Summary

You searched for: sol=16

Your search produced 27 matches

You can download all data as plain text or as JSON

1

New Number: 2.13 |  AESZ: 36  |  Superseeker: 16 1232  |  Hash: dea6fdf568a5907a24ba30fef2caf124  

Degree: 2

\(\theta^4-2^{4} x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{9} x^{2}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 720, 44800, 3312400, ...
--> OEIS
Normalized instanton numbers (n0=1): 16, 42, 1232, 32159, 990128, ... ; Common denominator:...

Discriminant

\((128z-1)(64z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

A*d

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

2

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  

3

New Number: 4.35 |  AESZ:  |  Superseeker: -16 -1744  |  Hash: cd392ce4c33f242f5d17e59976d0ea4f  

Degree: 4

\(\theta^4-2^{4} x\left(23\theta^4+14\theta^3+13\theta^2+6\theta+1\right)+2^{11} x^{2}\theta(21\theta^3+24\theta^2+18\theta+4)-2^{16} x^{3}(2\theta+1)(10\theta^3+7\theta^2-5\theta-4)-2^{23} x^{4}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 912, 67840, 5839120, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -106, -1744, -29526, -644016, ... ; Common denominator:...

Discriminant

\(-(16z+1)(128z-1)^3\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(\frac{ 3}{ 2}\)\(1\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Operator equivalent to 3.34, equivalent to
AESZ 107 $=d \ast d$.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

4

New Number: 4.41 |  AESZ: 220  |  Superseeker: 128 382592  |  Hash: 671a1aa788ead53985e13ad6774d0189  

Degree: 4

\(\theta^4-2^{4} x\left(20\theta^4+56\theta^3+38\theta^2+10\theta+1\right)-2^{10} x^{2}\left(84\theta^4+240\theta^3+261\theta^2+134\theta+25\right)-2^{16} x^{3}(2\theta+1)^2(23\theta^2+55\theta+39)-2^{23} x^{4}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 3600, 851200, 257328400, ...
--> OEIS
Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...

Discriminant

\(-(512z-1)(64z+1)^3\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 512}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(\frac{ 3}{ 2}\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Sporadic Operator.
Reducible to 3.32, so not a primary operator.
B-Incarnation: 81111- x 82--11

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

5

New Number: 4.65 |  AESZ:  |  Superseeker: 48 -9104  |  Hash: 5ec2790b5eda514313634b7aeb0a295c  

Degree: 4

\(\theta^4-2^{4} x\left(5\theta^4+34\theta^3+25\theta^2+8\theta+1\right)+2^{11} x^{2}\left(5\theta^4+47\theta^3+90\theta^2+47\theta+8\right)+2^{16} x^{3}\left(51\theta^4+192\theta^3+155\theta^2+48\theta+5\right)+2^{23} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 144, -70400, -9858800, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, -1298, -9104, 387230, 102374160, ... ; Common denominator:...

Discriminant

\((32768z^2-208z+1)(1+64z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity,
corresponding to Operator AESZ 295/4.64

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

6

New Number: 4.77 |  AESZ:  |  Superseeker: 1 68/9  |  Hash: f9623221ffe8be4c1e31a6e6ce195a37  

Degree: 4

\(\theta^4-x\left(16+80\theta+161\theta^2+162\theta^3+81\theta^4\right)+2^{3} x^{2}\left(303\theta^4+1212\theta^3+1952\theta^2+1480\theta+440\right)-2^{6} x^{3}(124\theta^2+372\theta+263)(2\theta+3)^2+2^{9} 3 5^{2} x^{4}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 280, 5152, 98200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...

