Summary

You searched for: Spectrum0=1,1,1,1

Your search produced 113 matches
 1-30  31-60  61-90  91-113 

You can download all data as plain text or as JSON

1

New Number: 5.104 |  AESZ: 357  |  Superseeker: 7/13 21/13  |  Hash: afee0651c9b3b8e98079f5c2d5bfa8a5  

Degree: 5

\(13^{2} \theta^4-13 x\left(441\theta^4+690\theta^3+631\theta^2+286\theta+52\right)+2^{4} x^{2}\left(5121\theta^4+15576\theta^3+21215\theta^2+13702\theta+3445\right)-2^{10} x^{3}\left(640\theta^4+2847\theta^3+5078\theta^2+4056\theta+1196\right)+2^{14} x^{4}\left(125\theta^4+562\theta^3+905\theta^2+624\theta+157\right)-2^{21} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 20, 112, 916, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/13, -10/13, 21/13, 296/13, 608/13, ... ; Common denominator:...

Discriminant

\(-(16z-1)(128z^2-13z+1)(-13+32z)^2\)

Local exponents

\(0\)\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 1}{ 16}\)\(\frac{ 13}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 358/5.105

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

2

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  

3

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  

4

New Number: 5.15 |  AESZ: 117  |  Superseeker: -52/3 -17428  |  Hash: 111a4ce3248a309bf6283916fd9f11c4  

Degree: 5

\(3^{2} \theta^4+2^{2} 3 x\left(256\theta^4+176\theta^3+133\theta^2+45\theta+6\right)+2^{7} x^{2}\left(2588\theta^4+1952\theta^3+584\theta^2+15\theta-15\right)+2^{12} x^{3}\left(3183\theta^4+2466\theta^3+1801\theta^2+711\theta+111\right)+2^{17} 7 x^{4}\left(134\theta^4+250\theta^3+180\theta^2+55\theta+5\right)-2^{22} 7^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 424, -36224, 3778216, ...
--> OEIS
Normalized instanton numbers (n0=1): -52/3, 1348/3, -17428, 884000, -163422880/3, ... ; Common denominator:...

Discriminant

\(-(16z+1)(256z^2-176z-1)(3+224z)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 3}{ 224}\)\(\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}\)\(0\)\(\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 212/5.31

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

5

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  

6

New Number: 5.18 |  AESZ: 124  |  Superseeker: 163/61 4795/61  |  Hash: 394b401a3162e31c79ede5b46973791d  

Degree: 5

\(61^{2} \theta^4-61 x\left(3029\theta^4+5572\theta^3+4677\theta^2+1891\theta+305\right)+x^{2}\left(1215215\theta^4+3428132\theta^3+4267228\theta^2+2572675\theta+611586\right)-3^{4} x^{3}\left(39370\theta^4+140178\theta^3+206807\theta^2+142191\theta+37332\right)+3^{8} x^{4}\left(566\theta^4+2230\theta^3+3356\theta^2+2241\theta+558\right)-3^{13} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 69, 1427, 35749, ...
--> OEIS
Normalized instanton numbers (n0=1): 163/61, 630/61, 4795/61, 48422/61, 599809/61, ... ; Common denominator:...

Discriminant

\(-(243z^3-200z^2+47z-1)(-61+81z)^2\)

Local exponents

\(0\) ≈\(0.023574\) ≈\(0.399736-0.121575I\) ≈\(0.399736+0.121575I\)\(\frac{ 61}{ 81}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This is operator "5.18" from ...

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

7

New Number: 5.1 |  AESZ: 17  |  Superseeker: 6/5 118/5  |  Hash: 370d10edbf5900002f79cf6163e106a5  

Degree: 5

\(5^{2} \theta^4-3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2 3 x^{2}\left(531\theta^4+828\theta^3+541\theta^2+155\theta+15\right)-2 3^{3} x^{3}\left(423\theta^4+2160\theta^3+4399\theta^2+3795\theta+1170\right)+3^{5} x^{4}\left(279\theta^4+1368\theta^3+2270\theta^2+1586\theta+402\right)-3^{10} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 3, 27, 381, 6219, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/5, 39/10, 118/5, 1443/10, 6108/5, ... ; Common denominator:...

