1
New Number: 4.51 | AESZ: | Superseeker: 992 63721056 | Hash: 1d45a05c9bcf007b5042b0f7a5672551
Degree: 4
\(\theta^4-2^{4} x\left(112\theta^4+416\theta^3+280\theta^2+72\theta+7\right)-2^{12} x^{2}\left(656\theta^4+896\theta^3-216\theta^2-160\theta-23\right)-2^{23} x^{3}\left(96\theta^4+24\theta^3+12\theta^2+6\theta+1\right)-2^{30} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 112, 93456, 124614400, 204621667600, ... --> OEIS Normalized instanton numbers (n0=1): 992, 98792, 63721056, 40943244128, 36122052633760, ... ; Common denominator:...
\(-(65536z^2+2816z-1)(1+512z)^2\)
| \(-\frac{ 11}{ 512}-\frac{ 5}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | \(0\) | \(s_2\) | \(s_1\) | \(-\frac{ 11}{ 512}+\frac{ 5}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
2
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:...
\(-(-1+432z)(16z+1)^2(192z+5)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 5}{ 192}\) | \(0\) | \(\frac{ 1}{ 432}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(\frac{ 1}{ 4}\) | \(1\) | \(0\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(\frac{ 3}{ 4}\) | \(3\) | \(0\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(1\) | \(4\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
3
New Number: 5.6 | AESZ: 23 | Superseeker: 4/3 44/3 | Hash: 65760d446ba9c3da587ce5bd9912745e
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(64\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+2^{7} x^{2}\left(194\theta^4+440\theta^3+527\theta^2+315\theta+75\right)-2^{12} x^{3}\left(94\theta^4+288\theta^3+397\theta^2+261\theta+66\right)+2^{17} x^{4}\left(22\theta^4+80\theta^3+117\theta^2+77\theta+19\right)-2^{23} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 104, 1664, 30376, ... --> OEIS Normalized instanton numbers (n0=1): 4/3, 13/3, 44/3, 278/3, 2336/3, ... ; Common denominator:...
\(-(-1+32z)(16z-1)^2(32z-3)^2\)
| \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(1\) | \(4\) | \(1\) |