Discriminant

\((25z-1)(24z-1)(-1+16z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 25}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 2}\)
\(0\)\(2\)\(2\)\(1\)\(3\)

Note:

Sporadic Operator.
B-Incarnation: SII4411

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

7

New Number: 5.105 |  AESZ: 358  |  Superseeker: -336 -4761360  |  Hash: f026b6514e3be9b730646bc9410b1049  

Degree: 5

\(\theta^4-2^{4} x\left(125\theta^4-62\theta^3-31\theta^2+1\right)+2^{11} x^{2}\left(640\theta^4-287\theta^3+377\theta^2+119\theta+11\right)-2^{16} x^{3}\left(5121\theta^4+4908\theta^3+5213\theta^2+2484\theta+503\right)+2^{23} 13 x^{4}\left(441\theta^4+1074\theta^3+1207\theta^2+670\theta+148\right)-2^{34} 13^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, -880, -180992, -12537584, ...
--> OEIS
Normalized instanton numbers (n0=1): -336, -30306, -4761360, -962369202, -225176272240, ... ; Common denominator:...

Discriminant

\(-(128z-1)(32768z^2-208z+1)(-1+832z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 832}\)\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 357/5.04

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

8

New Number: 5.108 |  AESZ: 365  |  Superseeker: 4 1268  |  Hash: f84624e83cd4eb2cc90693bd5627efcf  

Degree: 5

\(\theta^4-2^{2} x\left(99\theta^4+78\theta^3+65\theta^2+26\theta+4\right)+2^{6} x^{2}\left(938\theta^4+1382\theta^3+1269\theta^2+554\theta+92\right)-2^{10} x^{3}\left(4171\theta^4+8736\theta^3+8690\theta^2+3948\theta+680\right)+2^{15} 5 x^{4}(2\theta+1)(418\theta^3+951\theta^2+846\theta+260)-2^{19} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 720, 44800, 3245200, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 107/2, 1268, 89439/4, 396908, ... ; Common denominator:...

Discriminant

\(-(108z-1)(2048z^2-128z+1)(-1+80z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 2}\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 80}\)\(\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.108" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

9

New Number: 5.11 |  AESZ: 71  |  Superseeker: 112 378800  |  Hash: cf4de65b0566a4f6294132c167d227eb  

Degree: 5

\(\theta^4+2^{4} x\left(39\theta^4-42\theta^3-29\theta^2-8\theta-1\right)+2^{11} x^{2}\theta(37\theta^3-137\theta^2-10\theta-1)-2^{16} x^{3}\left(181\theta^4+456\theta^3+353\theta^2+132\theta+19\right)-2^{23} 5 x^{4}\left(36\theta^4+60\theta^3+36\theta^2+6\theta-1\right)+2^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 656, 40192, 3006736, ...
--> OEIS
Normalized instanton numbers (n0=1): 112, -4570, 378800, -40565898, 5098744272, ... ; Common denominator:...

Discriminant

\((16z-1)(128z-1)(128z+1)(1+320z)^2\)

Local exponents

\(-\frac{ 1}{ 128}\)\(-\frac{ 1}{ 320}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(1\)

Note:

This is operator "5.11" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

10

New Number: 5.120 |  AESZ:  |  Superseeker: 48 171120  |  Hash: 3eb6b52ff225f7b2f94716d73344b578  

Degree: 5

\(\theta^4-2^{4} x\left(41\theta^4+34\theta^3+25\theta^2+8\theta+1\right)+2^{10} x^{2}\left(126\theta^4+108\theta^3+33\theta^2+6\theta+1\right)-2^{14} x^{3}\left(564\theta^4+504\theta^3+429\theta^2+195\theta+34\right)+2^{21} x^{4}(2\theta+1)(44\theta^3+78\theta^2+59\theta+17)-2^{28} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1680, 298240, 64975120, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 2286, 171120, 17540830, 2229934864, ... ; Common denominator:...

Discriminant

\(-(16z-1)(4096z^2-384z+1)(-1+128z)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\)\(\frac{ 1}{ 128}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- x 821--1

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

11

New Number: 5.123 |  AESZ:  |  Superseeker: 96 266464  |  Hash: b9a4a4eae678c9ce13a407517f92c30e  

Degree: 5

\(\theta^4+2^{4} x\left(28\theta^4-40\theta^3-28\theta^2-8\theta-1\right)+2^{13} x^{2}\left(6\theta^4-12\theta^3+17\theta^2+10\theta+2\right)+2^{18} x^{3}\left(12\theta^4+72\theta^3+35\theta^2-3\theta-4\right)+2^{26} x^{4}(2\theta+1)(4\theta^3-6\theta^2-15\theta-7)-2^{34} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, -240, -24320, 2075920, ...
--> OEIS
Normalized instanton numbers (n0=1): 96, -4200, 266464, -20295944, 1778341408, ... ; Common denominator:...