Discriminant

\(-(27z-1)(27z^2+1)(-5+9z)^2\)

Local exponents

\(0-\frac{ 1}{ 9}\sqrt{ 3}I\)\(0\)\(0+\frac{ 1}{ 9}\sqrt{ 3}I\)\(\frac{ 1}{ 27}\)\(\frac{ 5}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 290/5.71
A-Incarnation: diagonal subfamily 1,1,1-section in $P^2 \times P^2 \times P^2$

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

8

New Number: 5.20 |  AESZ: 186  |  Superseeker: 49/19 1761/19  |  Hash: b3d164f22d02de1efcd62d3aa9ab5ce4  

Degree: 5

\(19^{2} \theta^4-19 x\left(700\theta^4+1238\theta^3+999\theta^2+380\theta+57\right)-x^{2}\left(64745\theta^4+368006\theta^3+609133\theta^2+412756\theta+102258\right)+3^{3} x^{3}\left(6397\theta^4+12198\theta^3-11923\theta^2-27360\theta-11286\right)+3^{6} x^{4}\left(64\theta^4+1154\theta^3+2425\theta^2+1848\theta+486\right)-3^{11} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 3, 51, 1029, 25299, ...
--> OEIS
Normalized instanton numbers (n0=1): 49/19, 252/19, 1761/19, 18990/19, 246159/19, ... ; Common denominator:...

Discriminant

\(-(z+1)(243z^2+35z-1)(-19+27z)^2\)

Local exponents

\(-1\)\(-\frac{ 35}{ 486}-\frac{ 13}{ 486}\sqrt{ 13}\)\(0\)\(-\frac{ 35}{ 486}+\frac{ 13}{ 486}\sqrt{ 13}\)\(\frac{ 19}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 187/5.21

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

9

New Number: 5.21 |  AESZ: 187  |  Superseeker: -107 -121311  |  Hash: 9a367922f464a13fa56d1c2e238faa34  

Degree: 5

\(\theta^4-x\left(64\theta^4-898\theta^3-653\theta^2-204\theta-27\right)-3^{2} x^{2}\left(6397\theta^4+13390\theta^3-10135\theta^2-7492\theta-1650\right)+3^{4} x^{3}\left(64745\theta^4-109026\theta^3-106415\theta^2-39528\theta-4626\right)+3^{9} 19 x^{4}\left(700\theta^4+1562\theta^3+1485\theta^2+704\theta+138\right)-3^{14} 19^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -27, 1971, -220941, 30762099, ...
--> OEIS
Normalized instanton numbers (n0=1): -107, -7701/4, -121311, -6204874, -518204863, ... ; Common denominator:...

Discriminant

\(-(243z+1)(243z^2-35z-1)(-1+171z)^2\)

Local exponents

\(\frac{ 35}{ 486}-\frac{ 13}{ 486}\sqrt{ 13}\)\(-\frac{ 1}{ 243}\)\(0\)\(\frac{ 1}{ 171}\)\(\frac{ 35}{ 486}+\frac{ 13}{ 486}\sqrt{ 13}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 186/ 5.20

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

10

New Number: 5.22 |  AESZ: 193  |  Superseeker: 129/7 41441/7  |  Hash: 44e6fc2823d5ff31e66059ba6b37f2ae  

Degree: 5

\(7^{2} \theta^4-7 x\left(1135\theta^4+2204\theta^3+1683\theta^2+581\theta+77\right)+x^{2}\left(28723\theta^4+40708\theta^3+13260\theta^2-1337\theta-896\right)-x^{3}\left(32126\theta^4+38514\theta^3+26511\theta^2+10731\theta+1806\right)+7 11 x^{4}\left(130\theta^4+254\theta^3+192\theta^2+65\theta+8\right)+11^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 11, 559, 42923, 3996751, ...
--> OEIS
Normalized instanton numbers (n0=1): 129/7, 1557/7, 41441/7, 1594332/7, 75470601/7, ... ; Common denominator:...

