1
New Number: 4.13 | AESZ: ~37 | Superseeker: -128 -1546624/3 | Hash: c03e4e4ca58f9f1f76c98c8616bc2cbd
Degree: 4
\(\theta^4-2^{2} x\left(640\theta^4+1280\theta^3+1534\theta^2+894\theta+201\right)+2^{4} 3 x^{2}\left(45056\theta^4+180224\theta^3+308352\theta^2+256256\theta+86363\right)-2^{19} x^{3}(320\theta^2+960\theta+957)(2\theta+3)^2+2^{30} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 804, 655260, 563879792, 505573095132, ... --> OEIS Normalized instanton numbers (n0=1): -128, -5232, -1546624/3, -64705008, -7960717440, ... ; Common denominator:...
\((1024z-1)^2(256z-1)^2\)
\(0\) | \(\frac{ 1}{ 1024}\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
2
New Number: 4.14 | AESZ: | Superseeker: -340 -15174100/3 | Hash: a961869d91c2f73091913e8f8c4b5fa0
Degree: 4
\(\theta^4-2^{2} x\left(1088\theta^4+2176\theta^3+2579\theta^2+1491\theta+330\right)+2^{7} 3 x^{2}\left(12352\theta^4+49408\theta^3+74070\theta^2+49324\theta+12325\right)-2^{12} x^{3}(1088\theta^2+3264\theta+3225)(2\theta+3)^2+2^{18} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 1320, 2233320, 4108451200, 7880762169000, ... --> OEIS Normalized instanton numbers (n0=1): -340, -31985, -15174100/3, -1036481610, -246612212640, ... ; Common denominator:...
\((1-2176z+4096z^2)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 17}{ 64}-\frac{ 3}{ 16}\sqrt{ 2}\) | \(\frac{ 17}{ 64}+\frac{ 3}{ 16}\sqrt{ 2}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
3
New Number: 4.15 | AESZ: | Superseeker: -76 415420 | Hash: d8c866a60b2b4edb0c88e03315fa2a7b
Degree: 4
\(\theta^4-2^{2} x\left(448\theta^4+896\theta^3+1077\theta^2+629\theta+142\right)+2^{7} x^{2}\left(11456\theta^4+45824\theta^3+86434\theta^2+81220\theta+30693\right)-2^{12} 3^{4} x^{3}(448\theta^2+1344\theta+1343)(2\theta+3)^2+2^{18} 3^{8} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 568, 207720, 25669504, -32774007128, ... --> OEIS Normalized instanton numbers (n0=1): -76, 2958, 415420, 17891650, -1211214176, ... ; Common denominator:...
\((331776z^2-896z+1)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 5184}-\frac{ 1}{ 1296}\sqrt{ 2}I\) | \(\frac{ 7}{ 5184}+\frac{ 1}{ 1296}\sqrt{ 2}I\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
4
New Number: 4.16 | AESZ: | Superseeker: -208 -1863312 | Hash: ff22b96c1af3d06292a97d4dee085628
Degree: 4
\(\theta^4-2^{4} x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{9} x^{2}\left(4864\theta^4+19456\theta^3+30088\theta^2+21264\theta+5849\right)-2^{18} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{26} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 944, 1093840, 1379945728, 1816122981136, ... --> OEIS Normalized instanton numbers (n0=1): -208, -15098, -1863312, -284211001, -50414626800, ... ; Common denominator:...
\((1-1536z+65536z^2)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 3}{ 256}-\frac{ 1}{ 128}\sqrt{ 2}\) | \(\frac{ 3}{ 256}+\frac{ 1}{ 128}\sqrt{ 2}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
5
New Number: 4.17 | AESZ: | Superseeker: -156 -1229332 | Hash: 245e2566c8da93abbfc4296923ccba12
Degree: 4
\(\theta^4-2^{2} 3 x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{4} 3^{2} x^{2}\left(7680\theta^4+30720\theta^3+41040\theta^2+20640\theta+2203\right)+2^{12} 3^{4} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{18} 3^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 708, 700740, 738956400, 811309522500, ... --> OEIS Normalized instanton numbers (n0=1): -156, -12549, -1229332, -175559052, -27542017056, ... ; Common denominator:...
\((-1+1152z+110592z^2)^2\)
\(-\frac{ 1}{ 192}-\frac{ 1}{ 288}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 192}+\frac{ 1}{ 288}\sqrt{ 3}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
\(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
6
New Number: 4.18 | AESZ: | Superseeker: -100 126580 | Hash: 3ab4956c5da76dad5e104e338e7c0128
Degree: 4
\(\theta^4-2^{2} x\left(704\theta^4+1408\theta^3+1697\theta^2+993\theta+225\right)+2^{4} x^{2}\left(187904\theta^4+751616\theta^3+1350224\theta^2+1197216\theta+429975\right)-2^{12} 5^{3} x^{3}(704\theta^2+2112\theta+2115)(2\theta+3)^2+2^{18} 5^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 900, 701100, 515510800, 365497137900, ... --> OEIS Normalized instanton numbers (n0=1): -100, -1260, 126580, 12033300, 1211646512, ... ; Common denominator:...
\((512000z^2-1408z+1)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 8000}-\frac{ 1}{ 4000}I\) | \(\frac{ 11}{ 8000}+\frac{ 1}{ 4000}I\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |