #### Local exponents $0$$\frac{ 1}{ 144}$$\frac{ 1}{ 128}$$\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 107$=d \ast d$Show more... or download as plain text | PDF | Maple | LaTex 28 New Number: 3.3 | AESZ: 228 | Superseeker: -68 -18628/3 | Hash: b15f49e2c20021dbc50eaf05a6fd3126 Degree: 3 $\theta^4+2^{2} x\left(176\theta^4+352\theta^3+289\theta^2+113\theta+18\right)+2^{11} x^{2}\left(80\theta^4+320\theta^3+449\theta^2+258\theta+54\right)+2^{16} 3 x^{3}(2\theta+5)(2\theta+1)(4\theta+3)(4\theta+9)$ Maple LaTex Coefficients of the holomorphic solution: 1, -72, 10152, -1739520, 327839400, ... --> OEIS Normalized instanton numbers (n0=1): -68, -835, -18628/3, 359052, 23710944, ... ; Common denominator:... #### Discriminant $(192z+1)(1+256z)^2$ #### Local exponents $-\frac{ 1}{ 192}$$-\frac{ 1}{ 256}$$0$$\infty$ $0$$0$$0$$\frac{ 1}{ 2}$ $1$$\frac{ 1}{ 2}$$0$$\frac{ 3}{ 4}$ $1$$\frac{ 1}{ 2}$$0$$\frac{ 9}{ 4}$ $2$$1$$0$$\frac{ 5}{ 2}$ #### Note: This is operator "3.3" from ... Show more... or download as plain text | PDF | Maple | LaTex 29 New Number: 3.4 | AESZ: | Superseeker: -9 -748 | Hash: 350ef7c6e038467a3f50bfbe164fa73a Degree: 3 $\theta^4+3^{2} x\left(33\theta^4+66\theta^3+57\theta^2+24\theta+4\right)+2^{3} 3^{6} x^{2}(\theta+1)^2(5\theta^2+10\theta+4)+2^{2} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$ Maple LaTex Coefficients of the holomorphic solution: 1, -36, 2268, -168840, 13664700, ... --> OEIS Normalized instanton numbers (n0=1): -9, -279/4, -748, -9612, -155448, ... ; Common denominator:... #### Discriminant $(81z+1)(1+108z)^2$ #### Local exponents $-\frac{ 1}{ 81}$$-\frac{ 1}{ 108}$$0$$\infty$ $0$$0$$0$$\frac{ 1}{ 2}$ $1$$\frac{ 1}{ 2}$$0$$1$ $1$$\frac{ 1}{ 2}$$0$$2$ $2$$1$$0$$\frac{ 5}{ 2}$ #### Note: Operator equivalent to AESZ 165=$f \ast f\$.

30

New Number: 3.5 |  AESZ:  |  Superseeker: 26 103520/9  |  Hash: 4ed9bc316d49a71649da0a1148f7ea9d

Degree: 3

$\theta^4-2 x\left(102\theta^4+204\theta^3+155\theta^2+53\theta+7\right)+2^{2} x^{2}(\theta+1)^2(396\theta^2+792\theta+311)-2^{4} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 14, 834, 78260, 8970850, ...
--> OEIS
Normalized instanton numbers (n0=1): 26, 348, 103520/9, 539764, 31290280, ... ; Common denominator:...

#### Discriminant

$-(196z-1)(4z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 196}$$\frac{ 1}{ 4}$$\infty$
$0$$0$$0$$\frac{ 1}{ 2}$
$0$$1$$\frac{ 1}{ 4}$$1$
$0$$1$$\frac{ 3}{ 4}$$2$
$0$$2$$1$$\frac{ 5}{ 2}$

#### Note:

Operator equivalent to AESZ 214