1
New Number: 2.60 | AESZ: 18 | Superseeker: 4 364 | Hash: bb479f8a4185bf4a943dba2d433e13e5
Degree: 2
\(\theta^4-2^{2} x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{4} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 108, 3280, 126700, ... --> OEIS Normalized instanton numbers (n0=1): 4, 39, 364, 6800, 662416/5, ... ; Common denominator:...
\(-(16z+1)(64z-1)\)
| \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 5}{ 4}\) |
| \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
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: 5.2 | AESZ: 19 | Superseeker: 80/23 4655/23 | Hash: 4532f44d62f644bf66aa7b153d4f5c5a
Degree: 5
\(23^{2} \theta^4-23 x\left(921\theta^4+2046\theta^3+1644\theta^2+621\theta+92\right)-x^{2}\left(380851\theta^4+1328584\theta^3+1772673\theta^2+1033528\theta+221168\right)-2 x^{3}\left(475861\theta^4+1310172\theta^3+1028791\theta^2+208932\theta-27232\right)-2^{2} 17 x^{4}\left(8873\theta^4+14020\theta^3+5139\theta^2-1664\theta-976\right)+2^{3} 3 17^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 84, 2200, 71140, ... --> OEIS Normalized instanton numbers (n0=1): 80/23, 1157/46, 4655/23, 71184/23, 1156690/23, ... ; Common denominator:...
\((54z-1)(z^2-11z-1)(23+34z)^2\)
| \(-\frac{ 23}{ 34}\) | \(\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(0\) | \(\frac{ 1}{ 54}\) | \(\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |
4
New Number: 5.47 | AESZ: 246 | Superseeker: -4/5 -108/5 | Hash: f51a0c39f9179dc6a561b9afb6f9d85f
Degree: 5
\(5^{2} \theta^4-2^{2} 5 x\left(12\theta^4+48\theta^3+49\theta^2+25\theta+5\right)-2^{4} x^{2}\left(544\theta^4+1792\theta^3+2444\theta^2+1580\theta+405\right)+2^{9} x^{3}\left(112\theta^4+960\theta^3+2306\theta^2+2130\theta+685\right)+2^{12} x^{4}\left(144\theta^4+768\theta^3+1308\theta^2+924\theta+235\right)+2^{20} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 44, 400, 5356, ... --> OEIS Normalized instanton numbers (n0=1): -4/5, 22/5, -108/5, 694/5, -1040, ... ; Common denominator:...
\((1+16z)(16z+5)^2(16z-1)^2\)
| \(-\frac{ 5}{ 16}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(1\) | \(1\) |
5
New Number: 5.4 | AESZ: 21 | Superseeker: 8/5 152/5 | Hash: 42a2bc0f0ee2a405ede956176c95721f
Degree: 5
\(5^{2} \theta^4-2^{2} 5 x\left(36\theta^4+84\theta^3+72\theta^2+30\theta+5\right)-2^{4} x^{2}\left(181\theta^4+268\theta^3+71\theta^2-70\theta-35\right)+2^{8} x^{3}(\theta+1)(37\theta^3+248\theta^2+375\theta+165)+2^{10} x^{4}\left(39\theta^4+198\theta^3+331\theta^2+232\theta+59\right)+2^{15} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 44, 688, 13036, ... --> OEIS Normalized instanton numbers (n0=1): 8/5, 57/10, 152/5, 253, 11552/5, ... ; Common denominator:...
\((4z+1)(32z-1)(4z-1)(8z+5)^2\)
| \(-\frac{ 5}{ 8}\) | \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(1\) |
6
New Number: 5.80 | AESZ: 311 | Superseeker: 25/13 875/13 | Hash: 8219f3f4bd56f6c2b2cc3ab9093b65d1
Degree: 5
\(13^{2} \theta^4-13 x\left(327\theta^4+1038\theta^3+857\theta^2+338\theta+52\right)-2^{4} x^{2}\left(12848\theta^4+42008\theta^3+52082\theta^2+28548\theta+5707\right)-2^{11} x^{3}\left(122\theta^4-1872\theta^3-6341\theta^2-5772\theta-1547\right)+2^{16} x^{4}(2\theta+1)(76\theta^3+426\theta^2+570\theta+227)+2^{23} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 84, 1840, 56980, ... --> OEIS Normalized instanton numbers (n0=1): 25/13, 1359/52, 875/13, 36572/13, 256800/13, ... ; Common denominator:...
\((8192z^3-896z^2-35z+1)(13+64z)^2\)
| \(-\frac{ 13}{ 64}\) | ≈\(-0.045147\) | \(0\) | ≈\(0.020117\) | ≈\(0.134405\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
7
New Number: 5.87 | AESZ: 321 | Superseeker: 35/9 3002/9 | Hash: b786027c217dd5d5c5abac7b1ecc570b
Degree: 5
\(3^{4} \theta^4-3^{2} x\left(191\theta^4+862\theta^3+683\theta^2+252\theta+36\right)-2^{5} x^{2}\left(7225\theta^4+24835\theta^3+30634\theta^2+16173\theta+3069\right)-2^{8} x^{3}\left(13251\theta^4+35856\theta^3+27641\theta^2+6966\theta+180\right)-2^{12} 5 x^{4}(2\theta+1)(314\theta^3+363\theta^2+68\theta-31)+2^{16} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 132, 4000, 179620, ... --> OEIS Normalized instanton numbers (n0=1): 35/9, 261/4, 3002/9, 126800/9, 1727129/9, ... ; Common denominator:...
\((32z+1)(32z^2-71z+1)(9+80z)^2\)
| \(-\frac{ 9}{ 80}\) | \(-\frac{ 1}{ 32}\) | \(0\) | \(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | \(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
8
New Number: 5.98 | AESZ: 341 | Superseeker: 87/13 21589/13 | Hash: eed12a307d671fcf681b9d108c5e4c9e
Degree: 5
\(13^{2} \theta^4-13 x\left(1217\theta^4+1474\theta^3+1127\theta^2+390\theta+52\right)-2^{4} x^{2}\left(5134\theta^4+83956\theta^3+142024\theta^2+83616\theta+16575\right)+2^{6} x^{3}\left(142492\theta^4+565032\theta^3+604615\theta^2+269841\theta+44070\right)-2^{11} 5 x^{4}(2\theta+1)(4324\theta^3+10698\theta^2+9903\theta+3110)+2^{16} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 180, 7600, 433300, ... --> OEIS Normalized instanton numbers (n0=1): 87/13, 1532/13, 21589/13, 589110/13, 17749920/13, ... ; Common denominator:...
\((27z+1)(256z^2-96z+1)(-13+160z)^2\)
| \(-\frac{ 1}{ 27}\) | \(0\) | \(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\) | \(\frac{ 13}{ 160}\) | \(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 4}{ 3}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
9
New Number: 11.20 | AESZ: | Superseeker: 21/4 1285/2 | Hash: b07e191c8c5d8b6a2c25e842f85fcaf0
Degree: 11
\(2^{4} \theta^4-2^{2} x\left(278\theta^4+394\theta^3+309\theta^2+112\theta+16\right)-x^{2}\left(11952+57616\theta+96951\theta^2+56722\theta^3+4615\theta^4\right)+2 x^{3}\left(129366\theta^4+473682\theta^3+531879\theta^2+282576\theta+62656\right)-x^{4}\left(1430728+5365104\theta+7153953\theta^2+3814866\theta^3+1139565\theta^4\right)-2 3 x^{5}\left(286602\theta^4-694990\theta^3-3072025\theta^2-2917584\theta-895328\right)+2^{2} x^{6}\left(1338547\theta^4+4488552\theta^3+821964\theta^2-3171240\theta-1633306\right)+2^{4} x^{7}\left(17380\theta^4-1361536\theta^3-2049918\theta^2-1043692\theta-152703\right)-2^{6} x^{8}\left(106051\theta^4+123172\theta^3+23589\theta^2-28382\theta-10873\right)+2^{10} x^{9}\left(4885\theta^4+15033\theta^3+20559\theta^2+13908\theta+3737\right)-2^{12} x^{10}\left(335\theta^4+1270\theta^3+1875\theta^2+1240\theta+307\right)+2^{17} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 116, 3856, 163636, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, 1965/32, 1285/2, 103095/8, 1157421/4, ... ; Common denominator:...
\((z-1)(16z^2-16z-1)(32z^2-71z+1)(4-27z-50z^2+16z^3)^2\)
| ≈\(-0.573963\) | \(\frac{ 1}{ 2}-\frac{ 1}{ 4}\sqrt{ 5}\) | \(0\) | \(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | ≈\(0.121762\) | \(1\) | \(\frac{ 1}{ 2}+\frac{ 1}{ 4}\sqrt{ 5}\) | \(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | ≈\(3.577201\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
10
New Number: 13.15 | AESZ: | Superseeker: 6 626/3 | Hash: 3e24fdfe8119ac950ce846460f109e44
Degree: 13
\(\theta^4-2 x\left(16\theta^4+50\theta^3+39\theta^2+14\theta+2\right)-2^{2} x^{2}\left(219\theta^4+390\theta^3+335\theta^2+214\theta+62\right)-2^{4} x^{3}\left(115\theta^4+1068\theta^3+2660\theta^2+2022\theta+582\right)+2^{6} x^{4}\left(122\theta^4-788\theta^3+151\theta^2-913\theta-696\right)-2^{8} 3 x^{5}\left(303\theta^4-1488\theta^3-2955\theta^2-2550\theta-827\right)-2^{10} 3 x^{6}\left(37\theta^4+714\theta^3-5760\theta^2-8319\theta-3550\right)-2^{13} 3 x^{7}\left(101\theta^4+82\theta^3+102\theta^2-1679\theta-1322\right)+2^{15} 3 x^{8}\left(48\theta^4+948\theta^3-461\theta^2-1447\theta-628\right)-2^{17} x^{9}\left(89\theta^4-4392\theta^3-6123\theta^2-450\theta+1902\right)-2^{20} x^{10}\left(121\theta^4-532\theta^3-3072\theta^2-3697\theta-1348\right)+2^{23} 5 x^{11}(\theta+1)(21\theta^3+63\theta^2+206\theta+218)+2^{25} 5^{2} x^{12}(\theta+2)(\theta+1)(2\theta^2-12\theta-27)+2^{27} 5^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 76, 1936, 57820, ... --> OEIS Normalized instanton numbers (n0=1): 6, 41/4, 626/3, 12349/8, 33062, ... ; Common denominator:...
\((4z-1)(4z+1)(16z^2+4z+1)(640z^3+96z^2+48z-1)(1+6z-48z^2+320z^3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 8}\sqrt{ 3}I\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 8}\sqrt{ 3}I\) | ≈\(-0.084967-0.266773I\) | ≈\(-0.084967+0.266773I\) | ≈\(-0.082432\) | \(0\) | ≈\(0.019933\) | ≈\(0.116216-0.156217I\) | ≈\(0.116216+0.156217I\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(3\) |
11
New Number: 7.6 | AESZ: | Superseeker: 1/3 5/3 | Hash: 24ba77c97bc4b46c39a41c77cc1d1ef4
Degree: 7
\(3^{2} \theta^4-3 x\left(112\theta^4+140\theta^3+133\theta^2+63\theta+12\right)+x^{2}\left(4393\theta^4+9340\theta^3+10903\theta^2+6360\theta+1488\right)-2 x^{3}\left(11669\theta^4+27720\theta^3+27019\theta^2+8460\theta-912\right)+2^{2} x^{4}\left(6799\theta^4-10288\theta^3-82183\theta^2-119168\theta-52672\right)+2^{3} 7 x^{5}(\theta+1)(2611\theta^3+15537\theta^2+26998\theta+14360)-2^{6} 7^{2} x^{6}(\theta+1)(\theta+2)(83\theta^2+105\theta-66)-2^{10} 7^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 28, 232, 2188, ... --> OEIS Normalized instanton numbers (n0=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...
