1
New Number: 3.1 | AESZ: 34 | Superseeker: 1 28/3 | Hash: e5461c5f5ae4d929328f66b8955a31f5
Degree: 3
\(\theta^4-x\left(35\theta^4+70\theta^3+63\theta^2+28\theta+5\right)+x^{2}(\theta+1)^2(259\theta^2+518\theta+285)-3^{2} 5^{2} x^{3}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ... --> OEIS Normalized instanton numbers (n0=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...
\(-(z-1)(25z-1)(9z-1)\)
| \(0\) | \(\frac{ 1}{ 25}\) | \(\frac{ 1}{ 9}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(2\) |
2
New Number: 3.32 | AESZ: | Superseeker: 128 382592 | Hash: 9b39b616939718654c472dbfb37cdd4e
Degree: 3
\(\theta^4-2^{4} x(6\theta^2+6\theta-1)(2\theta+1)^2-2^{10} x^{2}(60\theta^2+120\theta+97)(\theta+1)^2-2^{21} x^{3}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -16, 4624, 678656, 238896400, ... --> OEIS Normalized instanton numbers (n0=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...
\(-(512z-1)(1+64z)^2\)
| \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 512}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(1\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(2\) | \(2\) |
3
New Number: 12.7 | AESZ: | Superseeker: -24/7 117 | Hash: fedf397077a0af56af404f5156e1b5c0
Degree: 12
\(7^{2} \theta^4+2 3 7 x\left(111\theta^4+120\theta^3+102\theta^2+42\theta+7\right)+2^{2} 3 x^{2}\left(16827\theta^4+34008\theta^3+38464\theta^2+20846\theta+4494\right)+3^{3} x^{3}\left(178553\theta^4+439878\theta^3+528099\theta^2+313502\theta+74536\right)+2 3^{3} x^{4}\left(1355053\theta^4+3438698\theta^3+3854711\theta^2+2221354\theta+519896\right)+2^{2} 3^{4} x^{5}\left(2406561\theta^4+5708802\theta^3+5082043\theta^2+2161754\theta+336752\right)+2^{3} 3^{5} x^{6}\left(3133411\theta^4+6625998\theta^3+4266961\theta^2+238710\theta-485736\right)+2^{6} 3^{6} x^{7}\left(746186\theta^4+1366021\theta^3+743388\theta^2-203279\theta-212552\right)+2^{7} 3^{7} x^{8}\left(506499\theta^4+760668\theta^3+404459\theta^2-112958\theta-117216\right)+2^{11} 3^{8} x^{9}\left(27992\theta^4+34962\theta^3+7197\theta^2-14685\theta-7604\right)+2^{14} 3^{9} x^{10}\left(1381\theta^4+1244\theta^3-2460\theta^2-4030\theta-1571\right)-2^{18} 3^{10} x^{11}(22\theta^2+98\theta+105)(\theta+1)^2-2^{22} 3^{11} x^{12}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, -276, -8442, ... --> OEIS Normalized instanton numbers (n0=1): -24/7, -24/7, 117, -564, 948/7, ... ; Common denominator:...
\(-(6z+1)(10368z^5-864z^4-7371z^3-1440z^2-60z-1)(7+102z+648z^2+3456z^3)^2\)
| \(-\frac{ 1}{ 6}\) | ≈\(-0.097659\) | ≈\(-0.04492-0.136829I\) | ≈\(-0.04492+0.136829I\) | \(0\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(3\) | \(3\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(4\) | \(4\) | \(4\) | \(0\) | \(2\) | \(2\) |
4
New Number: 12.9 | AESZ: | Superseeker: 800 38825120 | Hash: 7e2f8423069147eb36cfd1d714d1996a
Degree: 12
\(\theta^4+2^{4} x\left(288\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{13} x^{2}\left(864\theta^4-240\theta^3+438\theta^2+96\theta-7\right)+2^{20} x^{3}\left(3856\theta^4+1152\theta^3+1036\theta^2+192\theta-53\right)+2^{30} x^{4}\left(636\theta^4-1440\theta^3-2303\theta^2-1988\theta-672\right)-2^{38} x^{5}\left(320\theta^4+7928\theta^3+14109\theta^2+11270\theta+3517\right)-2^{48} x^{6}\left(134\theta^4+1830\theta^3+3688\theta^2+3585\theta+1195\right)-2^{56} x^{7}\left(187\theta^4+356\theta^3-2355\theta^2-2866\theta-1199\right)-2^{65} x^{8}\left(91\theta^4+202\theta^3-1069\theta^2-2020\theta-948\right)-2^{74} x^{9}\left(2\theta^4-120\theta^3-211\theta^2-198\theta-69\right)+2^{84} x^{10}\left(\theta^4+44\theta^3+122\theta^2+121\theta+41\right)+2^{92} x^{11}(\theta^2+2\theta+2)(\theta+1)^2+2^{101} x^{12}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ... --> OEIS Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...
\((256z-1)(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2\)
| \(-\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | ≈\(-0.000552\) | \(0\) | ≈\(0.000276-0.00519I\) | ≈\(0.000276+0.00519I\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) |
5
New Number: 15.1 | AESZ: | Superseeker: 800 38825120 | Hash: c26e6797c51f4c09c1dfbc9e354ce168
Degree: 15
\(\theta^4+2^{4} x\left(240\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{12} x^{2}\left(912\theta^4-192\theta^3+948\theta^2+120\theta-35\right)-2^{21} x^{3}\left(240\theta^4-1152\theta^3+832\theta^2+156\theta-5\right)-2^{29} x^{4}\left(2064\theta^4+5280\theta^3+4834\theta^2+3988\theta+1289\right)+2^{36} x^{5}\left(928\theta^4-10496\theta^3-26568\theta^2-20840\theta-6149\right)+2^{44} x^{6}\left(5472\theta^4+47424\theta^3+81628\theta^2+53832\theta+15073\right)-2^{54} x^{7}\left(736\theta^4+1808\theta^3-13652\theta^2-22662\theta-9257\right)+2^{62} x^{8}\left(228\theta^4-11376\theta^3-49855\theta^2-49982\theta-17627\right)+2^{72} x^{9}\left(111\theta^4+2454\theta^3+5183\theta^2+855\theta-620\right)-2^{80} x^{10}\left(319\theta^4+1592\theta^3-3479\theta^2-8814\theta-4317\right)+2^{89} x^{11}\left(63\theta^4-102\theta^3-2675\theta^2-3688\theta-1502\right)+2^{98} x^{12}\left(10\theta^4+408\theta^3+1273\theta^2+1278\theta+431\right)-2^{108} x^{13}\left(4\theta^4+68\theta^3+179\theta^2+175\theta+59\right)+2^{116} x^{14}(5\theta^2+22\theta+22)(\theta+1)^2-2^{125} x^{15}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ... --> OEIS Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...
\(-(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2(256z-1)^4\)
| \(-\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\) | \(-\frac{ 1}{ 512}\) | ≈\(-0.000552\) | \(0\) | ≈\(0.000276-0.00519I\) | ≈\(0.000276+0.00519I\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) |
6
New Number: 6.12 | AESZ: | Superseeker: 19 2263 | Hash: 86993fb7955dee498aab7e103a0f457e
Degree: 6
\(\theta^4-x\left(33\theta^4+258\theta^3+199\theta^2+70\theta+10\right)-2^{2} x^{2}\left(1380\theta^4+2400\theta^3-173\theta^2-634\theta-185\right)-2^{4} x^{3}\left(7325\theta^4+2670\theta^3-668\theta^2-1035\theta-290\right)-2^{7} x^{4}\left(897\theta^4-3504\theta^3-10058\theta^2-8492\theta-2435\right)+2^{12} x^{5}(\theta+1)^2(858\theta^2+1566\theta+745)-2^{17} 5^{2} x^{6}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 10, 310, 14860, 869590, ... --> OEIS Normalized instanton numbers (n0=1): 19, -18, 2263, 4184, 1097345, ... ; Common denominator:...
\(-(z-1)(8z+1)(100z-1)(4z-1)(1+32z)^2\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 32}\) | \(0\) | \(\frac{ 1}{ 100}\) | \(\frac{ 1}{ 4}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) |
7
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:...
\((64z+1)^2(128z+1)^2(256z+1)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(4\) | \(0\) | \(2\) |
8
New Number: 6.16 | AESZ: | Superseeker: 2272 434311008 | Hash: f30ffc268310c175e914066ee270f47b
Degree: 6
\(\theta^4+2^{4} x\left(448\theta^4-544\theta^3-332\theta^2-60\theta-5\right)+2^{12} x^{2}\left(2576\theta^4-8416\theta^3+2808\theta^2+668\theta+35\right)-2^{20} x^{3}\left(9088\theta^4+5568\theta^3+5392\theta^2+3180\theta+667\right)-2^{28} 3^{2} x^{4}(2\theta+1)(744\theta^3+940\theta^2+798\theta+167)+2^{38} 3^{3} 5 x^{5}(16\theta^2+40\theta+33)(\theta+1)^2+2^{48} 3^{3} 5^{2} x^{6}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 30480, 9850112, 4649741584, ... --> OEIS Normalized instanton numbers (n0=1): 2272, -719992, 434311008, -343376572072, 316225589496736, ... ; Common denominator:...
\((768z-1)(256z-1)(256z+1)^2(3840z+1)^2\)
| \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 3840}\) | \(0\) | \(\frac{ 1}{ 768}\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) |
9
New Number: 8.79 | AESZ: | Superseeker: 22/5 68 | Hash: 064e5b590dd8b6a4daa1e905fbe693c2
Degree: 8
\(5^{2} \theta^4-2 5 x\left(338\theta^4+412\theta^3+371\theta^2+165\theta+30\right)+2^{2} x^{2}\left(46396\theta^4+103408\theta^3+125291\theta^2+76370\theta+19080\right)-2^{4} 3 x^{3}\left(115508\theta^4+357896\theta^3+524149\theta^2+375205\theta+106530\right)+2^{6} 3^{2} x^{4}\left(173456\theta^4+669024\theta^3+1118292\theta^2+883484\theta+269049\right)-2^{11} 3^{3} x^{5}\left(20272\theta^4+91616\theta^3+168594\theta^2+142006\theta+45053\right)+2^{14} 3^{4} x^{6}\left(5792\theta^4+29504\theta^3+58300\theta^2+51220\theta+16641\right)-2^{21} 3^{5} x^{7}(\theta+1)^2(58\theta^2+208\theta+201)+2^{26} 3^{6} x^{8}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 204, 4368, 112140, ... --> OEIS Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...
\((-1+48z)(16z-1)^2(48z-5)^2(12z-1)^3\)
| \(0\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 12}\) | \(\frac{ 5}{ 48}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) | \(3\) | \(2\) |
| \(0\) | \(2\) | \(1\) | \(2\) | \(4\) | \(2\) |
10
New Number: 9.1 | AESZ: | Superseeker: -4/7 955/63 | Hash: d32eab6005ac34ecc01a9db7675daa24
Degree: 9
\(7^{2} \theta^4-7 x\theta(-7-32\theta-50\theta^2+29\theta^3)+3 x^{2}\theta(532+1165\theta+512\theta^2+1235\theta^3)-2 3^{2} x^{3}\left(5373\theta^4+29040\theta^3+61493\theta^2+51786\theta+15876\right)+2^{2} 3^{3} x^{4}\left(10813\theta^4+68120\theta^3+160529\theta^2+154570\theta+53396\right)-2^{3} 3^{4} x^{5}\left(13929\theta^4+84348\theta^3+181015\theta^2+171080\theta+59172\right)+2^{5} 3^{5} x^{6}\left(6160\theta^4+35964\theta^3+69935\theta^2+58677\theta+18110\right)-2^{8} 3^{6} x^{7}\left(944\theta^4+5308\theta^3+10916\theta^2+9657\theta+3109\right)+2^{11} 3^{7} x^{8}(96\theta^2+300\theta+265)(\theta+1)^2-2^{15} 3^{9} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 0, 72, -432, ... --> OEIS Normalized instanton numbers (n0=1): -4/7, -4/7, 955/63, -262/7, -1002/7, ... ; Common denominator:...
\(-(6z-1)(27z^2-9z+1)(192z^2+16z+1)(7-18z+144z^2)^2\)
| \(-\frac{ 1}{ 24}-\frac{ 1}{ 24}\sqrt{ 2}I\) | \(-\frac{ 1}{ 24}+\frac{ 1}{ 24}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 48}\sqrt{ 103}I\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 48}\sqrt{ 103}I\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) | \(2\) |
11
New Number: 9.2 | AESZ: | Superseeker: 9/7 49/3 | Hash: 356d4564e48d7a04e815fa223b6ccc46
Degree: 9
\(7^{2} \theta^4+7 x\theta(165\theta^3-102\theta^2-65\theta-14)-2^{3} x^{2}\left(920\theta^4+11726\theta^3+15277\theta^2+9478\theta+2352\right)-2^{4} 3^{2} x^{3}\left(4035\theta^4+19554\theta^3+29157\theta^2+20706\theta+5761\right)-2^{8} 3^{2} x^{4}\left(4156\theta^4+17951\theta^3+28198\theta^2+21045\theta+6096\right)-2^{11} 3^{3} x^{5}\left(1538\theta^4+6560\theta^3+10755\theta^2+8234\theta+2420\right)-2^{13} 3^{4} x^{6}\left(695\theta^4+3051\theta^3+5285\theta^2+4191\theta+1259\right)-2^{14} 3^{5} x^{7}\left(385\theta^4+1802\theta^3+3319\theta^2+2754\theta+855\right)-2^{18} 3^{6} x^{8}(\theta+1)^2(15\theta^2+48\theta+43)-2^{20} 3^{7} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 144, 3240, ... --> OEIS Normalized instanton numbers (n0=1): 9/7, 47/7, 49/3, 1370/7, 10063/7, ... ; Common denominator:...
\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(7+72z+288z^2)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 5}I\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 5}I\) | \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) |
12
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:...
\(-(9z+1)(2z+1)(z+1)(128z^2+64z-1)(-3-2z+64z^2)^2\)
| \(-1\) | \(-\frac{ 1}{ 4}-\frac{ 3}{ 16}\sqrt{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 1}{ 64}-\frac{ 1}{ 64}\sqrt{ 193}\) | \(-\frac{ 1}{ 9}\) | \(0\) | \(-\frac{ 1}{ 4}+\frac{ 3}{ 16}\sqrt{ 2}\) | \(\frac{ 1}{ 64}+\frac{ 1}{ 64}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) |
13
New Number: 9.8 | AESZ: | Superseeker: 6/17 688/17 | Hash: 0574d9effd306eb6c9288752b7670904
Degree: 9
\(17^{2} \theta^4-2 17 x\left(164\theta^4-164\theta^3-167\theta^2-85\theta-17\right)-2^{2} x^{2}\left(35300\theta^4+95864\theta^3+121575\theta^2+70856\theta+16235\right)+2^{2} x^{3}\left(427984\theta^4-277824\theta^3-1460293\theta^2-1490475\theta-492694\right)+2^{4} x^{4}\left(2088512\theta^4+6692704\theta^3+7319011\theta^2+3820745\theta+794302\right)-2^{6} x^{5}\left(1379872\theta^4-6413120\theta^3-11843583\theta^2-9110135\theta-2589134\right)-2^{8} x^{6}\left(13237904\theta^4+37140384\theta^3+64254239\theta^2+57084594\theta+19379105\right)-2^{10} 3^{2} 5 x^{7}\left(255072\theta^4+803200\theta^3+1114259\theta^2+709496\theta+167515\right)+2^{12} 3^{3} 5^{2} 7 x^{8}(2224\theta^2+11008\theta+12225)(\theta+1)^2+2^{18} 3^{3} 5^{4} 7^{2} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2, 18, -20, 1330, ... --> OEIS Normalized instanton numbers (n0=1): 6/17, 83/17, 688/17, 7350/17, 5150, ... ; Common denominator:...
\((4z-1)(12z+1)(1600z^3+272z^2+8z-1)(-17+164z+1680z^2)^2\)
| \(-\frac{ 41}{ 840}-\frac{ 1}{ 840}\sqrt{ 8821}\) | ≈\(-0.106819-0.053966I\) | ≈\(-0.106819+0.053966I\) | \(-\frac{ 1}{ 12}\) | \(0\) | ≈\(0.043637\) | \(-\frac{ 41}{ 840}+\frac{ 1}{ 840}\sqrt{ 8821}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(2\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) |
14
New Number: 9.9 | AESZ: | Superseeker: 256/31 28062/31 | Hash: 924a831431fc249044fe63cfea0eb535
Degree: 9
\(31^{2} \theta^4-31 x\left(2836\theta^4+4790\theta^3+3728\theta^2+1333\theta+186\right)-x^{2}\left(1539241\theta^2+1291677\theta+342550-558095\theta^4+131134\theta^3\right)+x^{3}\left(6495560\theta^2+387046\theta^4+6264048\theta^3+558+2100591\theta\right)+x^{4}\left(3388169\theta-7521396\theta^3-5037573\theta^4+2030450-2351908\theta^2\right)-2 x^{5}\left(2014896\theta^4+11047341\theta^3+24693967\theta^2+23008058\theta+7682256\right)+x^{6}\left(37321692\theta+8697364+6817193\theta^4+33832842\theta^3+56561513\theta^2\right)+2 11 x^{7}\left(351229\theta^4+2420534\theta^3+6030705\theta^2+6243956\theta+2275780\right)+2^{2} 11^{2} x^{8}(3667\theta^2+17036\theta+18316)(\theta+1)^2+2^{3} 11^{4} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 178, 7404, 370674, ... --> OEIS Normalized instanton numbers (n0=1): 256/31, 1982/31, 28062/31, 591475/31, 15400630/31, ... ; Common denominator:...
\((2z+1)(121z^2-86z+1)(z+1)^2(22z^2+147z-31)^2\)
| \(-\frac{ 147}{ 44}-\frac{ 1}{ 44}\sqrt{ 24337}\) | \(-1\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 43}{ 121}-\frac{ 24}{ 121}\sqrt{ 3}\) | \(-\frac{ 147}{ 44}+\frac{ 1}{ 44}\sqrt{ 24337}\) | \(\frac{ 43}{ 121}+\frac{ 24}{ 121}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(2\) |
| \(4\) | \(1\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) |