1
New Number: 4.43 | AESZ: 225 | Superseeker: 93984 25265152551072 | Hash: 5993002ccf811247be9232b089dd8e3a
Degree: 4
\(\theta^4+2^{4} x\left(22192\theta^4-17056\theta^3-9576\theta^2-1048\theta-49\right)+2^{20} x^{2}\left(33648\theta^4-44688\theta^3+16224\theta^2+1764\theta+17\right)+2^{34} 5 x^{3}\left(6512\theta^4-6144\theta^3-4440\theta^2-1536\theta-193\right)-2^{55} 5^{2} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 784, 3226896, 20413907200, 157477179235600, ... --> OEIS Normalized instanton numbers (n0=1): 93984, -1084521600, 25265152551072, -787700706860008320, 28889437619654310485088, ... ; Common denominator:...
\(-(536870912z^2-27392z-1)(1+163840z)^2\)
≈\(-2.5e-05\) | \(-\frac{ 1}{ 163840}\) | \(0\) | \(s_2\) | \(s_1\) | ≈\(7.6e-05\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
2
New Number: 4.47 | AESZ: 239 | Superseeker: 1584 171534960 | Hash: 8e610c3437d7f38e552038bc55399495
Degree: 4
\(\theta^4+2^{4} 3 x\left(9\theta^4-198\theta^3-131\theta^2-32\theta-3\right)-2^{11} 3^{2} x^{2}\left(486\theta^4+1215\theta^3+81\theta^2-27\theta-5\right)-2^{16} 3^{5} x^{3}\left(891\theta^4+972\theta^3+675\theta^2+216\theta+25\right)-2^{23} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 144, 147600, 239904000, 479672701200, ... --> OEIS Normalized instanton numbers (n0=1): 1584, -17874, 171534960, 30012731550, 105934107802896, ... ; Common denominator:...
\(-(432z+1)(3456z-1)(1+1728z)^2\)
\(-\frac{ 1}{ 432}\) | \(-\frac{ 1}{ 1728}\) | \(0\) | \(\frac{ 1}{ 3456}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 3}\) |
\(1\) | \(3\) | \(0\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(2\) | \(4\) | \(0\) | \(2\) | \(\frac{ 2}{ 3}\) |
3
New Number: 4.48 | AESZ: 241 | Superseeker: 320 19748928 | Hash: b4d16d8dd1eb7839630ecf8e8d242023
Degree: 4
\(\theta^4-2^{4} x\left(152\theta^4+160\theta^3+110\theta^2+30\theta+3\right)+2^{10} 3 x^{2}\left(428\theta^4+176\theta^3-299\theta^2-170\theta-25\right)-2^{17} 3^{2} x^{3}\left(136\theta^4-216\theta^3-180\theta^2-51\theta-5\right)-2^{24} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 26640, 21907200, 22048765200, ... --> OEIS Normalized instanton numbers (n0=1): 320, 61084, 19748928, 9428973876, 5618509433280, ... ; Common denominator:...
\(-(64z+1)(1728z-1)(-1+384z)^2\)
\(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 1728}\) | \(\frac{ 1}{ 384}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
\(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
4
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:...
\(-(65536z^2+2816z-1)(1+512z)^2\)
\(-\frac{ 11}{ 512}-\frac{ 5}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | \(0\) | \(s_2\) | \(s_1\) | \(-\frac{ 11}{ 512}+\frac{ 5}{ 512}\sqrt{ 5}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
5
New Number: 4.56 | AESZ: 277 | Superseeker: 4192 2124587232 | Hash: 9d905a8d31566f4976cbeb2d3bf0624c
Degree: 4
\(\theta^4+2^{4} x\left(576\theta^4-1152\theta^3-724\theta^2-148\theta-13\right)-2^{17} x^{2}\left(32\theta^4+992\theta^3-166\theta^2-57\theta-6\right)-2^{26} 3 x^{3}\left(832\theta^4+768\theta^3+556\theta^2+192\theta+25\right)-2^{40} 3^{2} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 208, 254736, 490988800, 1163138813200, ... --> OEIS Normalized instanton numbers (n0=1): 4192, -1708008, 2124587232, -2777042329304, 4857272052090400, ... ; Common denominator:...
\(-(1024z+1)(4096z-1)(1+6144z)^2\)
\(-\frac{ 1}{ 1024}\) | \(-\frac{ 1}{ 6144}\) | \(0\) | \(\frac{ 1}{ 4096}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(3\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(2\) | \(4\) | \(0\) | \(2\) | \(\frac{ 1}{ 2}\) |
6
New Number: 4.60 | AESZ: 288 | Superseeker: 3616 264403872 | Hash: 3373ebdbe30d220b5562cfd77d4e8f96
Degree: 4
\(\theta^4-2^{4} x\left(496\theta^4+1568\theta^3+1060\theta^2+276\theta+27\right)-2^{15} 3 x^{2}\left(32\theta^4-760\theta^3-1570\theta^2-651\theta-81\right)+2^{22} 3^{2} x^{3}\left(1616\theta^4+6912\theta^3+5092\theta^2+1416\theta+135\right)+2^{34} 3^{3} x^{4}(4\theta+1)(3\theta+1)(3\theta+2)(4\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 432, 982800, 3259872000, 12958462717200, ... --> OEIS Normalized instanton numbers (n0=1): 3616, 114144, 264403872, 424149521656, 710239010095456, ... ; Common denominator:...
\((6912z-1)(4096z-1)(1+1536z)^2\)
\(-\frac{ 1}{ 1536}\) | \(0\) | \(\frac{ 1}{ 6912}\) | \(\frac{ 1}{ 4096}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 3}\) |
\(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 4}\) |
7
New Number: 4.64 | AESZ: 295 | Superseeker: -5408 -4296119968 | Hash: e40629f953a095a2a764c68394321139
Degree: 4
\(\theta^4-2^{4} x\left(816\theta^4-1440\theta^3-904\theta^2-184\theta-17\right)+2^{18} x^{2}\left(80\theta^4-592\theta^3+432\theta^2+164\theta+23\right)+2^{30} x^{3}\left(80\theta^4-384\theta^3-296\theta^2-96\theta-11\right)+2^{45} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -272, 93456, 194502400, -587215823600, ... --> OEIS Normalized instanton numbers (n0=1): -5408, -3839480, -4296119968, -6482749129792, -11816577914904160, ... ; Common denominator:...
\((8388608z^2+3328z+1)(-1+8192z)^2\)
\(-\frac{ 13}{ 65536}-\frac{ 7}{ 65536}\sqrt{ 7}I\) | \(-\frac{ 13}{ 65536}+\frac{ 7}{ 65536}\sqrt{ 7}I\) | \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 1}{ 8192}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
\(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(\frac{ 1}{ 2}\) |
8
New Number: 4.66 | AESZ: 300 | Superseeker: -1616 -283183120 | Hash: edc54887effd2ebcaa636dcc93baf0b7
Degree: 4
\(\theta^4+2^{4} x\left(371\theta^4+862\theta^3+591\theta^2+160\theta+15\right)+2^{11} 5 x^{2}\left(224\theta^4+2069\theta^3+3277\theta^2+1363\theta+159\right)-2^{16} 5^{2} x^{3}\left(2089\theta^4+7500\theta^3+5533\theta^2+1500\theta+135\right)+2^{23} 5^{3} x^{4}(5\theta+1)(5\theta+2)(5\theta+3)(5\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -240, 378000, -941740800, 2908743037200, ... --> OEIS Normalized instanton numbers (n0=1): -1616, 265534, -283183120, 351860487150, -525536710386800, ... ; Common denominator:...
\((6400000z^2+6576z+1)(-1+320z)^2\)
≈\(-0.000842\) | ≈\(-0.000186\) | \(0\) | \(s_2\) | \(s_1\) | \(\frac{ 1}{ 320}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 5}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 5}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 5}\) |
\(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(\frac{ 4}{ 5}\) |
9
New Number: 1.10 | AESZ: 10 | Superseeker: 928 170869536 | Hash: 51f8135aba94201bd0bbe9b2287a92d5
Degree: 1
\(\theta^4-2^{4} x(4\theta+1)^2(4\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 144, 176400, 341510400, 811620810000, ... --> OEIS Normalized instanton numbers (n0=1): 928, 245616, 170869536, 174999877936, 221984814405088, ... ; Common denominator:...
\(\)
No data for singularities
10
New Number: 1.14 | AESZ: 14 | Superseeker: 1248 683015008 | Hash: 03af56f4ae0cea2c4b219620b08dc49b
Degree: 1
\(\theta^4-2^{4} 3 x(6\theta+1)(2\theta+1)^2(6\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 240, 498960, 1633632000, 6558930378000, ... --> OEIS Normalized instanton numbers (n0=1): 1248, 597192, 683015008, 1149904141056, 2394928461766560, ... ; Common denominator:...
\(1-6912z\)
\(0\) | \(\frac{ 1}{ 6912}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 6}\) |
\(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(2\) | \(\frac{ 5}{ 6}\) |