Discriminant

\((z^3+84z^2-159z+1)(-7+11z)^2\)

Local exponents

≈\(-85.852157\)\(0\) ≈\(0.00631\)\(\frac{ 7}{ 11}\) ≈\(1.845846\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 198/5.25

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

11

New Number: 5.23 |  AESZ: 194  |  Superseeker: 126/17 11700/17  |  Hash: 6bf19665aa6705f30ef88df42bc4eac4  

Degree: 5

\(17^{2} \theta^4-17 x\left(1465\theta^4+2768\theta^3+2200\theta^2+816\theta+119\right)+2 x^{2}\left(62015\theta^4+131582\theta^3+125017\theta^2+65926\theta+15300\right)-2 3^{3} x^{3}\left(4325\theta^4+10914\theta^3+12803\theta^2+7446\theta+1700\right)+3^{6} x^{4}\left(265\theta^4+836\theta^3+1118\theta^2+700\theta+168\right)-3^{10} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 7, 183, 7225, 345079, ...
--> OEIS
Normalized instanton numbers (n0=1): 126/17, 848/17, 11700/17, 229808/17, 5539258/17, ... ; Common denominator:...

Discriminant

\(-(-1+81z)(27z-17)^2(z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 17}{ 27}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(2\)\(4\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 199/5.26

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

12

New Number: 5.25 |  AESZ: 198  |  Superseeker: -84/11 -9052/11  |  Hash: a1f924763b047c2720d99cfca5ca63db  

Degree: 5

\(11^{2} \theta^4+7 11 x\left(130\theta^4+266\theta^3+210\theta^2+77\theta+11\right)-x^{2}\left(11198+55253\theta+103725\theta^2+89990\theta^3+32126\theta^4\right)+x^{3}\left(1716+20625\theta+63474\theta^2+74184\theta^3+28723\theta^4\right)-7 x^{4}\left(1135\theta^4+2336\theta^3+1881\theta^2+713\theta+110\right)+7^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -7, 199, -8359, 423751, ...
--> OEIS
Normalized instanton numbers (n0=1): -84/11, 639/11, -9052/11, 189021/11, -4838013/11, ... ; Common denominator:...

Discriminant

\((z^3-159z^2+84z+1)(-11+7z)^2\)

Local exponents

≈\(-0.011648\)\(0\) ≈\(0.541757\)\(\frac{ 11}{ 7}\) ≈\(158.469891\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 193/5.22

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

13

New Number: 5.26 |  AESZ: 199  |  Superseeker: -2 3820/9  |  Hash: f7b5c9e3ad50b0885d03c98d07a051f1  

Degree: 5

\(\theta^4-x\left(15+88\theta+200\theta^2+224\theta^3+265\theta^4\right)+2 3 x^{2}\left(4325\theta^4+6386\theta^3+6011\theta^2+2718\theta+468\right)-2 3^{2} x^{3}\left(62015\theta^4+116478\theta^3+102361\theta^2+37422\theta+4824\right)+3^{6} 17 x^{4}\left(1465\theta^4+3092\theta^3+2686\theta^2+1140\theta+200\right)-3^{10} 17^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 15, 567, 28113, 1584279, ...
--> OEIS
Normalized instanton numbers (n0=1): -2, 28, 3820/9, 3924, 21606, ... ; Common denominator:...

Discriminant

\(-(z-1)(81z-1)^2(51z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 1}{ 51}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)
\(0\)\(\frac{ 1}{ 2}\)\(3\)\(1\)\(1\)
\(0\)\(1\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 194/5.23.

