1
New Number: 5.129 | AESZ: | Superseeker: -26 -8344 | Hash: 6c96cbe2aa88f7096e6b9f02e290d167
Degree: 5
\(\theta^4+2 x\left(24\theta^4+228\theta^3+181\theta^2+67\theta+10\right)-2^{2} 5 x^{2}\left(584\theta^4+392\theta^3-1717\theta^2-1320\theta-300\right)-2^{4} 3 5^{2} x^{3}\left(128\theta^4+2328\theta^3+3008\theta^2+1563\theta+290\right)+2^{6} 3^{2} 5^{3} x^{4}(2\theta+1)(266\theta^3+831\theta^2+883\theta+315)-2^{8} 3^{3} 5^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 900, -52400, 3482500, ... --> OEIS Normalized instanton numbers (n0=1): -26, -561/2, -8344, -278334, -11536332, ... ; Common denominator:...
\(-(20z-1)(108z+1)(80z+1)(-1+60z)^2\)
| \(-\frac{ 1}{ 80}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 1}{ 60}\) | \(\frac{ 1}{ 20}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 5.134 | AESZ: | Superseeker: 176 1215248/3 | Hash: 5bd656df18dc5d02b2f2a068ba88ab74
Degree: 5
\(\theta^4+2^{2} x\left(4\theta^4-352\theta^3-250\theta^2-74\theta-9\right)-2^{4} 3 x^{2}\left(3168\theta^4+5952\theta^3-3712\theta^2-2648\theta-519\right)-2^{8} 3^{3} x^{3}\left(2912\theta^4-3008\theta^3-3152\theta^2-1160\theta-145\right)+2^{12} 3^{3} 5 x^{4}(2\theta+1)(824\theta^3+1668\theta^2+1342\theta+405)+2^{16} 3^{4} 5^{2} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 4572, 918000, 228519900, ... --> OEIS Normalized instanton numbers (n0=1): 176, -3238, 1215248/3, -18807038, 3651829680, ... ; Common denominator:...
\((48z-1)(432z-1)(16z+1)(1+240z)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 240}\) | \(0\) | \(\frac{ 1}{ 432}\) | \(\frac{ 1}{ 48}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
3
New Number: 5.34 | AESZ: 217 | Superseeker: 17/7 5095/21 | Hash: e8743aeac19deca699ff90aaef6b8ea7
Degree: 5
\(7^{2} \theta^4+7 x\theta(-14-73\theta-118\theta^2+13\theta^3)-2^{3} 3 x^{2}\left(3378\theta^4+13446\theta^3+18869\theta^2+11158\theta+2352\right)-2^{4} 3^{3} x^{3}\left(3628\theta^4+17920\theta^3+31668\theta^2+22596\theta+5383\right)-2^{8} 3^{3} x^{4}(2\theta+1)(572\theta^3+2370\theta^2+2896\theta+1095)-2^{10} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 720, 37800, ... --> OEIS Normalized instanton numbers (n0=1): 17/7, 254/7, 5095/21, 29600/7, 491991/7, ... ; Common denominator:...
\(-(16z+1)(27z+1)(48z-1)(7+24z)^2\)
| \(-\frac{ 7}{ 24}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 27}\) | \(0\) | \(\frac{ 1}{ 48}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
4
New Number: 5.37 | AESZ: 221 | Superseeker: 492/5 872164/5 | Hash: b7ce7a734c057660ce3d6341a7572078
Degree: 5
\(5^{2} \theta^4-2^{2} 5 x\left(404\theta^4+1096\theta^3+773\theta^2+225\theta+25\right)-2^{4} x^{2}\left(66896\theta^4+137408\theta^3+101096\theta^2+52800\theta+11625\right)-2^{8} 3 5 x^{3}(2\theta+1)(5672\theta^3+9500\theta^2+8422\theta+2689)-2^{15} 3^{2} x^{4}(2\theta+1)(1208\theta^3+2892\theta^2+2842\theta+969)-2^{20} 3^{3} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 20, 2988, 618320, 156299500, ... --> OEIS Normalized instanton numbers (n0=1): 492/5, 10376/5, 872164/5, 91316176/5, 12181916784/5, ... ; Common denominator:...
\(-(-1+432z)(16z+1)^2(192z+5)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 5}{ 192}\) | \(0\) | \(\frac{ 1}{ 432}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 1}{ 4}\) | \(1\) | \(0\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(\frac{ 3}{ 4}\) | \(3\) | \(0\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(1\) | \(4\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
5
New Number: 5.40 | AESZ: 226 | Superseeker: 62/5 4060/3 | Hash: 92f95cd33ac4bf18c2d05ce3040c5203
Degree: 5
\(5^{2} \theta^4-2 5 x\left(328\theta^4+692\theta^3+551\theta^2+205\theta+30\right)+2^{2} 3 x^{2}\left(5352\theta^4+25416\theta^3+38387\theta^2+23020\theta+4860\right)-2^{4} 3^{3} x^{3}\left(352\theta^4+4520\theta^3+12108\theta^2+10205\theta+2630\right)-2^{6} 3^{3} x^{4}(2\theta+1)(586\theta^3+3039\theta^2+3947\theta+1527)-2^{8} 3^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 396, 19920, 1241100, ... --> OEIS Normalized instanton numbers (n0=1): 62/5, 55, 4060/3, 28790, 861786, ... ; Common denominator:...
\(-(16z-1)(108z-1)(12z-1)(5+12z)^2\)
| \(-\frac{ 5}{ 12}\) | \(0\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
6
New Number: 5.45 | AESZ: 242 | Superseeker: -18 1568/3 | Hash: 562c18d54c0080ebb0bb01b14a8241ce
Degree: 5
\(\theta^4+2 3 x\left(72\theta^4+108\theta^3+91\theta^2+37\theta+6\right)+2^{2} 3^{3} x^{2}\left(648\theta^4+1800\theta^3+2211\theta^2+1248\theta+260\right)+2^{4} 3^{5} x^{3}\left(1344\theta^4+4968\theta^3+7320\theta^2+4749\theta+1072\right)+2^{6} 3^{7} x^{4}(2\theta+1)(630\theta^3+2241\theta^2+2617\theta+971)+2^{8} 3^{10} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -36, 2484, -208080, 19221300, ... --> OEIS Normalized instanton numbers (n0=1): -18, 99/2, 1568/3, 22698, -165960, ... ; Common denominator:...
\((1+144z)(36z+1)^2(108z+1)^2\)
| \(-\frac{ 1}{ 36}\) | \(-\frac{ 1}{ 108}\) | \(-\frac{ 1}{ 144}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 5}{ 6}\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 7}{ 6}\) |
| \(4\) | \(1\) | \(2\) | \(0\) | \(\frac{ 3}{ 2}\) |