Summary

You searched for: dim_h=9

Your search produced 10 matches

You can download all data as plain text or as JSON

1

New Number: 2.10 |  AESZ: 70  |  Superseeker: 27 18089  |  Hash: 3d2adae6eaf26a56c76b8b67d92cc5df  

Degree: 2

\(\theta^4-3 x(3\theta+1)(3\theta+2)(10\theta^2+10\theta+3)+3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1350, 156240, 22141350, ...
--> OEIS
Normalized instanton numbers (n0=1): 27, 432, 18089, 997785, 68438142, ... ; Common denominator:...

Discriminant

\((243z-1)(27z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 243}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast c$.

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

2

New Number: 2.16 |  AESZ: 65  |  Superseeker: 240 19105840  |  Hash: 13ba368bcbb10731ac8727b510731ff2  

Degree: 2

\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{9} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 277200, 457416960, 904864680720, ...
--> OEIS
Normalized instanton numbers (n0=1): 240, 57102, 19105840, 14810143935, 10017820614480, ... ; Common denominator:...

Discriminant

\((3456z-1)(1728z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3456}\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*d

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

3

New Number: 2.2 |  AESZ: 15  |  Superseeker: 21 15894  |  Hash: c8053e0e9c05ef468263fafd5e3fc764  

Degree: 2

\(\theta^4-3 x(3\theta+1)(3\theta+2)(7\theta^2+7\theta+2)-2^{3} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ...
--> OEIS
Normalized instanton numbers (n0=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...

Discriminant

\(-(27z+1)(216z-1)\)

Local exponents

\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 216}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(2\)\(0\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast a$.

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

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

4

New Number: 2.5 |  AESZ: 25  |  Superseeker: 20 8220  |  Hash: 93279abcbeeade30c29508de7784e582  

Degree: 2

\(\theta^4-2^{2} x(2\theta+1)^2(11\theta^2+11\theta+3)-2^{4} x^{2}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 684, 58800, 6129900, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 277, 8220, 352994, 18651536, ... ; Common denominator:...

Discriminant

\(1-176z-256z^2\)

Local exponents

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

Note:

Hadamard product $A\ast b$

A-incarnation: X(1,2,2) in G(2,5)

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

5

New Number: 4.42 |  AESZ: 222  |  Superseeker: 69/5 29081/5  |  Hash: aad7a72e711c9c463396d319e0bf7603  

Degree: 4

\(5^{2} \theta^4-5 x\left(407\theta^4+1198\theta^3+909\theta^2+310\theta+40\right)-2^{7} x^{2}\left(2103\theta^4+6999\theta^3+8358\theta^2+4050\theta+680\right)-2^{12} x^{3}\left(1387\theta^4+3840\theta^3+3081\theta^2+960\theta+100\right)-2^{21} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 504, 36800, 3518200, ...
--> OEIS
Normalized instanton numbers (n0=1): 69/5, 1383/4, 29081/5, 346080, 72023607/5, ... ; Common denominator:...

Discriminant

\(-(8192z^2+107z-1)(5+64z)^2\)

Local exponents

\(-\frac{ 5}{ 64}\)\(-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43

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

6

New Number: 5.12 |  AESZ: 74  |  Superseeker: -30 -14632  |  Hash: e668180adb7c88d4e5fbab5eb7ee61c7  

Degree: 5

\(\theta^4-2 3 x\left(99\theta^4+36\theta^3+39\theta^2+21\theta+4\right)+2^{2} 3^{2} x^{2}\left(3807\theta^4+3564\theta^3+3798\theta^2+1683\theta+284\right)-2^{3} 3^{5} x^{3}\left(7857\theta^4+13608\theta^3+14562\theta^2+7317\theta+1444\right)+2^{4} 3^{9} x^{4}\left(2592\theta^4+7128\theta^3+8550\theta^2+4851\theta+1052\right)-2^{5} 3^{13} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1152, 71520, 5101200, ...
--> OEIS
Normalized instanton numbers (n0=1): -30, -516, -14632, -4227807/8, -22139868, ... ; Common denominator:...

Discriminant

\(-(-1+54z)(162z-1)^2(108z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 162}\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 54}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(4\)\(1\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.12" from ...

