1
New Number: 2.64 | AESZ: 182 | Superseeker: 1 7 | Hash: 89ba4729efa82413b33fe6928ff8d2c9
Degree: 2
\(\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ... --> OEIS Normalized instanton numbers (n0=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...
\((27z-1)(16z-1)\)
\(0\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 6}\) |
\(0\) | \(1\) | \(1\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 7}{ 6}\) |
2
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 LaTexCoefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ... --> OEIS Normalized instanton numbers (n0=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...
\((32z-1)(27z-1)\)
\(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 27}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |
3
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 LaTexCoefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ... --> OEIS Normalized instanton numbers (n0=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...
\(-(z-1)(25z-1)(9z-1)\)
\(0\) | \(\frac{ 1}{ 25}\) | \(\frac{ 1}{ 9}\) | \(1\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
\(0\) | \(2\) | \(2\) | \(2\) | \(2\) |
4
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 LaTexCoefficients of the holomorphic solution: 1, 16, 280, 5152, 98200, ... --> OEIS Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...
\((25z-1)(24z-1)(-1+16z)^2\)
\(0\) | \(\frac{ 1}{ 25}\) | \(\frac{ 1}{ 24}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 5}{ 2}\) |
\(0\) | \(2\) | \(2\) | \(1\) | \(3\) |
5
New Number: 5.102 | AESZ: 352 | Superseeker: 1 -12 | Hash: fc8b141522720827b1dd2cd28a232c1b
Degree: 5
\(\theta^4-x\left(70\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+3 x^{2}\left(675\theta^4+1602\theta^3+1933\theta^2+1130\theta+258\right)-2^{2} 3^{3} x^{3}\left(271\theta^4+888\theta^3+1259\theta^2+831\theta+207\right)+2^{2} 3^{5} x^{4}\left(212\theta^4+808\theta^3+1189\theta^2+773\theta+186\right)-2^{4} 3^{7} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 54, 492, 3510, ... --> OEIS Normalized instanton numbers (n0=1): 1, -7/8, -12, -131/4, 90, ... ; Common denominator:...
\(-(16z-1)(432z^2-36z+1)(-1+9z)^2\)
\(0\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
\(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(\frac{ 5}{ 4}\) |
6
New Number: 5.93 | AESZ: 333 | Superseeker: 1 2668/3 | Hash: dc274781605ee4262d8745e3fa3a8057
Degree: 5
\(\theta^4+x\theta^2(71\theta^2-2\theta-1)+2^{3} 3 x^{2}\left(154\theta^4+334\theta^3+461\theta^2+248\theta+48\right)+2^{6} 3^{2} x^{3}(5\theta+3)(31\theta^3+39\theta^2-25\theta-21)+2^{9} 3^{4} x^{4}(2\theta+1)(2\theta^3-33\theta^2-56\theta-24)-2^{12} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -72, 1440, 22680, ... --> OEIS Normalized instanton numbers (n0=1): 1, -66, 2668/3, -2774, -167786, ... ; Common denominator:...
\(-(9z-1)(2304z^2+32z+1)(1+24z)^2\)
\(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 144}-\frac{ 1}{ 72}\sqrt{ 2}I\) | \(-\frac{ 1}{ 144}+\frac{ 1}{ 72}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 9}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
\(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
\(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
7
New Number: 6.21 | AESZ: | Superseeker: 1 11 | Hash: 319d6b2f1541de5252840442cc6f8dcd
Degree: 6
\(\theta^4+x\left(6+27\theta+47\theta^2+40\theta^3+20\theta^4\right)-x^{2}(143\theta^2+286\theta+120)(\theta+1)^2-2 3^{2} x^{3}(\theta+2)(\theta+1)(291\theta^2+873\theta+766)-2^{2} 3^{3} 5 x^{4}(\theta+3)(\theta+1)(41\theta^2+164\theta+196)+2^{3} 3^{3} 5^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+150)+2^{5} 3^{5} 5^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 60, -480, 5040, ... --> OEIS Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...
\((6z-1)(15z-1)(9z+1)(12z+1)(10z+1)^2\)
\(-\frac{ 1}{ 9}\) | \(-\frac{ 1}{ 10}\) | \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 1}{ 15}\) | \(\frac{ 1}{ 6}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
\(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(4\) |
\(2\) | \(1\) | \(2\) | \(0\) | \(2\) | \(2\) | \(5\) |
8
New Number: 7.10 | AESZ: | Superseeker: 1 11 | Hash: b1c277f62ba740f9f7e0371ba53e4194
Degree: 7
\(\theta^4-x\left(76\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+x^{2}\left(2209\theta^4+4228\theta^3+4745\theta^2+2726\theta+648\right)-2 3^{2} x^{3}\left(1735\theta^4+4646\theta^3+6099\theta^2+4072\theta+1124\right)+2^{2} 3^{3} x^{4}\left(2085\theta^4+7388\theta^3+11695\theta^2+9140\theta+2844\right)-2^{3} 3^{3} x^{5}(\theta+1)(3707\theta^3+14055\theta^2+20242\theta+10704)+2^{6} 3^{5} x^{6}(\theta+1)(\theta+2)(86\theta^2+285\theta+262)-2^{7} 3^{8} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 60, 816, 13104, ... --> OEIS Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...
\(-(3z-1)(18z-1)(27z-1)(12z-1)^2(-1+2z)^2\)
\(0\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 18}\) | \(\frac{ 1}{ 12}\) | \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
\(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
\(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(1\) | \(3\) |
9
New Number: 8.55 | AESZ: | Superseeker: 1 68/9 | Hash: 39ed8ce7572bc79a333f77c892033bcf
Degree: 8
\(\theta^4-x\left(33\theta^4+98\theta^3+105\theta^2+56\theta+12\right)+2^{3} x^{2}\left(34\theta^4+276\theta^3+609\theta^2+582\theta+216\right)+2^{4} 3 x^{3}\left(11\theta^4-170\theta^3-941\theta^2-1520\theta-846\right)-2^{7} 3^{2} x^{4}(2\theta^2+6\theta+5)(4\theta^2+12\theta-31)+2^{8} 3 x^{5}\left(11\theta^4+302\theta^3+1183\theta^2+1652\theta+726\right)+2^{11} x^{6}\left(34\theta^4+132\theta^3-39\theta^2-708\theta-747\right)-2^{12} x^{7}\left(33\theta^4+298\theta^3+1005\theta^2+1492\theta+816\right)+2^{16} x^{8}\left((\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 120, 1216, 13080, ... --> OEIS Normalized instanton numbers (n0=1): 1, -2, 68/9, -30, 150, ... ; Common denominator:...
\((z-1)(16z-1)(16z^2-16z+1)(4z-1)^2(4z+1)^2\)
\(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 3}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 3}\) | \(1\) | \(\infty\) |
---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(3\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) |
\(3\) | \(0\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(3\) |
\(4\) | \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(3\) |