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

14

New Number: 5.27 |  AESZ: 202  |  Superseeker: -113/19 -8515/19  |  Hash: 3bf3c283277de7b3808ad309fac9b7a1  

Degree: 5

\(19^{2} \theta^4+19 x\left(1370\theta^4+2620\theta^3+2089\theta^2+779\theta+114\right)+x^{2}\left(39521\theta^4-3916\theta^3-106779\theta^2-95266\theta-25384\right)-2^{3} x^{3}\left(1649\theta^4+19779\theta^3+29667\theta^2+17613\theta+3876\right)-2^{4} 5 x^{4}(\theta+1)(499\theta^3+1411\theta^2+1378\theta+456)-2^{9} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 142, -4920, 205326, ...
--> OEIS
Normalized instanton numbers (n0=1): -113/19, 2921/76, -8515/19, 146869/19, -3105422/19, ... ; Common denominator:...

Discriminant

\(-(z-1)(32z^2+71z+1)(19+20z)^2\)

Local exponents

\(-\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\)\(-\frac{ 19}{ 20}\)\(-\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\)\(0\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 203/5.28

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

15

New Number: 5.28 |  AESZ: 203  |  Superseeker: -13/5 -6729/5  |  Hash: dfab012366b4bc6f7af83dc79f28b802  

Degree: 5

\(5^{2} \theta^4+5 x\theta(499\theta^3+86\theta^2+53\theta+10)+2^{4} x^{2}\left(1649\theta^4-13183\theta^3-19776\theta^2-11020\theta-2200\right)-2^{6} x^{3}\left(39521\theta^4+162000\theta^3+142095\theta^2+51540\theta+6540\right)-2^{11} 19 x^{4}\left(1370\theta^4+2860\theta^3+2449\theta^2+1019\theta+174\right)-2^{16} 19^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 88, -1728, 99576, ...
--> OEIS
Normalized instanton numbers (n0=1): -13/5, 427/5, -6729/5, 173044/5, -952275, ... ; Common denominator:...

Discriminant

\(-(32z-1)(32z^2+71z+1)(5+152z)^2\)

Local exponents

\(-\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\)\(-\frac{ 5}{ 152}\)\(-\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\)\(0\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 202 /5.27

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

16

New Number: 5.31 |  AESZ: 212  |  Superseeker: -20/7 -104  |  Hash: f72aa947ba945355102b3fef56e0af0f  

Degree: 5

\(7^{2} \theta^4+2 7 x\left(134\theta^4+286\theta^3+234\theta^2+91\theta+14\right)-2^{2} x^{2}\left(3183\theta^4+10266\theta^3+13501\theta^2+8225\theta+1918\right)+2^{3} x^{3}\left(2588\theta^4+8400\theta^3+10256\theta^2+5649\theta+1190\right)-2^{4} 3 x^{4}\left(256\theta^4+848\theta^3+1141\theta^2+717\theta+174\right)+2^{8} 3^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 64, -1408, 37216, ...
--> OEIS
Normalized instanton numbers (n0=1): -20/7, 57/4, -104, 16385/14, -110508/7, ... ; Common denominator:...

Discriminant

\((4z-1)(16z^2-44z-1)(6z-7)^2\)

Local exponents

\(\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\)\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 7}{ 6}\)\(\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point corresponding to Operator AESZ 117 /5.515.

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

17

New Number: 5.46 |  AESZ: 243  |  Superseeker: -42 -41706  |  Hash: 93c30005b5a976a2b7c5206d5e679a45  

Degree: 5

\(\theta^4+x\left(295\theta^4+572\theta^3+424\theta^2+138\theta+17\right)+2 x^{2}\left(843\theta^4+744\theta^3-473\theta^2-481\theta-101\right)+2 x^{3}\left(1129\theta^4-516\theta^3-725\theta^2-159\theta+4\right)-3 x^{4}\left(173\theta^4+352\theta^3+290\theta^2+114\theta+18\right)-3^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -17, 1549, -215585, 36505501, ...
--> OEIS
Normalized instanton numbers (n0=1): -42, 875, -41706, 2954224, -257813864, ... ; Common denominator:...