Discriminant

\(-(64z-1)(16384z^2+1)(1+256z)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0-\frac{ 1}{ 128}I\)\(0\)\(0+\frac{ 1}{ 128}I\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as fibre product 62211- x 812--1

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

12

New Number: 5.16 |  AESZ: 118  |  Superseeker: 55 116555  |  Hash: d950d38dab80e3772855675af0cdb950  

Degree: 5

\(\theta^4-x\left(465\theta^4+594\theta^3+431\theta^2+134\theta+16\right)+2^{4} x^{2}\left(2625\theta^4+1911\theta^3-946\theta^2-884\theta-176\right)-2^{6} x^{3}\left(16105\theta^4-3624\theta^3-5241\theta^2-1284\theta-36\right)-2^{11} 7 x^{4}\left(155\theta^4+334\theta^3+306\theta^2+139\theta+26\right)+2^{16} 7^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1816, 310336, 64483576, ...
--> OEIS
Normalized instanton numbers (n0=1): 55, 1915, 116555, 10661240, 1227998285, ... ; Common denominator:...

Discriminant

\((z-1)(1024z^2+352z-1)(-1+56z)^2\)

Local exponents

\(-\frac{ 11}{ 64}-\frac{ 5}{ 64}\sqrt{ 5}\)\(0\)\(-\frac{ 11}{ 64}+\frac{ 5}{ 64}\sqrt{ 5}\)\(\frac{ 1}{ 56}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 22/5.5

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

13

New Number: 5.29 |  AESZ: 208  |  Superseeker: 274/7 281388/7  |  Hash: f1d6dfa8a5cdcc2513dfca4243565b2f  

Degree: 5

\(7^{2} \theta^4-2 7 x\left(1056\theta^4+1884\theta^3+1397\theta^2+455\theta+56\right)+2^{2} 3 x^{2}\left(22760\theta^4+13672\theta^3-22537\theta^2-18116\theta-3584\right)-2^{4} x^{3}\left(53312\theta^4-162120\theta^3-195172\theta^2-78561\theta-11130\right)-2^{6} 19 x^{4}(1189\theta^2+2533\theta+1646)(2\theta+1)^2+2^{11} 19^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1440, 196000, 32418400, ...
--> OEIS
Normalized instanton numbers (n0=1): 274/7, 6115/7, 281388/7, 2815228, 1699166270/7, ... ; Common denominator:...

Discriminant

\((4z+1)(512z^2-284z+1)(-7+76z)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 71}{ 256}-\frac{ 17}{ 256}\sqrt{ 17}\)\(\frac{ 7}{ 76}\)\(\frac{ 71}{ 256}+\frac{ 17}{ 256}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.29" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

14

New Number: 5.89 |  AESZ: 329  |  Superseeker: 48 25200  |  Hash: 8c526b3b825d5ad6a3d0fb83ee4e6059  

Degree: 5

\(\theta^4-2^{4} x\left(8\theta^4+34\theta^3+25\theta^2+8\theta+1\right)-2^{8} x^{2}\left(87\theta^4+150\theta^3+32\theta^2-2\theta-1\right)-2^{12} x^{3}\left(202\theta^4+240\theta^3+211\theta^2+102\theta+19\right)-2^{16} 3 x^{4}(2\theta+1)(22\theta^3+45\theta^2+38\theta+12)-2^{20} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1200, 136960, 19010320, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 270, 25200, 968066, 80892688, ... ; Common denominator:...

