1
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:...
\(-(65536z^2+2816z-1)(1+512z)^2\)
| \(-\frac{ 11}{ 512}-\frac{ 5}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | \(0\) | \(s_2\) | \(s_1\) | \(-\frac{ 11}{ 512}+\frac{ 5}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
2
New Number: 5.104 | AESZ: 357 | Superseeker: 7/13 21/13 | Hash: afee0651c9b3b8e98079f5c2d5bfa8a5
Degree: 5
\(13^{2} \theta^4-13 x\left(441\theta^4+690\theta^3+631\theta^2+286\theta+52\right)+2^{4} x^{2}\left(5121\theta^4+15576\theta^3+21215\theta^2+13702\theta+3445\right)-2^{10} x^{3}\left(640\theta^4+2847\theta^3+5078\theta^2+4056\theta+1196\right)+2^{14} x^{4}\left(125\theta^4+562\theta^3+905\theta^2+624\theta+157\right)-2^{21} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 20, 112, 916, ... --> OEIS Normalized instanton numbers (n0=1): 7/13, -10/13, 21/13, 296/13, 608/13, ... ; Common denominator:...
\(-(16z-1)(128z^2-13z+1)(-13+32z)^2\)
| \(0\) | \(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\) | \(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 13}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
3
New Number: 12.17 | AESZ: | Superseeker: 4 52 | Hash: e65be092d4832d3740d2a3078755f447
Degree: 12
\(\theta^4+2^{2} x\left(24\theta^4+6\theta^3+11\theta^2+8\theta+2\right)+2^{4} x^{2}\left(209\theta^4+2\theta^3+23\theta^2-10\right)+2^{7} x^{3}\left(223\theta^4-1218\theta^3-2225\theta^2-2088\theta-776\right)-2^{10} x^{4}\left(1409\theta^4+9634\theta^3+19337\theta^2+18420\theta+6872\right)-2^{13} x^{5}\left(6527\theta^4+35858\theta^3+78357\theta^2+78428\theta+30414\right)-2^{17} x^{6}\left(6276\theta^4+37704\theta^3+91143\theta^2+97914\theta+40036\right)-2^{21} x^{7}\left(2923\theta^4+22130\theta^3+61939\theta^2+73401\theta+32138\right)-2^{24} x^{8}\left(602\theta^4+10928\theta^3+42765\theta^2+60182\theta+29287\right)+2^{26} x^{9}\left(2352\theta^4+7392\theta^3-7024\theta^2-31968\theta-21891\right)+2^{29} x^{10}\left(1584\theta^4+11904\theta^3+24696\theta^2+19776\theta+4915\right)-2^{35} x^{11}\left(16\theta^4-176\theta^3-784\theta^2-1036\theta-449\right)-2^{39} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1152, 19216, ... --> OEIS Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...
\(-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 16}\) | ≈\(-0.057187-0.018391I\) | ≈\(-0.057187+0.018391I\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | ≈\(0.270624\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
4
New Number: 8.29 | AESZ: 304 | Superseeker: -5 -641 | Hash: cf055a245b1537ed4f2609fa56cf67aa
Degree: 8
\(\theta^4+x\left(82\theta^4+98\theta^3+77\theta^2+28\theta+4\right)-x^{2}\left(636+2916\theta+4463\theta^2+1850\theta^3-553\theta^4\right)-2^{2} x^{3}\left(6087\theta^4+22542\theta^3+27199\theta^2+14916\theta+3136\right)-2^{5} x^{4}\left(7241\theta^4+22750\theta^3+42326\theta^2+29943\theta+7272\right)+2^{7} x^{5}\left(7524\theta^4+1998\theta^3-23019\theta^2-24627\theta-7186\right)+2^{8} x^{6}\left(22961\theta^4+93930\theta^3+88283\theta^2+28194\theta+1624\right)-2^{10} 13 x^{7}\left(1505\theta^4+3274\theta^3+2919\theta^2+1282\theta+236\right)+2^{14} 13^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 112, -3712, 155536, ... --> OEIS Normalized instanton numbers (n0=1): -5, 469/8, -641, 50173/4, -276231, ... ; Common denominator:...
\((16z-1)(64z^3-432z^2-76z-1)(-1-11z+52z^2)^2\)
| ≈\(-0.157556\) | \(\frac{ 11}{ 104}-\frac{ 1}{ 104}\sqrt{ 329}\) | ≈\(-0.014327\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 11}{ 104}+\frac{ 1}{ 104}\sqrt{ 329}\) | ≈\(6.921883\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
5
New Number: 8.42 | AESZ: | Superseeker: -4 140 | Hash: 7bc3855c04953ca11620400320722844
Degree: 8
\(\theta^4+2^{2} x\left(26\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(305\theta^4+662\theta^3+781\theta^2+436\theta+94\right)+2^{8} x^{3}\left(519\theta^4+1278\theta^3+1541\theta^2+933\theta+213\right)+2^{10} x^{4}\left(2266\theta^4+4988\theta^3+3535\theta^2+633\theta-162\right)+2^{14} 3 x^{5}\left(569\theta^4+1184\theta^3+740\theta^2-81\theta-128\right)+2^{18} 3 x^{6}\left(254\theta^4+354\theta^3+161\theta^2-33\theta-28\right)+2^{22} 3^{2} x^{7}\left(23\theta^4+34\theta^3+8\theta^2-9\theta-4\right)-2^{27} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1664, 23056, ... --> OEIS Normalized instanton numbers (n0=1): -4, 1/2, 140, 1025/2, -9196, ... ; Common denominator:...
\(-(32z+1)(1024z^3-896z^2-48z-1)(1+12z+192z^2)^2\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 96}\sqrt{ 39}I\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 96}\sqrt{ 39}I\) | ≈\(-0.025859-0.019623I\) | ≈\(-0.025859+0.019623I\) | \(0\) | ≈\(0.926719\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(1\) |