Discriminant

\(-(z^3+57z^2-289z-1)(3z+1)^2\)

Local exponents

≈\(-61.684843\)\(-\frac{ 1}{ 3}\) ≈\(-0.003458\)\(0\) ≈\(4.688301\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

A-incarnation: $7 \times 7$ linear Pfaffian in $P^7$.
There is a second MUM point at infinity, associated to
the 7 fold linear section of $G(2,7)$ AESZ 27/5.7

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

18

New Number: 5.47 |  AESZ: 246  |  Superseeker: -4/5 -108/5  |  Hash: f51a0c39f9179dc6a561b9afb6f9d85f  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(12\theta^4+48\theta^3+49\theta^2+25\theta+5\right)-2^{4} x^{2}\left(544\theta^4+1792\theta^3+2444\theta^2+1580\theta+405\right)+2^{9} x^{3}\left(112\theta^4+960\theta^3+2306\theta^2+2130\theta+685\right)+2^{12} x^{4}\left(144\theta^4+768\theta^3+1308\theta^2+924\theta+235\right)+2^{20} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 44, 400, 5356, ...
--> OEIS
Normalized instanton numbers (n0=1): -4/5, 22/5, -108/5, 694/5, -1040, ... ; Common denominator:...

Discriminant

\((1+16z)(16z+5)^2(16z-1)^2\)

Local exponents

\(-\frac{ 5}{ 16}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(3\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(4\)\(2\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 247/5.48

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

19

New Number: 5.48 |  AESZ: 247  |  Superseeker: 608 22293216  |  Hash: 6c0503129f3500c26cf001c1908a17f7  

Degree: 5

\(\theta^4+2^{4} x\left(144\theta^4-192\theta^3-132\theta^2-36\theta-5\right)+2^{13} x^{2}\left(112\theta^4-512\theta^3+98\theta^2+50\theta+13\right)-2^{20} x^{3}\left(544\theta^4+384\theta^3+332\theta^2+108\theta+21\right)-2^{30} 5 x^{4}\left(12\theta^4-23\theta^2-23\theta-7\right)+2^{40} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 80, 11024, 1850624, 343952656, ...
--> OEIS
Normalized instanton numbers (n0=1): 608, -85544, 22293216, -7629059800, 3042437418016, ... ; Common denominator:...

Discriminant

\((1+256z)(1280z+1)^2(256z-1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 1280}\)\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(2\)\(4\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operaor AESZ 246/ 5.47

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

20

New Number: 5.4 |  AESZ: 21  |  Superseeker: 8/5 152/5  |  Hash: 42a2bc0f0ee2a405ede956176c95721f  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(36\theta^4+84\theta^3+72\theta^2+30\theta+5\right)-2^{4} x^{2}\left(181\theta^4+268\theta^3+71\theta^2-70\theta-35\right)+2^{8} x^{3}(\theta+1)(37\theta^3+248\theta^2+375\theta+165)+2^{10} x^{4}\left(39\theta^4+198\theta^3+331\theta^2+232\theta+59\right)+2^{15} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 44, 688, 13036, ...
--> OEIS
Normalized instanton numbers (n0=1): 8/5, 57/10, 152/5, 253, 11552/5, ... ; Common denominator:...

