1
New Number: 2.31 | AESZ: 7** | Superseeker: 96 -12064 | Hash: 2c494088fc85599f73fb344776dbbb28
Degree: 2
\(\theta^4-2^{4} x(2\theta+1)^2(32\theta^2+32\theta+13)+2^{16} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 208, 107280, 70739200, 52362595600, ... --> OEIS Normalized instanton numbers (n0=1): 96, -3560, -12064, 1941800, -489007584, ... ; Common denominator:...
\((1024z-1)^2\)
\(0\) | \(\infty\) | \(\frac{ 1}{ 1024}\) |
---|---|---|
\(0\) | \(\frac{ 1}{ 2}\) | \(0\) |
\(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 4}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 4}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(1\) |
2
New Number: 2.32 | AESZ: | Superseeker: 60 307860 | Hash: c2f30268af49d0bdc6a36f8b0fce3367
Degree: 2
\(\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(32\theta^2+32\theta+13)+2^{12} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 312, 268200, 297104640, 370278354600, ... --> OEIS Normalized instanton numbers (n0=1): 60, -7635, 307860, -44194980, 3687387360, ... ; Common denominator:...
\((1728z-1)^2\)
\(0\) | \(\frac{ 1}{ 1728}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(\frac{ 3}{ 4}\) | \(\frac{ 4}{ 3}\) |
\(0\) | \(1\) | \(\frac{ 5}{ 3}\) |
3
New Number: 2.33 | AESZ: | Superseeker: -160 -539680 | Hash: 83a66e92381baa083f87a13e02375bc9
Degree: 2
\(\theta^4-2^{4} x(4\theta+1)(4\theta+3)(32\theta^2+32\theta+13)+2^{16} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 624, 1251600, 3268151040, 9627237219600, ... --> OEIS Normalized instanton numbers (n0=1): -160, -6920, -539680, -54568560, -6402958560, ... ; Common denominator:...
\((4096z-1)^2\)
\(0\) | \(\frac{ 1}{ 4096}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
\(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 3}{ 4}\) |
\(0\) | \(\frac{ 3}{ 4}\) | \(\frac{ 5}{ 4}\) |
\(0\) | \(1\) | \(\frac{ 7}{ 4}\) |
4
New Number: 2.34 | AESZ: | Superseeker: -3936 -10892932064 | Hash: 3047f1b969ee26b92708d8eab03c0aed
Degree: 2
\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(32\theta^2+32\theta+13)+2^{16} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3120, 41302800, 722261379840, 14304149060881680, ... --> OEIS Normalized instanton numbers (n0=1): -3936, 3550992, -10892932064, 48014348072136, -264897451764337440, ... ; Common denominator:...
\((27648z-1)^2\)
\(0\) | \(\frac{ 1}{ 27648}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 6}\) |
\(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 5}{ 6}\) |
\(0\) | \(\frac{ 3}{ 4}\) | \(\frac{ 7}{ 6}\) |
\(0\) | \(1\) | \(\frac{ 11}{ 6}\) |
5
New Number: 3.5 | AESZ: | Superseeker: 26 103520/9 | Hash: 4ed9bc316d49a71649da0a1148f7ea9d
Degree: 3
\(\theta^4-2 x\left(102\theta^4+204\theta^3+155\theta^2+53\theta+7\right)+2^{2} x^{2}(\theta+1)^2(396\theta^2+792\theta+311)-2^{4} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 14, 834, 78260, 8970850, ... --> OEIS Normalized instanton numbers (n0=1): 26, 348, 103520/9, 539764, 31290280, ... ; Common denominator:...
\(-(196z-1)(4z-1)^2\)
\(0\) | \(\frac{ 1}{ 196}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(1\) | \(\frac{ 1}{ 4}\) | \(1\) |
\(0\) | \(1\) | \(\frac{ 3}{ 4}\) | \(2\) |
\(0\) | \(2\) | \(1\) | \(\frac{ 5}{ 2}\) |
6
New Number: 5.17 | AESZ: 119 | Superseeker: 28/3 3892/3 | Hash: dc8ec37012f2c92c83e6519935956eeb
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(256\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+2^{7} x^{2}\left(3104\theta^4+7040\theta^3+8012\theta^2+4452\theta+927\right)-2^{15} x^{3}\left(752\theta^4+2304\theta^3+3042\theta^2+1854\theta+405\right)+2^{21} x^{4}(2\theta+1)(176\theta^3+552\theta^2+622\theta+231)-2^{31} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1128, 67200, 4634280, ... --> OEIS Normalized instanton numbers (n0=1): 28/3, 394/3, 3892/3, 108262/3, 1044128, ... ; Common denominator:...
\(-(-1+128z)(64z-1)^2(128z-3)^2\)
\(0\) | \(\frac{ 3}{ 128}\) | \(\frac{ 1}{ 128}\) | \(\infty\) | \(\frac{ 1}{ 64}\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(0\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 4}\) |
\(0\) | \(3\) | \(1\) | \(1\) | \(\frac{ 3}{ 4}\) |
\(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) | \(1\) |
7
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:...
\(-(-1+432z)(16z+1)^2(192z+5)^2\)
\(0\) | \(-\frac{ 1}{ 16}\) | \(\infty\) | \(\frac{ 1}{ 432}\) | \(-\frac{ 5}{ 192}\) |
---|---|---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(0\) | \(0\) |
\(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 5}{ 6}\) | \(1\) | \(1\) |
\(0\) | \(\frac{ 3}{ 4}\) | \(\frac{ 7}{ 6}\) | \(1\) | \(3\) |
\(0\) | \(1\) | \(\frac{ 3}{ 2}\) | \(2\) | \(4\) |
8
New Number: 2.71 | AESZ: | Superseeker: 0 0 | Hash: 757b011780c5986bd45a5bf434c76c28
Degree: 2
\(\theta^4-2^{5} x(2\theta+1)^2(2\theta^2+2\theta+1)+2^{8} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 2160, 181760, 17021200, ... --> OEIS Normalized instanton numbers (n0=1): 0, -20, 0, -865, 0, ... ; Common denominator:...
\((-1+128z)^2\)
\(0\) | \(\frac{ 1}{ 128}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 3}{ 4}\) |
\(0\) | \(\frac{ 3}{ 4}\) | \(\frac{ 5}{ 4}\) |
\(0\) | \(1\) | \(\frac{ 3}{ 2}\) |