Discriminant

\(-(16384z^3+3072z^2+224z-1)(1+48z)^2\)

Local exponents

≈\(-0.095858-0.072741I\) ≈\(-0.095858+0.072741I\)\(-\frac{ 1}{ 48}\)\(0\) ≈\(0.004215\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.89" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

15

New Number: 5.91 |  AESZ: 331  |  Superseeker: 112 186800  |  Hash: a30093d8c1ab2f66122cef8935b79efb  

Degree: 5

\(\theta^4+2^{4} x\left(18\theta^4-48\theta^3-33\theta^2-9\theta-1\right)-2^{9} x^{2}\left(86\theta^4+512\theta^3+125\theta^2+45\theta+10\right)-2^{14} x^{3}\left(1138\theta^4+2040\theta^3+1883\theta^2+879\theta+157\right)-2^{19} 7 x^{4}(2\theta+1)(186\theta^3+375\theta^2+317\theta+100)-2^{27} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1488, 183040, 27611920, ...
--> OEIS
Normalized instanton numbers (n0=1): 112, -2242, 186800, -11675813, 1250599376, ... ; Common denominator:...

Discriminant

\(-(32z+1)(256z-1)(64z+1)(1+224z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 224}\)\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.91" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

16

New Number: 5.9 |  AESZ: 56  |  Superseeker: -16 -3280  |  Hash: 58a7f24bf18cb98b526885069667f9f0  

Degree: 5

\(\theta^4-2^{4} x\left(22\theta^4+8\theta^3+9\theta^2+5\theta+1\right)+2^{9} x^{2}\left(94\theta^4+88\theta^3+97\theta^2+45\theta+8\right)-2^{14} x^{3}\left(194\theta^4+336\theta^3+371\theta^2+195\theta+41\right)+2^{19} 3 x^{4}\left(64\theta^4+176\theta^3+217\theta^2+129\theta+30\right)-2^{27} 3^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 464, 17152, 725776, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -178, -3280, -76197, -2046896, ... ; Common denominator:...

Discriminant

\(-(-1+32z)(96z-1)^2(64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 96}\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(4\)\(1\)\(2\)\(1\)

Note:

There is a second MUM-point hiding at infinity, corresponding to Operator...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

17

New Number: 10.7 |  AESZ:  |  Superseeker: 4 -628/9  |  Hash: d5910f048831bb407eb8998c7c57e09f  

Degree: 10

\(\theta^4-2^{2} x\left(48\theta^4+48\theta^3+45\theta^2+21\theta+4\right)+2^{6} x^{2}\left(261\theta^4+489\theta^3+590\theta^2+364\theta+93\right)-2^{6} x^{3}\left(13530\theta^4+35628\theta^3+50795\theta^2+36813\theta+10853\right)+2^{8} 3 x^{4}\left(38616\theta^4+128020\theta^3+206502\theta^2+165712\theta+53013\right)-2^{10} x^{5}\left(685404\theta^4+2714928\theta^3+4854121\theta^2+4193537\theta+1415126\right)+2^{13} x^{6}\left(1419108\theta^4+6542898\theta^3+12841310\theta^2+11823966\theta+4167463\right)-2^{14} x^{7}\left(8117226\theta^4+43045764\theta^3+92299521\theta^2+90336771\theta+33184985\right)+2^{16} x^{8}\left(15319683\theta^4+93106380\theta^3+218052374\theta^2+226725820\theta+86734943\right)-2^{19} 5^{2} x^{9}(2\theta+3)(171838\theta^3+939735\theta^2+1668155\theta+905358)+2^{22} 3 5^{4} 17^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 292, 5728, 115012, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...

Discriminant

\((12z-1)(18496z^3-2352z^2+84z-1)(16z-1)^2(400z^2-32z+1)^2\)

Local exponents

\(0\) ≈\(0.024764-0.009119I\) ≈\(0.024764+0.009119I\)\(\frac{ 1}{ 25}-\frac{ 3}{ 100}I\)\(\frac{ 1}{ 25}+\frac{ 3}{ 100}I\)\(\frac{ 1}{ 16}\) ≈\(0.077634\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(3\)

Note:

This is operator "10.7" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

18

New Number: 11.6 |  AESZ:  |  Superseeker: 95/102 1421/102  |  Hash: e79a3108441c74cdc23a53a603a6181e  

Degree: 11

\(2^{2} 3^{2} 17^{2} \theta^4-2 3 17 x\theta(116\theta^3+1414\theta^2+911\theta+204)-x^{2}\left(2596259\theta^4+9892670\theta^3+14508941\theta^2+9947652\theta+2663424\right)-3 x^{3}\left(8561767\theta^4+41744696\theta^3+79668236\theta^2+68977704\theta+22655832\right)-2^{2} x^{4}\left(28089475\theta^4+171762758\theta^3+396877187\theta^2+402013525\theta+149622901\right)-2 x^{5}\left(127339346\theta^4+963856934\theta^3+2636877099\theta^2+3042828449\theta+1247694978\right)-x^{6}\left(283337071\theta^4+2758627602\theta^3+9101625228\theta^2+11995897911\theta+5385015134\right)-2 x^{7}\left(43252385\theta^4+777895672\theta^3+3537873325\theta^2+5604936458\theta+2806067360\right)+2^{2} 3 x^{8}(\theta+1)(7613560\theta^3+27844427\theta^2-51849552\theta-134696600)+x^{9}(\theta+1)(\theta+2)(60585089\theta^2+495871401\theta+595115780)-2^{3} 3 5^{2} x^{10}(\theta+3)(\theta+2)(\theta+1)(10279\theta-113205)-2^{4} 5^{4} 7 97 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 16, 114, 1680, ...
--> OEIS
Normalized instanton numbers (n0=1): 95/102, 58/17, 1421/102, 1451/17, 31474/51, ... ; Common denominator:...

Discriminant

\(-(-1+7z+219z^2+1115z^3+1934z^4+679z^5)(z+1)^2(100z^2-197z-102)^2\)

Local exponents

\(-1\)\(\frac{ 197}{ 200}-\frac{ 1}{ 200}\sqrt{ 79609}\)\(0\)\(\frac{ 197}{ 200}+\frac{ 1}{ 200}\sqrt{ 79609}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 3}\)\(1\)\(0\)\(1\)\(1\)\(2\)
\(\frac{ 2}{ 3}\)\(3\)\(0\)\(3\)\(1\)\(3\)
\(1\)\(4\)\(0\)\(4\)\(2\)\(4\)

Note:

This is operator "11.6" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

19

New Number: 14.1 |  AESZ:  |  Superseeker: 0 0  |  Hash: a8cf56492aecc07971e82c9104785180  

Degree: 14

\(\theta^4-x\left(13\theta^4+14\theta^3+16\theta^2+9\theta+2\right)+x^{2}\left(33\theta^4-88\theta^3-265\theta^2-324\theta-148\right)+x^{3}\left(217\theta^4+2362\theta^3+6403\theta^2+8178\theta+4160\right)-2 x^{4}\left(677\theta^4+4134\theta^3+8089\theta^2+6210\theta+360\right)+2^{2} 3 x^{5}\left(151\theta^4-1266\theta^3-11610\theta^2-28955\theta-25110\right)+2^{2} x^{6}\left(1895\theta^4+37302\theta^3+176991\theta^2+355848\theta+268836\right)-2^{2} x^{7}\left(9635\theta^4+89170\theta^3+185885\theta^2-107394\theta-522464\right)+2^{3} x^{8}\left(5907\theta^4-10636\theta^3-416125\theta^2-1666326\theta-2051920\right)+2^{5} x^{9}\left(2947\theta^4+80284\theta^3+519934\theta^2+1328475\theta+1205150\right)-2^{6} x^{10}\left(6122\theta^4+84852\theta^3+397555\theta^2+722745\theta+356430\right)+2^{6} 3 x^{11}\left(2259\theta^4+13398\theta^3-46549\theta^2-456244\theta-796656\right)+2^{7} 3^{2} x^{12}(\theta+4)(371\theta^3+8580\theta^2+53325\theta+101564)-2^{10} 3^{3} x^{13}(\theta+4)(\theta+5)(51\theta^2+519\theta+1330)+2^{11} 3^{4} 5 x^{14}(\theta+4)(\theta+5)^2(\theta+6)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 16, 48, 264, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 1/4, 0, -1/2, 0, ... ; Common denominator:...

Discriminant

\((z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 6}-\frac{ 1}{ 6}\sqrt{ 5}I\)\(\frac{ 1}{ 6}\)\(\frac{ 1}{ 6}+\frac{ 1}{ 6}\sqrt{ 5}I\)\(\frac{ 1}{ 5}\)\(\frac{ 1}{ 4}\)\(\frac{ 1}{ 2}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(0\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(5\)
\(-1\)\(1\)\(1\)\(0\)\(3\)\(1\)\(3\)\(1\)\(1\)\(-1\)\(1\)\(5\)
\(1\)\(2\)\(2\)\(0\)\(4\)\(2\)\(4\)\(2\)\(2\)\(1\)\(2\)\(6\)

Note:

This is operator "14.1" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

20

New Number: 6.3 |  AESZ:  |  Superseeker: 178/7 129516/7  |  Hash: ec9e21dc2ccd3b4b4156ae1438454b96  

Degree: 6

\(7^{2} \theta^4-2 7 x\left(1488\theta^4+1452\theta^3+1125\theta^2+399\theta+56\right)+2^{2} x^{2}\left(766392\theta^4+1184952\theta^3+1010797\theta^2+454076\theta+83776\right)-2^{4} x^{3}\left(12943616\theta^4+28354200\theta^3+30710572\theta^2+16054731\theta+3215254\right)+2^{6} x^{4}\left(105973188\theta^4+333359304\theta^3+436182381\theta^2+261265857\theta+57189166\right)-2^{11} 127 x^{5}(\theta+1)(390972\theta^3+1350660\theta^2+1486781\theta+460439)+2^{14} 23^{2} 127^{2} x^{6}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 864, 80800, 9624160, ...
--> OEIS
Normalized instanton numbers (n0=1): 178/7, 3375/7, 129516/7, 6515900/7, 409239710/7, ... ; Common denominator:...

Discriminant

\((1-248z+8464z^2)(508z-7)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 31}{ 2116}-\frac{ 3}{ 529}\sqrt{ 3}\)\(\frac{ 7}{ 508}\)\(\frac{ 31}{ 2116}+\frac{ 3}{ 529}\sqrt{ 3}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 3}\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(\frac{ 2}{ 3}\)\(2\)
\(0\)\(2\)\(4\)\(2\)\(1\)\(\frac{ 5}{ 2}\)

Note:

This is operator "6.3" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

21

New Number: 8.19 |  AESZ: 201  |  Superseeker: 32 7584  |  Hash: d21570c07bca6887061716b2d727fa75  

Degree: 8

\(\theta^4-2^{4} x\left(13\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(9\theta^4+192\theta^3+249\theta^2+114\theta+20\right)+2^{12} x^{3}\left(379\theta^4+246\theta^3-569\theta^2-318\theta-60\right)-2^{16} x^{4}\left(749\theta^4+2560\theta^3-1722\theta^2-1862\theta-474\right)-2^{20} 13 x^{5}\left(251\theta^4-10\theta^3+262\theta^2+145\theta+27\right)+2^{24} 13 x^{6}\left(471\theta^4+96\theta^3+17\theta^2+96\theta+42\right)+2^{28} 13^{2} x^{7}\left(41\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-2^{35} 13^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 752, 49408, 3805456, ...
--> OEIS
Normalized instanton numbers (n0=1): 32, -152, 7584, -160593, 7055200, ... ; Common denominator:...