Discriminant

\((4z+1)(32z-1)(4z-1)(8z+5)^2\)

Local exponents

\(-\frac{ 5}{ 8}\)\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 71/5.11

A-Incarnation: (2,0),(02),(1,1),(1,1),(1,1) intersection in $P^4 \times P^4$

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

21

New Number: 5.56 |  AESZ: 262  |  Superseeker: -28/5 -1268/5  |  Hash: 4899f97226a5ec3b1ded2994470e9fdc  

Degree: 5

\(5^{2} \theta^4+2^{2} 5 x\left(136\theta^4+224\theta^3+197\theta^2+85\theta+15\right)+2^{4} x^{2}\left(5584\theta^4+16192\theta^3+21924\theta^2+14800\theta+3955\right)+2^{11} x^{3}\left(608\theta^4+2280\theta^3+3642\theta^2+2745\theta+780\right)+2^{14} x^{4}\left(464\theta^4+1888\theta^3+2956\theta^2+2012\theta+501\right)+2^{24} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 236, -6384, 217836, ...
--> OEIS
Normalized instanton numbers (n0=1): -28/5, 153/5, -1268/5, 18598/5, -320048/5, ... ; Common denominator:...

Discriminant

\((1+64z)(32z+5)^2(16z+1)^2\)

Local exponents

\(-\frac{ 5}{ 32}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(0\)\(1\)
\(3\)\(1\)\(1\)\(0\)\(1\)
\(4\)\(1\)\(2\)\(0\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to the Operator AESZ 263/5.57

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

22

New Number: 5.57 |  AESZ: 263  |  Superseeker: 1312 58156704  |  Hash: 2157fe92de97f7b684b3cbd7b8bdf280  

Degree: 5

\(\theta^4+2^{4} x\left(464\theta^4-32\theta^3+76\theta^2+92\theta+21\right)+2^{15} x^{2}\left(608\theta^4+152\theta^3+450\theta^2+131\theta+5\right)+2^{22} x^{3}\left(5584\theta^4+6144\theta^3+6852\theta^2+2808\theta+471\right)+2^{34} 5 x^{4}\left(136\theta^4+320\theta^3+341\theta^2+181\theta+39\right)+2^{46} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -336, 198416, -142318848, 112152177936, ...
--> OEIS
Normalized instanton numbers (n0=1): 1312, -211968, 58156704, -19819112104, 7519377878624, ... ; Common denominator:...

Discriminant

\((1+256z)(1024z+1)^2(2560z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 1024}\)\(-\frac{ 1}{ 2560}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)
\(2\)\(1\)\(4\)\(0\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 262/5.56

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

23

New Number: 5.58 |  AESZ: 266  |  Superseeker: -18/5 -642/5  |  Hash: 5d46913a13c5fa5fa6a547d8b5646133  

Degree: 5

\(5^{2} \theta^4-3 5 x\left(27\theta^4+108\theta^3+124\theta^2+70\theta+15\right)-2 3^{2} x^{2}\left(1377\theta^4+4536\theta^3+6507\theta^2+4455\theta+1220\right)+2 3^{5} x^{3}\left(567\theta^4+4860\theta^3+11583\theta^2+10665\theta+3445\right)+3^{8} x^{4}\left(729\theta^4+3888\theta^3+6606\theta^2+4662\theta+1184\right)+3^{15} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 171, 3087, 69579, ...
--> OEIS
Normalized instanton numbers (n0=1): -18/5, 117/10, -642/5, 1197, -76788/5, ... ; Common denominator:...

Discriminant

\((1+27z)(27z+5)^2(27z-1)^2\)

Local exponents

\(-\frac{ 5}{ 27}\)\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(0\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 267/5.59

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

24

New Number: 5.59 |  AESZ: 267  |  Superseeker: 1818 467810538  |  Hash: 924287a9ba8517571071ec73d860af7e  

Degree: 5

\(\theta^4+3^{2} x\left(729\theta^4-972\theta^3-684\theta^2-198\theta-31\right)+2 3^{8} x^{2}\left(567\theta^4-2592\theta^3+405\theta^2+189\theta+70\right)-2 3^{14} x^{3}\left(1377\theta^4+972\theta^3+1161\theta^2+459\theta+113\right)-3^{22} 5 x^{4}\left(27\theta^4-38\theta^2-38\theta-12\right)+3^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 279, 124011, 64869777, 36848978379, ...
--> OEIS
Normalized instanton numbers (n0=1): 1818, -681336, 467810538, -422903176767, 446062311232740, ... ; Common denominator:...