\(-(2z+1)(8z-1)(7z-1)(16z-1)(z+1)(-3+14z)^2\)
| \(-1\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 7}\) | \(\frac{ 3}{ 14}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(3\) |
12
New Number: 8.18 | AESZ: 197 | Superseeker: 3 1621/13 | Hash: 4cc8bdba73e5fa6cb4089fa5296429de
Degree: 8
\(13^{2} \theta^4-13^{2} x\left(41\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-2^{3} 13 x^{2}\left(471\theta^4+1788\theta^3+2555\theta^2+1534\theta+338\right)+2^{6} 13 x^{3}\left(251\theta^4+1014\theta^3+1798\theta^2+1413\theta+405\right)+2^{9} x^{4}\left(749\theta^4+436\theta^3-4908\theta^2-6266\theta-2145\right)-2^{12} x^{5}\left(379\theta^4+1270\theta^3+967\theta^2-42\theta-178\right)-2^{15} x^{6}\left(9\theta^4-156\theta^3-273\theta^2-156\theta-28\right)+2^{18} x^{7}\left(13\theta^4+26\theta^3+20\theta^2+7\theta+1\right)-2^{21} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 68, 1552, 43156, ... --> OEIS Normalized instanton numbers (n0=1): 3, 226/13, 1621/13, 20666/13, 289056/13, ... ; Common denominator:...
\(-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2\)
| \(-\frac{ 1}{ 8}\sqrt{ 13}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}\) | \(\frac{ 1}{ 8}\sqrt{ 13}\) | \(\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
13
New Number: 8.24 | AESZ: 286 | Superseeker: 3 437/3 | Hash: 94afcd38a40c3a3e54fc3c57b4b85459
Degree: 8
\(3^{2} \theta^4-3^{2} x\left(38\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-3 x^{2}\left(2045\theta^4+5702\theta^3+7535\theta^2+4170\theta+852\right)+2^{3} 3 x^{3}\left(2208\theta^4+5925\theta^3+7925\theta^2+5607\theta+1512\right)+2^{3} x^{4}\left(60287\theta^4+56374\theta^3-215983\theta^2-268986\theta-85452\right)-2^{4} x^{5}\left(205651\theta^4+605608\theta^3+603579\theta^2+204622\theta+8104\right)-2^{7} x^{6}\left(51414\theta^4-273267\theta^3-502700\theta^2-305649\theta-63398\right)+2^{8} 37 x^{7}\left(7909\theta^4+18122\theta^3+17595\theta^2+8462\theta+1672\right)-2^{13} 37^{2} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 72, 1696, 49960, ... --> OEIS Normalized instanton numbers (n0=1): 3, 539/24, 437/3, 18531/8, 90274/3, ... ; Common denominator:...