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

7

New Number: 5.35 |  AESZ: 218  |  Superseeker: 138/7 42984/7  |  Hash: a76111af659715caf2c4344eedd9d678  

Degree: 5

\(7^{2} \theta^4-2 3 7 x\left(192\theta^4+396\theta^3+303\theta^2+105\theta+14\right)+2^{2} 3 x^{2}\left(1188\theta^4+11736\theta^3+20431\theta^2+12152\theta+2436\right)+2^{2} 3^{3} x^{3}\left(532\theta^4+504\theta^3-3455\theta^2-3829\theta-1036\right)-2^{4} 3^{4} x^{4}(2\theta+1)(36\theta^3+306\theta^2+421\theta+156)-2^{6} 3^{4} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 612, 48000, 4580100, ...
--> OEIS
Normalized instanton numbers (n0=1): 138/7, 1506/7, 42984/7, 235596, 78950334/7, ... ; Common denominator:...

Discriminant

\(-(1296z^3-864z^2+168z-1)(7+12z)^2\)

Local exponents

\(-\frac{ 7}{ 12}\)\(0\) ≈\(0.006145\) ≈\(0.330261-0.128447I\) ≈\(0.330261+0.128447I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.35" from ...

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

8

New Number: 5.51 |  AESZ: 250  |  Superseeker: 308/23 70799/23  |  Hash: 9c19794a84073d1c6dfd11c8a7c9a740  

Degree: 5

\(23^{2} \theta^4-23 x\left(3271\theta^4+5078\theta^3+3896\theta^2+1357\theta+184\right)+x^{2}\left(1357863\theta^4+999924\theta^3-787393\theta^2-850862\theta-205712\right)-2^{3} x^{3}\left(775799\theta^4-272481\theta^3-218821\theta^2+176709\theta+100234\right)-2^{4} 61 x^{4}\left(1005\theta^4-15654\theta^3-36317\theta^2-27938\theta-7304\right)-2^{9} 61^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 324, 19304, 1388260, ...
--> OEIS
Normalized instanton numbers (n0=1): 308/23, 3526/23, 70799/23, 2148684/23, 81402822/23, ... ; Common denominator:...

Discriminant

\(-(512z^3+113z^2+121z-1)(-23+244z)^2\)

Local exponents

≈\(-0.114451-0.474453I\) ≈\(-0.114451+0.474453I\)\(0\) ≈\(0.008199\)\(\frac{ 23}{ 244}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.51" from ...

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

9

New Number: 5.70 |  AESZ: 287  |  Superseeker: 361/21 120472/21  |  Hash: 97932196c46a8712f6dcb11165d698be  

Degree: 5

\(3^{2} 7^{2} \theta^4-3 7 x\left(3289\theta^4+6098\theta^3+4645\theta^2+1596\theta+210\right)+2^{2} 5 x^{2}\left(7712\theta^4-46168\theta^3-106885\theta^2-67410\theta-13629\right)+2^{4} x^{3}\left(106636\theta^4+493416\theta^3+420211\theta^2+116361\theta+6090\right)-2^{8} 5 x^{4}(2\theta+1)(1916\theta^3+2622\theta^2+1077\theta+91)-2^{12} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 510, 38260, 3473470, ...
--> OEIS
Normalized instanton numbers (n0=1): 361/21, 4780/21, 120472/21, 1537864/7, 216261320/21, ... ; Common denominator:...

Discriminant

\(-(64z^3+800z^2+149z-1)(-21+80z)^2\)

Local exponents

≈\(-12.310784\) ≈\(-0.195701\)\(0\) ≈\(0.006485\)\(\frac{ 21}{ 80}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.70" from ...

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

10

New Number: 8.26 |  AESZ: 301  |  Superseeker: 193/11 48570/11  |  Hash: a91db18876a9dfbf42b88f8d64c55d85  

Degree: 8

\(11^{2} \theta^4-11 x\left(1517\theta^4+3136\theta^3+2393\theta^2+825\theta+110\right)-x^{2}\left(24266+106953\theta+202166\theta^2+207620\theta^3+90362\theta^4\right)-x^{3}\left(53130+217437\theta+415082\theta^2+507996\theta^3+245714\theta^4\right)-x^{4}\left(15226+183269\theta+564786\theta^2+785972\theta^3+407863\theta^4\right)-x^{5}\left(25160+279826\theta+728323\theta^2+790148\theta^3+434831\theta^4\right)-2^{3} x^{6}\left(36361\theta^4+70281\theta^3+73343\theta^2+37947\theta+7644\right)-2^{4} 5 x^{7}\left(1307\theta^4+3430\theta^3+3877\theta^2+2162\theta+488\right)-2^{9} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 466, 32392, 2727826, ...
--> OEIS
Normalized instanton numbers (n0=1): 193/11, 1973/11, 48570/11, 1689283/11, 72444183/11, ... ; Common denominator:...

Discriminant

\(-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2\)

Local exponents

\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\)\(-1\)\(-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I\)\(-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I\)\(0\)\(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(3\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(1\)\(4\)\(4\)\(0\)\(2\)\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.27.

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