Discriminant

\((1+729z)(3645z+1)^2(729z-1)^2\)

Local exponents

\(-\frac{ 1}{ 729}\)\(-\frac{ 1}{ 3645}\)\(0\)\(\frac{ 1}{ 729}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(0\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 266/5.58

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

25

New Number: 5.5 |  AESZ: 22  |  Superseeker: 10/7 295/7  |  Hash: 5b96eae0872756be1130d4b12ffe60a6  

Degree: 5

\(7^{2} \theta^4-7 x\left(155\theta^4+286\theta^3+234\theta^2+91\theta+14\right)-x^{2}\left(16105\theta^4+68044\theta^3+102261\theta^2+66094\theta+15736\right)+2^{3} x^{3}\left(2625\theta^4+8589\theta^3+9071\theta^2+3759\theta+476\right)-2^{4} x^{4}\left(465\theta^4+1266\theta^3+1439\theta^2+806\theta+184\right)+2^{9} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 34, 488, 9826, ...
--> OEIS
Normalized instanton numbers (n0=1): 10/7, 65/7, 295/7, 3065/7, 4245, ... ; Common denominator:...

Discriminant

\((32z-1)(z^2-11z-1)(4z-7)^2\)

Local exponents

\(\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\)\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 7}{ 4}\)\(\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 118/5.16
A-Incarnation: five (1,1) sections in ${\bf P}^4 \times {\bf P}^4$.Quotient by ${\bf Z}/2$ of this:
the Reye congruence Calabi-Yau threefold.

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

26

New Number: 5.60 |  AESZ: 268  |  Superseeker: -828/5 -4270932/5  |  Hash: 638e2881183378c7a47b7508d9acc072  

Degree: 5

\(5^{2} \theta^4-2^{2} 3 5 x\left(108\theta^4+432\theta^3+661\theta^2+445\theta+105\right)-2^{4} 3^{2} x^{2}\left(44064\theta^4+145152\theta^3+239004\theta^2+186300\theta+58045\right)+2^{9} 3^{5} x^{3}\left(9072\theta^4+77760\theta^3+180954\theta^2+164970\theta+53965\right)+2^{12} 3^{8} x^{4}\left(11664\theta^4+62208\theta^3+104940\theta^2+73836\theta+18659\right)+2^{20} 3^{15} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 252, 87084, 31502448, 12121584876, ...
--> OEIS
Normalized instanton numbers (n0=1): -828/5, 25533/5, -4270932/5, 598304142/5, -24767201520, ... ; Common denominator:...

Discriminant

\((1+432z)(432z+5)^2(432z-1)^2\)

Local exponents

\(-\frac{ 5}{ 432}\)\(-\frac{ 1}{ 432}\)\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(\frac{ 3}{ 2}\)\(1\)

Note:

There is a second MUM-point at infinity, correspondint to
Operator AESZ 269/5.61

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

27

New Number: 5.61 |  AESZ: 269  |  Superseeker: 549216 5134247872650720  |  Hash: f6285c6dd849b8edc6913a248c74c2ac  

Degree: 5

\(\theta^4+2^{4} 3^{2} x\left(11664\theta^4-15552\theta^3-11700\theta^2-3924\theta-781\right)+2^{13} 3^{8} x^{2}\left(9072\theta^4-41472\theta^3+2106\theta^2-54\theta+1261\right)-2^{20} 3^{14} x^{3}\left(44064\theta^4+31104\theta^3+67932\theta^2+32508\theta+9661\right)-2^{30} 3^{22} 5 x^{4}\left(108\theta^4+13\theta^2+13\theta-3\right)+2^{40} 3^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 112464, 16304096016, 2572332025515264, 423329707157060783376, ...
--> OEIS
Normalized instanton numbers (n0=1): 549216, -39437661960, 5134247872650720, -893529522332436373560, 182442495912657901797814560, ... ; Common denominator:...