\(-(-1+40z+504z^2-3088z^3+8192z^4)(-3-3z+148z^2)^2\)
| \(\frac{ 3}{ 296}-\frac{ 1}{ 296}\sqrt{ 1785}\) | ≈\(-0.070843\) | \(0\) | ≈\(0.020383\) | \(\frac{ 3}{ 296}+\frac{ 1}{ 296}\sqrt{ 1785}\) | ≈\(0.213707\) | ≈\(0.213707\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(\frac{ 5}{ 4}\) |
14
New Number: 8.47 | AESZ: | Superseeker: 31/3 43174/9 | Hash: b79bf25fcecf028aa40c1a6a8233efe7
Degree: 8
\(3^{4} \theta^4-3^{3} x\left(367\theta^4+398\theta^3+295\theta^2+96\theta+12\right)-2^{4} 3^{3} x^{2}\left(200\theta^4+2081\theta^3+3614\theta^2+2009\theta+392\right)+2^{6} 3 x^{3}\left(72449\theta^4+102684\theta^3-48579\theta^2-77922\theta-22536\right)+2^{10} x^{4}\left(109873\theta^4+619970\theta^3+56260\theta^2-219027\theta-78216\right)-2^{14} 7 x^{5}\left(40669\theta^4-18266\theta^3-36570\theta^2-16190\theta-1955\right)-2^{17} 7 x^{6}\left(80805\theta^4+76590\theta^3+51265\theta^2+23076\theta+4780\right)-2^{24} 7^{2} x^{7}\left(437\theta^4+1117\theta^3+1236\theta^2+664\theta+140\right)-2^{29} 3 7^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 228, 12640, 901540, ... --> OEIS Normalized instanton numbers (n0=1): 31/3, 1964/9, 43174/9, 1469755/9, 19813517/3, ... ; Common denominator:...
\(-(27z+1)(2048z^3+768z^2+112z-1)(-9+168z+3584z^2)^2\)
| ≈\(-0.191715-0.145483I\) | ≈\(-0.191715+0.145483I\) | \(-\frac{ 3}{ 128}-\frac{ 3}{ 896}\sqrt{ 273}\) | \(-\frac{ 1}{ 27}\) | \(0\) | ≈\(0.00843\) | \(-\frac{ 3}{ 128}+\frac{ 3}{ 896}\sqrt{ 273}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 4}{ 3}\) |
15
New Number: 9.5 | AESZ: | Superseeker: 17/3 4127/9 | Hash: 98a7e046a956f1c9ec13973072ab8283
Degree: 9
\(3^{2} \theta^4-3 x\left(152\theta^4+316\theta^3+245\theta^2+87\theta+12\right)-x^{2}\left(5808+25608\theta+43193\theta^2+31076\theta^3+8807\theta^4\right)-2 x^{3}\left(10633\theta^4+106320\theta^3+235087\theta^2+185292\theta+52896\right)+2^{2} x^{4}\left(65651\theta^4+19144\theta^3-434467\theta^2-508704\theta-175376\right)+2^{3} x^{5}\left(151497\theta^4+645060\theta^3+272053\theta^2-269230\theta-183720\right)-2^{8} x^{6}\left(3386\theta^4-52470\theta^3-83275\theta^2-46299\theta-7926\right)-2^{10} x^{7}\left(11425\theta^4+14072\theta^3-3794\theta^2-13632\theta-5575\right)-2^{15} x^{8}(590\theta^2+1126\theta+597)(\theta+1)^2-2^{20} 3^{2} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 108, 3496, 137548, ... --> OEIS Normalized instanton numbers (n0=1): 17/3, 257/6, 4127/9, 23827/3, 496999/3, ... ; Common denominator:...
\(-(9z+1)(2z+1)(z+1)(128z^2+64z-1)(-3-2z+64z^2)^2\)
| \(-1\) | \(-\frac{ 1}{ 4}-\frac{ 3}{ 16}\sqrt{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 1}{ 64}-\frac{ 1}{ 64}\sqrt{ 193}\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 1}{ 4}+\frac{ 3}{ 16}\sqrt{ 2}\) | \(\frac{ 1}{ 64}+\frac{ 1}{ 64}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) |
16
New Number: 24.14 | AESZ: | Superseeker: 16/3 -880/81 | Hash: 13173bd8cb75baee8a898c9c6303c117
Degree: 24
\(3^{3} \theta^4-2^{2} 3^{2} x\left(30\theta^4+68\theta^3+54\theta^2+20\theta+3\right)+2^{4} 3 x^{2}\left(129\theta^4+1036\theta^3+1445\theta^2+626\theta+57\right)+2^{6} x^{3}\left(6560\theta^4+16168\theta^3+28438\theta^2+29162\theta+11793\right)-2^{10} x^{4}\left(4293\theta^4-840\theta^3-26162\theta^2-17539\theta-3471\right)+2^{10} x^{5}\left(4576\theta^4-45960\theta^3-527326\theta^2-531090\theta-17739\right)+2^{12} x^{6}\left(253469\theta^4+268652\theta^3-420979\theta^2-1072742\theta-642319\right)-2^{14} x^{7}\left(268866\theta^4-966996\theta^3-216550\theta^2-153200\theta-178363\right)-2^{16} x^{8}\left(275621\theta^4+368724\theta^3+3817808\theta^2+1152648\theta-238416\right)+2^{19} x^{9}\left(1243022\theta^4-155108\theta^3-180362\theta^2+244748\theta+432025\right)+2^{21} x^{10}\left(71199\theta^4+1979580\theta^3+6105329\theta^2+7846418\theta+3871903\right)-2^{23} x^{11}\left(2529316\theta^4+8376456\theta^3+16354702\theta^2+16114830\theta+6536563\right)-2^{27} x^{12}\left(6408\theta^4-138306\theta^3+103491\theta^2+823698\theta+691409\right)+2^{27} x^{13}\left(2135212\theta^4+13297720\theta^3+38159702\theta^2+52119782\theta+27312351\right)-2^{29} x^{14}\left(16747\theta^4+2690700\theta^3+12019727\theta^2+19459890\theta+113394717\right)-2^{31} x^{15}\left(904020\theta^4+7252460\theta^3+24658966\theta^2+39551016\theta+23394717\right)-2^{32} x^{16}\left(80943\theta^4-2350848\theta^3-16468568\theta^2-35556904\theta-24607808\right)+2^{34} x^{17}\left(439874\theta^4+3498636\theta^3+9750362\theta^2+12302316\theta+5737785\right)+2^{36} x^{18}\left(71951\theta^4+208996\theta^3-152285\theta^2-1478458\theta-1394681\right)-2^{38} x^{19}\left(76872\theta^4+678456\theta^3+1854170\theta^2+1720414\theta+306971\right)-2^{42} x^{20}\left(2563\theta^4+5100\theta^3+1540\theta^2-9969\theta-11723\right)+2^{42} x^{21}\left(5752\theta^4+39608\theta^3+102098\theta^2+114550\theta+48355\right)+2^{44} x^{22}\left(1489\theta^4+8620\theta^3+16833\theta^2+13450\theta+3789\right)-2^{46} 5 x^{23}\left(106\theta^4+684\theta^3+1682\theta^2+1872\theta+797\right)+2^{48} 5^{2} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 52, 464, 1412, ... --> OEIS Normalized instanton numbers (n0=1): 16/3, -133/18, -880/81, -247636/243, 44329772416/11390625, ... ; Common denominator:...
\(27-1080z+26194765020135424z^22-37295434414161920z^23+7036874417766400z^24+1038209024z^6-4405100544z^7-18063097856z^8+651701518336z^9+149315125248z^10-347647537840128z^16+7556977777442816z^17+6192z^2+419840z^3-4396032z^4+4685824z^5+4944435070631936z^18-21217440432128z^11-860067201024z^12+286583303438336z^13-8990977163264z^14-1941368167464960z^15-21130414462599168z^19-11272193207959552z^20+25297563531870208z^21\)
No data for singularities
17
New Number: 24.15 | AESZ: | Superseeker: -88 -460066696/273375 | Hash: 887043ef505443b5b0c0fc70e222c6e8
Degree: 24
\(5^{2} \theta^4-2^{2} 5 x\left(106\theta^4+286\theta^3+40\theta+5\right)+2^{4} x^{2}\left(1489\theta^4+3292\theta^3+849\theta^2-1910\theta-915\right)+2^{6} x^{3}\left(5752\theta^4+6408\theta^3+2498\theta^2+2610\theta+2815\right)-2^{10} x^{4}\left(2563\theta^4+15404\theta^3+32452\theta^2+36945\theta+14583\right)-2^{10} x^{5}\left(76872\theta^4-63480\theta^3-371638\theta^2+14698\theta+85127\right)+2^{12} x^{6}\left(71951\theta^4+366612\theta^3+320563\theta^2+663798\theta+432343\right)+2^{14} x^{7}\left(439874\theta^4+20356\theta^3-684478\theta^2-1208532\theta-816503\right)-2^{16} x^{8}\left(80943\theta^4+2998392\theta^3-420848\theta^2+482984\theta+733600\right)-2^{19} x^{9}\left(904030\theta^4-20220\theta^3+2840926\theta^2+984288\theta-626651\right)-2^{21} x^{10}\left(16747\theta^4-2556724\theta^3-3722545\theta^2-3133478\theta-767489\right)+2^{23} x^{11}\left(2135212\theta^4+3783976\theta^3+9618470\theta^2+9273170\theta+3493227\right)-2^{27} x^{12}\left(6408\theta^4+189570\theta^3+1087119\theta^2+1454994\theta+666953\right)-2^{27} x^{13}\left(2529316\theta^4+11858072\theta^3+26799550\theta^2+29724618\theta+13183119\right)+2^{29} x^{14}\left(71199\theta^4-1409988\theta^3-4063265\theta^2-4901254\theta-2096633\right)+2^{31} x^{15}\left(1243022\theta^4+10099284\theta^3+30582814\theta^2+40671804\theta+20350297\right)-2^{32} x^{16}\left(275621\theta^4-1482272\theta^3-11690728\theta^2-21308424\theta-12360464\right)-2^{34} x^{17}\left(268866\theta^4+3117924\theta^3+12038210\theta^2+19494664\theta+11299661\right)+2^{36} x^{18}\left(252469\theta^4+1751100\theta^3+4026365\theta^2+4244010\theta+1709537\right)+2^{38} x^{19}\left(4576\theta^4+82568\theta^3-141742\theta^2-880262\theta-783621\right)-2^{42} x^{20}\left(4293\theta^4+35184\theta^3+81910\theta^2+60347\theta+2367\right)+2^{42} x^{21}\left(6560\theta^4+36312\theta^3+88870\theta^2+100494\theta+42837\right)+2^{44} 3 x^{22}\left(3129\theta^4-4\theta^3-1675\theta^2-315\theta-1639\right)-2^{46} 3^{2} x^{23}\left(30\theta^4+172\theta^3+366\theta^2+340\theta+115\right)+2^{48} 3^{3} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 124, 1946288/405, 472190641/2025, ... --> OEIS Normalized instanton numbers (n0=1): -88, -429/50, -460066696/273375, -147036093041/4860000, -1648362827374336/2373046875, ... ; Common denominator:...
\(25-2120z+165137850398932992z^22-18999560927969280z^23+7599824371187712z^24+294711296z^6+7206895616z^7-5304680448z^8-473972080640z^9-35121004544z^10-1183783181090816z^16-4619082708025344z^17+23824z^2+368128z^3-2624512z^4-78716928z^5+17349537572061184z^18+17911456464896z^11-860067201024z^12-339479046914048z^13+38224672063488z^14+2669369419104256z^15+1257841302175744z^19-18880813672169472z^20+28851185112842240z^21\)
No data for singularities
18
New Number: 24.17 | AESZ: | Superseeker: -24 -9598768/30375 | Hash: 1eb6cea72aa2a282481ca5e3b2422017
Degree: 24
\(5^{2} \theta^4+2^{2} 5 x\left(47\theta^4-23\theta^3-20\theta-5\right)-2^{4} x^{2}\left(179\theta^4-5548\theta^3-7291\theta^2-4350\theta-905\right)-2^{7} x^{3}\left(2935\theta^4-7002\theta^3+8317\theta^2+33810\theta+15415\right)-2^{10} x^{4}\left(5449\theta^4+91862\theta^3+82862\theta^2-10173\theta-6981\right)+2^{12} x^{5}\left(16533\theta^4-102630\theta^3-137351\theta^2-442384\theta-214109\right)+2^{14} x^{6}\left(377045\theta^4+2384088\theta^3+768917\theta^2+3480360\theta+214109\right)-2^{17} x^{7}\left(238805\theta^4+58138\theta^3-4280001\theta^2-3095246\theta-1210167\right)-2^{20} x^{8}\left(2326731\theta^4+9363624\theta^3+12365844\theta^2+16867914\theta+8008789\right)+2^{23} x^{9}\left(27688\theta^4+2998464\theta^3+263994\theta^2+1516404\theta-885283\right)+2^{26} x^{10}\left(5764462\theta^4+2998464\theta^3+263994\theta^2+1516404\theta-885283\right)-2^{29} x^{11}\left(11329982\theta^4+30867704\theta^3+61886406\theta^2+61158272\theta+23162227\right)-2^{32} x^{12}\left(2120418\theta^4+36058992\theta^3+87838628\theta^2+106632978\theta+502460529\right)+2^{35} x^{13}\left(16849298\theta^4+91712872\theta^3+212023454\theta^2+244238244\theta+110360529\right)-2^{38} x^{14}\left(10049328\theta^4+37236768\theta^3+66644650\theta^2+63907082\theta+25441423\right)-2^{41} x^{15}\left(4736512\theta^4+53071212\theta^3+174736084\theta^2+241175316\theta+122040421\right)+2^{44} x^{16}\left(8122336\theta^4+67434512\theta^3+211414476\theta^2+291782162\theta+149636409\right)-2^{47} x^{17}\left(3596934\theta^4+30695376\theta^3+102692394\theta^2+149709348\theta+804776873\right)+2^{50} x^{18}\left(344350\theta^4+4792416\theta^3+22792344\theta^2+40780218\theta+25076261\right)+2^{53} x^{19}\left(255290\theta^4+1201696\theta^3+241498\theta^2-4145416\theta-4163853\right)-2^{56} x^{20}\left(91962\theta^4+642936\theta^3+1364188\theta^2+959498\theta+45723\right)+2^{59} x^{21}\left(6076\theta^4+85188\theta^3+269096\theta^2+322380\theta+129693\right)+2^{62} 3 x^{22}\left(777\theta^4+2264\theta^3+431\theta^2-3906\theta-3016\right)-2^{65} 3^{2} x^{23}\left(51\theta^4+314\theta^3+741\theta^2+794\theta+326\right)+2^{68} 3^{3} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, -36, 8912/15, 688859/150, ... --> OEIS Normalized instanton numbers (n0=1): -24, 802/25, -9598768/30375, 31786366/5625, -5158982190959/52734375, ... ; Common denominator:...
\(25+940z+10749840108954241204224z^22-16934111059665368383488z^23+7968993439842526298112z^24+6177505280z^6-31300648960z^7-2439754285056z^8+232263778304z^9+386846496391168z^10+142889646027257675776z^16-506223456939883364352z^17-2864z^2-375680z^3-5579776z^4+67719168z^5+387703632921257574400z^18-6082737769283584z^11-9107125963849728z^12+578937470964465664z^13-2762338246833733632z^14-10415700038201114624z^15+2299447897742827847680z^19-6626560462915928850432z^20+3502575530995601113088z^21\)
No data for singularities