Discriminant

\(-(128z-1)(16z+1)(256z^2-96z+1)(-1+3328z^2)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 208}\sqrt{ 13}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\)\(\frac{ 1}{ 208}\sqrt{ 13}\)\(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(1\)

Note:

This operator has a second MUM-point, corresponding to operator 8.18

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

22

New Number: 8.27 |  AESZ: 302  |  Superseeker: 109/5 16777/5  |  Hash: e18ddbe4d66a3648b349130bcf119dc7  

Degree: 8

\(5^{2} \theta^4-5 x\left(1307\theta^4+1798\theta^3+1429\theta^2+530\theta+80\right)+2^{4} x^{2}\left(36361\theta^4+75163\theta^3+80666\theta^2+43340\theta+9120\right)-2^{6} x^{3}\left(434831\theta^4+949176\theta^3+966865\theta^2+545700\theta+118340\right)+2^{11} x^{4}\left(407863\theta^4+845480\theta^3+654048\theta^2+219839\theta+18634\right)-2^{16} x^{5}\left(245714\theta^4+474860\theta^3+365378\theta^2+71595\theta-11507\right)+2^{21} x^{6}\left(90362\theta^4+153828\theta^3+121478\theta^2+35967\theta+2221\right)-2^{26} 11 x^{7}\left(1517\theta^4+2932\theta^3+2087\theta^2+621\theta+59\right)-2^{31} 11^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 664, 41920, 3350776, ...
--> OEIS
Normalized instanton numbers (n0=1): 109/5, 867/4, 16777/5, 662976/5, 26339071/5, ... ; Common denominator:...

Discriminant

\(-(-1+143z+32z^2)(32z-1)^2(2816z^2-136z+5)^2\)

Local exponents

\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\)\(0\)\(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\)\(\frac{ 17}{ 704}-\frac{ 1}{ 704}\sqrt{ 591}I\)\(\frac{ 17}{ 704}+\frac{ 1}{ 704}\sqrt{ 591}I\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(4\)\(1\)\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.26

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

23

New Number: 8.56 |  AESZ:  |  Superseeker: 80 266256  |  Hash: b561c9f1501dce5c055c95391a2176d3  

Degree: 8

\(\theta^4-2^{4} x\left(34\theta^4+44\theta^3+31\theta^2+9\theta+1\right)+2^{9} x^{2}\left(94\theta^4-14\theta^3-168\theta^2-98\theta-19\right)-2^{12} x^{3}\left(368\theta^4-1104\theta^3-1505\theta^2-549\theta-60\right)+2^{16} x^{4}\left(28\theta^4-2740\theta^3-154\theta^2+928\theta+331\right)+2^{20} x^{5}\left(678\theta^4+1116\theta^3-2997\theta^2-2295\theta-505\right)-2^{26} x^{6}\left(94\theta^4-561\theta^3-508\theta^2-132\theta+6\right)-2^{28} 5 x^{7}\left(92\theta^4+160\theta^3+97\theta^2+17\theta-2\right)-2^{32} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 2512, 533248, 138259216, ...
--> OEIS
Normalized instanton numbers (n0=1): 80, 3554, 266256, 31532007, 4663446128, ... ; Common denominator:...

Discriminant

\(-(16z+1)(4096z^3+4864z^2+432z-1)(1-64z+1280z^2)^2\)

Local exponents

≈\(-1.090586\) ≈\(-0.099171\)\(-\frac{ 1}{ 16}\)\(0\) ≈\(0.002257\)\(\frac{ 1}{ 40}-\frac{ 1}{ 80}I\)\(\frac{ 1}{ 40}+\frac{ 1}{ 80}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)\(3\)\(1\)
\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)\(4\)\(1\)

Note:

This is operator "8.56" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

24

New Number: 8.64 |  AESZ:  |  Superseeker: 0 -32768  |  Hash: 00b5810e4a2d21fec464e4e87169df86  

Degree: 8

\(\theta^4-2^{4} x\left(32\theta^4+16\theta^3+14\theta^2+6\theta+1\right)+2^{10} x^{2}\left(86\theta^4+176\theta^3+184\theta^2+76\theta+13\right)-2^{16} x^{3}\left(61\theta^4+510\theta^3+620\theta^2+327\theta+68\right)-2^{22} x^{4}\left(110\theta^4-260\theta^3-942\theta^2-608\theta-141\right)+2^{26} x^{5}\left(708\theta^4+2160\theta^3-666\theta^2-1230\theta-397\right)+2^{32} x^{6}\left(134\theta^4-1536\theta^3-1488\theta^2-492\theta-29\right)-2^{38} 5 x^{7}\left(73\theta^4+170\theta^3+168\theta^2+83\theta+17\right)-2^{44} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 272, -15104, -2814704, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, -1116, -32768, -2011784, -92274688, ... ; Common denominator:...