Discriminant

\((1+186624z)(933120z+1)^2(186624z-1)^2\)

Local exponents

\(-\frac{ 1}{ 186624}\)\(-\frac{ 1}{ 933120}\)\(0\)\(\frac{ 1}{ 186624}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(\frac{ 3}{ 2}\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 268/5.60

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

28

New Number: 5.62 |  AESZ: 270  |  Superseeker: -76/5 -2100  |  Hash: 256e3b3a92e3fd332be8b01f71853ea4  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(48\theta^4+192\theta^3+251\theta^2+155\theta+35\right)-2^{4} x^{2}\left(8704\theta^4+28672\theta^3+43664\theta^2+31760\theta+9265\right)+2^{11} x^{3}\left(1792\theta^4+15360\theta^3+36248\theta^2+33240\theta+10795\right)+2^{16} x^{4}\left(2304\theta^4+12288\theta^3+20816\theta^2+14672\theta+3719\right)+2^{30} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 28, 1324, 63856, 3489004, ...
--> OEIS
Normalized instanton numbers (n0=1): -76/5, 367/5, -2100, 43436, -6582256/5, ... ; Common denominator:...

Discriminant

\((1+64z)(64z+5)^2(64z-1)^2\)

Local exponents

\(-\frac{ 5}{ 64}\)\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 4}\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(\frac{ 5}{ 4}\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 271/ 5.63

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

29

New Number: 5.63 |  AESZ: 271  |  Superseeker: 10912 71557619232  |  Hash: c20fda7ad02ecc06f9b3f74bf4327d05  

Degree: 5

\(\theta^4+2^{4} x\left(2304\theta^4-3072\theta^3-2224\theta^2-688\theta-121\right)+2^{17} x^{2}\left(1792\theta^4-8192\theta^3+920\theta^2+344\theta+235\right)-2^{28} x^{3}\left(8704\theta^4+6144\theta^3+9872\theta^2+4368\theta+1201\right)-2^{44} 5 x^{4}\left(48\theta^4-37\theta^2-37\theta-13\right)+2^{60} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1936, 5433616, 17299986688, 58672579116304, ...
--> OEIS
Normalized instanton numbers (n0=1): 10912, -20731504, 71557619232, -326717237089712, 1743820693922321120, ... ; Common denominator:...

Discriminant

\((1+4096z)(20480z+1)^2(4096z-1)^2\)

Local exponents

\(-\frac{ 1}{ 4096}\)\(-\frac{ 1}{ 20480}\)\(0\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 4}\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(\frac{ 5}{ 4}\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 270 /5.62

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

30

New Number: 5.68 |  AESZ: 279  |  Superseeker: -10/17 10  |  Hash: 06f80606fbeb2b0cc9559df633f1f59d  

Degree: 5

\(17^{2} \theta^4+17 x\left(286\theta^4+734\theta^3+656\theta^2+289\theta+51\right)+3^{2} x^{2}\left(4110\theta^4+22074\theta^3+37209\theta^2+26265\theta+6800\right)-3^{5} x^{3}\left(1521\theta^4+7344\theta^3+12936\theta^2+9945\theta+2822\right)+3^{8} x^{4}\left(123\theta^4+552\theta^3+879\theta^2+603\theta+152\right)-3^{12} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -3, 9, 51, -1431, ...
--> OEIS
Normalized instanton numbers (n0=1): -10/17, -19/17, 10, -369/17, -1413/17, ... ; Common denominator:...

Discriminant

\(-(729z^3-189z^2-20z-1)(-17+27z)^2\)

Local exponents

≈\(-0.044921-0.04372I\) ≈\(-0.044921+0.04372I\)\(0\) ≈\(0.349102\)\(\frac{ 17}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 280/5.69

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


 1-30  31-60  61-90  91-113