Summary

You searched for: c3=-128

Your search produced 7 matches

You can download all data as plain text or as JSON

1

New Number: 2.52 |  AESZ: 16  |  Superseeker: 4 644/3  |  Hash: 05af0662662bfbec63e3186c4f363313  

Degree: 2

\(\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{8} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 168, 5120, 190120, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 20, 644/3, 3072, 52512, ... ; Common denominator:...

Discriminant

\((64z-1)(16z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \alpha$
A-Incarnation: diagonal subfamily of 1,1,1,1-intersection in $P^1 \times P^1 \times P^1 \times \P^1$
B-Incarnations:
Fibre products: 62211- x 632--1, S62211

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

2

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

Degree: 2

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

Maple   LaTex

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

Discriminant

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

Local exponents

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

Note:

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

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

3

New Number: 2.69 |  AESZ: 205  |  Superseeker: 1 5  |  Hash: 4fb2e7002e630237d0458c3985cd6a18  

Degree: 2

\(\theta^4-x\left(59\theta^4+118\theta^3+105\theta^2+46\theta+8\right)+2^{5} 3 x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...

Discriminant

\((32z-1)(27z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "2.69" from ...

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

4

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  

5

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  

6

New Number: 5.87 |  AESZ: 321  |  Superseeker: 35/9 3002/9  |  Hash: b786027c217dd5d5c5abac7b1ecc570b  

Degree: 5

\(3^{4} \theta^4-3^{2} x\left(191\theta^4+862\theta^3+683\theta^2+252\theta+36\right)-2^{5} x^{2}\left(7225\theta^4+24835\theta^3+30634\theta^2+16173\theta+3069\right)-2^{8} x^{3}\left(13251\theta^4+35856\theta^3+27641\theta^2+6966\theta+180\right)-2^{12} 5 x^{4}(2\theta+1)(314\theta^3+363\theta^2+68\theta-31)+2^{16} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 132, 4000, 179620, ...
--> OEIS
Normalized instanton numbers (n0=1): 35/9, 261/4, 3002/9, 126800/9, 1727129/9, ... ; Common denominator:...

Discriminant

\((32z+1)(32z^2-71z+1)(9+80z)^2\)

Local exponents

\(-\frac{ 9}{ 80}\)\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\)\(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.87" from ...

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

7

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