Discriminant

\(-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2\)

Local exponents

≈\(-0.23168\)\(-\frac{ 1}{ 160}-\frac{ 1}{ 320}\sqrt{ 14}\)\(0\)\(-\frac{ 1}{ 160}+\frac{ 1}{ 320}\sqrt{ 14}\) ≈\(0.006465-0.004906I\) ≈\(0.006465+0.004906I\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

This is operator "8.64" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

25

New Number: 8.70 |  AESZ:  |  Superseeker: 32 8608  |  Hash: 664bcad4360eb63fde0fdd3018aed2f2  

Degree: 8

\(\theta^4-2^{4} x\left(19\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{9} x^{2}\left(61\theta^4+94\theta^3+89\theta^2+47\theta+10\right)-2^{14} x^{3}\left(134\theta^4+156\theta^3+37\theta^2+18\theta+6\right)+2^{19} x^{4}\left(192\theta^4+216\theta^3+58\theta^2-32\theta-17\right)-2^{24} x^{5}\left(191\theta^4+158\theta^3+183\theta^2+68\theta+6\right)+2^{29} x^{6}\left(125\theta^4+138\theta^3+135\theta^2+72\theta+16\right)-2^{35} x^{7}\left(20\theta^4+46\theta^3+47\theta^2+24\theta+5\right)+2^{41} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 848, 72448, 7745296, ...
--> OEIS
Normalized instanton numbers (n0=1): 32, 504, 8608, 475061, 28268384, ... ; Common denominator:...

Discriminant

\((16z-1)(32z-1)(1024z^2-192z+1)(1-32z+2048z^2)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\)\(\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 7}I\)\(\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 7}I\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

This is operator "8.70" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

26

New Number: 1.3 |  AESZ: 3  |  Superseeker: 32 26016  |  Hash: e7a9c334fb603aceccc0517dab63e7d4  

Degree: 1

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1296, 160000, 24010000, ...
--> OEIS
Normalized instanton numbers (n0=1): 32, 608, 26016, 1606496, 122373984, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

A-incarnation: X(2,2,2,2) in P^7.

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

27

New Number: 8.88 |  AESZ:  |  Superseeker: 571/15 394769/15  |  Hash: 96ea6b0b71373481f874100af7f89d67  

Degree: 8

\(3^{2} 5^{2} \theta^4-3 5 x\left(4063\theta^4+7682\theta^3+5731\theta^2+1890\theta+240\right)+2 x^{2}\left(605228\theta^4+1651274\theta^3+1743713\theta^2+827790\theta+149520\right)-2^{2} x^{3}\left(122453\theta^4+9232248\theta^3+20066474\theta^2+11895930\theta+2347980\right)-2^{3} x^{4}\left(14154736\theta^4-3374404\theta^3-69996921\theta^2-57156850\theta-13566428\right)+2^{4} x^{5}\left(30476536\theta^4+168961384\theta^3-11782973\theta^2-90041748\theta-28710648\right)+2^{6} 23 x^{6}\left(1194624\theta^4-7988712\theta^3-9497764\theta^2-3726021\theta-451296\right)-2^{8} 7 23^{2} x^{7}(2\theta+1)(8454\theta^3+5577\theta^2-4303\theta-3155)+2^{10} 7^{2} 23^{3} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1224, 146320, 21334600, ...
--> OEIS
Normalized instanton numbers (n0=1): 571/15, 3038/5, 394769/15, 23541584/15, 352406944/3, ... ; Common denominator:...

Discriminant

\((1-261z+2952z^2-12368z^3+23552z^4)(-15+74z+1288z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_3\)\(s_2\)\(s_5\)\(s_4\)\(s_6\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(3\)\(1\)\(3\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(4\)\(2\)\(4\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "8.88" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex