1
New Number: 2.11 | AESZ: 69 | Superseeker: 64 246848 | Hash: 729adc350de26d9415643078ed8d3867
Degree: 2
\(\theta^4-2^{2} x(4\theta+1)(4\theta+3)(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 6300, 1718640, 575675100, ... --> OEIS Normalized instanton numbers (n0=1): 64, 2616, 246848, 32024824, 5160268864, ... ; Common denominator:...
\((576z-1)(64z-1)\)
\(0\) | \(\frac{ 1}{ 576}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 4}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 4}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 4}\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 7}{ 4}\) |
2
New Number: 5.14 | AESZ: 116 | Superseeker: 64 23360 | Hash: 0b366ad8c78b6697205c5a7fff270f5b
Degree: 5
\(\theta^4-2^{5} x\left(10\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(52\theta^4+472\theta^3+832\theta^2+492\theta+103\right)+2^{16} x^{3}\left(14\theta^4+12\theta^3-96\theta^2-105\theta-29\right)-2^{18} x^{4}(2\theta+1)(56\theta^3+468\theta^2+646\theta+249)-2^{24} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 2448, 273920, 38525200, ... --> OEIS Normalized instanton numbers (n0=1): 64, 12, 23360, 654490, 53956288, ... ; Common denominator:...
\(-(-1+256z)(32z+1)^2(64z-1)^2\)
\(-\frac{ 1}{ 32}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 4}\) |
\(3\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 5}{ 4}\) |
\(4\) | \(0\) | \(2\) | \(1\) | \(\frac{ 3}{ 2}\) |
3
New Number: 12.2 | AESZ: | Superseeker: 64 39744 | Hash: b92032007ecbbf3af5801c4b1e4cf97a
Degree: 12
\(\theta^4+2^{5} x\theta(4\theta^3-10\theta^2-6\theta-1)-2^{8} x^{2}\left(92\theta^4+248\theta^3+200\theta^2+228\theta+89\right)-2^{14} x^{3}\left(84\theta^4+336\theta^3+664\theta^2+132\theta-51\right)+2^{18} x^{4}\left(944\theta^4+1312\theta^3+8928\theta^2+7384\theta+2567\right)-2^{26} x^{5}\left(176\theta^4-1456\theta^3-3477\theta^2-3814\theta-1741\right)-2^{32} x^{6}\left(216\theta^4+1200\theta^3+576\theta^2+1314\theta+697\right)+2^{38} x^{7}\left(456\theta^4+624\theta^3-3085\theta^2-5590\theta-3089\right)-2^{43} x^{8}\left(176\theta^4-3616\theta^3-2404\theta^2-288\theta+1027\right)-2^{50} x^{9}\left(208\theta^4+1824\theta^3+2581\theta^2+1434\theta+73\right)+2^{57} x^{10}\left(122\theta^4-44\theta^3-718\theta^2-1005\theta-410\right)-2^{62} 5 x^{11}\left(4\theta^4-32\theta^3-145\theta^2-190\theta-82\right)-2^{66} 5^{2} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 1424, 13312, 4213008, ... --> OEIS Normalized instanton numbers (n0=1): 64, -692, 39744, -2001358, 95440576, ... ; Common denominator:...
\(-(-1+64z+4096z^2)(64z-1)^2(64z+1)^2(655360z^3-4096z^2+96z+1)^2\)
\(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | \(-\frac{ 1}{ 64}\) | ≈\(-0.006598\) | \(0\) | ≈\(0.006424-0.013784I\) | ≈\(0.006424+0.013784I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
---|---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
\(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) |
\(2\) | \(1\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) | \(\frac{ 3}{ 2}\) |
4
New Number: 6.15 | AESZ: | Superseeker: 64 76608 | Hash: 0130ee676bad42a2e117bca3367f8cf0
Degree: 6
\(\theta^4+2^{4} x\left(56\theta^4+16\theta^3+22\theta^2+14\theta+3\right)+2^{10} x^{2}\left(308\theta^4+272\theta^3+347\theta^2+174\theta+35\right)+2^{18} x^{3}\left(212\theta^4+384\theta^3+473\theta^2+282\theta+69\right)+2^{26} x^{4}\left(77\theta^4+232\theta^3+327\theta^2+226\theta+62\right)+2^{35} x^{5}(7\theta^2+17\theta+13)(\theta+1)^2+2^{42} x^{6}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -48, 3088, -231168, 19207440, ... --> OEIS Normalized instanton numbers (n0=1): 64, -1732, 76608, -4429212, 296488640, ... ; Common denominator:...
\((64z+1)^2(128z+1)^2(256z+1)^2\)
\(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) |
\(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(2\) |
\(1\) | \(1\) | \(4\) | \(0\) | \(2\) |
5
New Number: 6.18 | AESZ: | Superseeker: 3 64 | Hash: b127e33287ed87a366c178fc4678cdc4
Degree: 6
\(\theta^4-x\left(18+94\theta+199\theta^2+210\theta^3+105\theta^4\right)+2 x^{2}\left(2095\theta^4+8380\theta^3+13298\theta^2+9836\theta+2850\right)-2^{2} 3^{2} x^{3}\left(2310\theta^4+13860\theta^3+30739\theta^2+29847\theta+10763\right)+2^{3} 3^{3} x^{4}\left(4044\theta^4+32352\theta^3+91997\theta^2+109172\theta+45693\right)-2^{4} 3^{3} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(61\theta^2+305\theta+345)+2^{5} 3^{5} 5^{2} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 348, 7320, 168840, ... --> OEIS Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...
\((6z-1)(15z-1)(14z-1)(42z-1)(18z-1)(10z-1)\)
\(0\) | \(\frac{ 1}{ 42}\) | \(\frac{ 1}{ 18}\) | \(\frac{ 1}{ 15}\) | \(\frac{ 1}{ 14}\) | \(\frac{ 1}{ 10}\) | \(\frac{ 1}{ 6}\) | \(\infty\) |
---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(4\) |
\(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(5\) |
6
New Number: 7.3 | AESZ: | Superseeker: 3 64 | Hash: 8413250555ca536f1bdccfeed506ea4e
Degree: 7
\(\theta^4+x\theta(39\theta^3-30\theta^2-19\theta-4)+2 x^{2}\left(16\theta^4-1070\theta^3-1057\theta^2-676\theta-192\right)-2^{2} 3^{2} x^{3}(3\theta+2)(171\theta^3+566\theta^2+600\theta+316)-2^{5} 3^{3} x^{4}\left(384\theta^4+1542\theta^3+2635\theta^2+2173\theta+702\right)-2^{6} 3^{3} x^{5}(\theta+1)(1393\theta^3+5571\theta^2+8378\theta+4584)-2^{10} 3^{5} x^{6}(\theta+1)(\theta+2)(31\theta^2+105\theta+98)-2^{12} 3^{7} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 192, 3384, ... --> OEIS Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...
\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(1+18z)^2\)
\(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 12}\) | \(-\frac{ 1}{ 18}\) | \(0\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
\(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(2\) |
\(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(3\) |