1
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:...
\(-(432z+1)(3456z-1)(1+1728z)^2\)
\(-\frac{ 1}{ 432}\) | \(-\frac{ 1}{ 1728}\) | \(0\) | \(\frac{ 1}{ 3456}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 3}\) |
\(1\) | \(3\) | \(0\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(2\) | \(4\) | \(0\) | \(2\) | \(\frac{ 2}{ 3}\) |
2
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:...
\(-(64z+1)(1728z-1)(-1+384z)^2\)
\(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 1728}\) | \(\frac{ 1}{ 384}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
\(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
3
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:...
\(-(65536z^2+2816z-1)(1+512z)^2\)
\(-\frac{ 11}{ 512}-\frac{ 5}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | \(0\) | \(s_2\) | \(s_1\) | \(-\frac{ 11}{ 512}+\frac{ 5}{ 512}\sqrt{ 5}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
4
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:...
\((6912z-1)(4096z-1)(1+1536z)^2\)
\(-\frac{ 1}{ 1536}\) | \(0\) | \(\frac{ 1}{ 6912}\) | \(\frac{ 1}{ 4096}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 3}\) |
\(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 4}\) |
5
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:...
\((6400000z^2+6576z+1)(-1+320z)^2\)
≈\(-0.000842\) | ≈\(-0.000186\) | \(0\) | \(s_2\) | \(s_1\) | \(\frac{ 1}{ 320}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 5}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 5}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(\frac{ 3}{ 5}\) |
\(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(\frac{ 4}{ 5}\) |
6
New Number: 5.22 | AESZ: 193 | Superseeker: 129/7 41441/7 | Hash: 44e6fc2823d5ff31e66059ba6b37f2ae
Degree: 5
\(7^{2} \theta^4-7 x\left(1135\theta^4+2204\theta^3+1683\theta^2+581\theta+77\right)+x^{2}\left(28723\theta^4+40708\theta^3+13260\theta^2-1337\theta-896\right)-x^{3}\left(32126\theta^4+38514\theta^3+26511\theta^2+10731\theta+1806\right)+7 11 x^{4}\left(130\theta^4+254\theta^3+192\theta^2+65\theta+8\right)+11^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 11, 559, 42923, 3996751, ... --> OEIS Normalized instanton numbers (n0=1): 129/7, 1557/7, 41441/7, 1594332/7, 75470601/7, ... ; Common denominator:...
\((z^3+84z^2-159z+1)(-7+11z)^2\)
≈\(-85.852157\) | \(0\) | ≈\(0.00631\) | \(\frac{ 7}{ 11}\) | ≈\(1.845846\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
\(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
7
New Number: 5.29 | AESZ: 208 | Superseeker: 274/7 281388/7 | Hash: f1d6dfa8a5cdcc2513dfca4243565b2f
Degree: 5
\(7^{2} \theta^4-2 7 x\left(1056\theta^4+1884\theta^3+1397\theta^2+455\theta+56\right)+2^{2} 3 x^{2}\left(22760\theta^4+13672\theta^3-22537\theta^2-18116\theta-3584\right)-2^{4} x^{3}\left(53312\theta^4-162120\theta^3-195172\theta^2-78561\theta-11130\right)-2^{6} 19 x^{4}(1189\theta^2+2533\theta+1646)(2\theta+1)^2+2^{11} 19^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 1440, 196000, 32418400, ... --> OEIS Normalized instanton numbers (n0=1): 274/7, 6115/7, 281388/7, 2815228, 1699166270/7, ... ; Common denominator:...
\((4z+1)(512z^2-284z+1)(-7+76z)^2\)
\(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 71}{ 256}-\frac{ 17}{ 256}\sqrt{ 17}\) | \(\frac{ 7}{ 76}\) | \(\frac{ 71}{ 256}+\frac{ 17}{ 256}\sqrt{ 17}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
\(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
8
New Number: 1.12 | AESZ: 12 | Superseeker: 7776 66942277344 | Hash: ad7e2e881b3939396323eb746eb17a58
Degree: 1
\(\theta^4-2^{4} 3 x(6\theta+1)(4\theta+1)(4\theta+3)(6\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 720, 5821200, 75473798400, 1205906199498000, ... --> OEIS Normalized instanton numbers (n0=1): 7776, 13952088, 66942277344, 475338414733416, 4184555647748620320, ... ; Common denominator:...
\(1-27648z\)
\(0\) | \(\frac{ 1}{ 27648}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 6}\) |
\(0\) | \(1\) | \(\frac{ 1}{ 4}\) |
\(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
\(0\) | \(2\) | \(\frac{ 5}{ 6}\) |
9
New Number: 1.2 | AESZ: 2 | Superseeker: 231200 1700894366474400 | Hash: 709cba5c90462e9488c8a3dbbee8f89c
Degree: 1
\(\theta^4-2^{4} 5 x(10\theta+1)(10\theta+3)(10\theta+7)(10\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 15120, 3491888400, 1304290155168000, 601680868708529610000, ... --> OEIS Normalized instanton numbers (n0=1): 231200, 12215785600, 1700894366474400, 350154658851324656000, 89338191421813572850115680, ... ; Common denominator:...
\(1-800000z\)
\(0\) | \(\frac{ 1}{ 800000}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 10}\) |
\(0\) | \(1\) | \(\frac{ 3}{ 10}\) |
\(0\) | \(1\) | \(\frac{ 7}{ 10}\) |
\(0\) | \(2\) | \(\frac{ 9}{ 10}\) |