1
New Number: 5.26 | AESZ: 199 | Superseeker: -2 3820/9 | Hash: f7b5c9e3ad50b0885d03c98d07a051f1
Degree: 5
\(\theta^4-x\left(15+88\theta+200\theta^2+224\theta^3+265\theta^4\right)+2 3 x^{2}\left(4325\theta^4+6386\theta^3+6011\theta^2+2718\theta+468\right)-2 3^{2} x^{3}\left(62015\theta^4+116478\theta^3+102361\theta^2+37422\theta+4824\right)+3^{6} 17 x^{4}\left(1465\theta^4+3092\theta^3+2686\theta^2+1140\theta+200\right)-3^{10} 17^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 15, 567, 28113, 1584279, ... --> OEIS Normalized instanton numbers (n0=1): -2, 28, 3820/9, 3924, 21606, ... ; Common denominator:...
\(-(z-1)(81z-1)^2(51z-1)^2\)
| \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 1}{ 51}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(4\) | \(2\) | \(1\) |
2
New Number: 8.31 | AESZ: 315 | Superseeker: 38 26135 | Hash: 44be55b95bb1c725c5aaa2c9a6635e89
Degree: 8
\(5^{2} \theta^4-5^{2} x\left(239\theta^4+496\theta^3+368\theta^2+120\theta+15\right)-2 3 5 x^{2}\left(1727\theta^4+3206\theta^3+2341\theta^2+1090\theta+245\right)-3^{2} 5 x^{3}\left(1519\theta^4+7338\theta^3+14271\theta^2+8340\theta+1690\right)+3^{3} x^{4}\left(10358\theta^4-16622\theta^3-49763\theta^2-37900\theta-10210\right)+3^{4} 5 x^{5}\left(922\theta^4+3526\theta^3-1357\theta^2-3028\theta-1031\right)-3^{5} x^{6}\left(1219\theta^4-6030\theta^3-6441\theta^2-1740\theta+160\right)-2^{2} 3^{6} x^{7}\left(162\theta^4+234\theta^3+65\theta^2-52\theta-25\right)-2^{4} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 15, 1179, 140505, 20362059, ... --> OEIS Normalized instanton numbers (n0=1): 38, 3068/5, 26135, 7871998/5, 117518569, ... ; Common denominator:...
\(-(z+1)(81z^3+351z^2+246z-1)(-5-15z+36z^2)^2\)
| ≈\(-3.452681\) | \(-1\) | ≈\(-0.884694\) | \(\frac{ 5}{ 24}-\frac{ 1}{ 24}\sqrt{ 105}\) | \(0\) | ≈\(0.004042\) | \(\frac{ 5}{ 24}+\frac{ 1}{ 24}\sqrt{ 105}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(1\) |
3
New Number: 8.32 | AESZ: 317 | Superseeker: 69/4 14365/12 | Hash: cda8cce31025f51636125bea67a820d1
Degree: 8
\(2^{4} \theta^4-2^{2} 3 x\left(162\theta^4+414\theta^3+335\theta^2+128\theta+20\right)+3^{3} x^{2}\left(1219\theta^4+10906\theta^3+18963\theta^2+11824\theta+2708\right)+3^{5} 5 x^{3}\left(922\theta^4+162\theta^3-6403\theta^2-6576\theta-1964\right)-3^{7} x^{4}\left(10358\theta^4+58054\theta^3+62251\theta^2+29672\theta+4907\right)-3^{9} 5 x^{5}\left(1519\theta^4-1262\theta^3+1371\theta^2+4264\theta+1802\right)+2 3^{11} 5 x^{6}\left(1727\theta^4+3702\theta^3+3085\theta^2+882\theta+17\right)-3^{13} 5^{2} x^{7}\left(239\theta^4+460\theta^3+314\theta^2+84\theta+6\right)-3^{16} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 15, 459, 19545, 1019259, ... --> OEIS Normalized instanton numbers (n0=1): 69/4, -30, 14365/12, 3015/2, 1376205/4, ... ; Common denominator:...
\(-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2\)
| ≈\(-9.163702\) | \(\frac{ 1}{ 18}-\frac{ 1}{ 90}\sqrt{ 105}\) | \(0\) | ≈\(0.010727\) | \(\frac{ 1}{ 27}\) | ≈\(0.041864\) | \(\frac{ 1}{ 18}+\frac{ 1}{ 90}\sqrt{ 105}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
4
New Number: 24.11 | AESZ: | Superseeker: 53/5 -309836/1215 | Hash: 682b45ff9c4177035e08e594ea968a40
Degree: 24
\(5^{2} \theta^4-5 x\theta(780\theta^3+233\theta+45)+x^{2}\left(29459\theta^4+155852\theta^3+133609\theta^2+27010\theta-6000\right)-3^{2} x^{3}\left(170942\theta^4+5388\theta^3+123841\theta^2+538965\theta+289950\right)-2^{2} 3^{3} x^{4}\left(299324\theta^4+1917922\theta^3+2469992\theta^2+1887645\theta+792630\right)+3^{4} x^{5}\left(13371098\theta^4-15702340\theta^3-56878373\theta^2-21939359\theta-1565760\right)+3^{7} x^{6}\left(10056623\theta^4+51572556\theta^3+34820569\theta^2+76534814\theta+46490824\right)-3^{7} x^{7}\left(235027408\theta^4-62481208\theta^3-620667755\theta^2-694808037\theta-436763790\right)-3^{8} x^{8}\left(1103983063\theta^4+6898242712\theta^3+5618673632\theta^2+8342492360\theta+4306904496\right)+2 3^{10} x^{9}\left(1567811420\theta^4+1125299280\theta^3+2679400693\theta^2+929271741\theta-931458972\right)+2 3^{12} x^{10}\left(1091890963\theta^4+8818792004\theta^3+14797099953\theta^2+16119935558\theta+6720833160\right)-2 3^{14} x^{11}\left(4132995702\theta^4+11210477796\theta^3+22335304201\theta^2+21391532585\theta+7680128002\right)-2^{3} 3^{16} x^{12}\left(36094918\theta^4+2244000840\theta^3+5817619373\theta^2+7236866988\theta+3390157938\right)+2 3^{18} x^{13}\left(5245867146\theta^4+28750482372\theta^3+67038993743\theta^2+76465169633\theta+33958775428\right)-2 3^{20} x^{14}\left(2325299271\theta^4+9056959668\theta^3+15535709593\theta^2+13710343706\theta+4772169024\right)-2 3^{22} x^{15}\left(1937917032\theta^4+18692730384\theta^3+60632460723\theta^2+83153628009\theta+41806101938\right)+3^{24} x^{16}\left(3589458339\theta^4+31443345792\theta^3+101210591864\theta^2+140988740840\theta+71945494016\right)-3^{26} x^{17}\left(917154124\theta^4+7902286936\theta^3+25304271327\theta^2+35059224115\theta+17843355880\right)+3^{28} x^{18}\left(32843719\theta^4+454332780\theta^3+2174878229\theta^2+3835061490\theta+2302959008\right)+3^{30} x^{19}\left(28756154\theta^4+169682932\theta^3+218616787\theta^2-103588009\theta-230015838\right)-2^{2} 3^{32} x^{20}\left(1138248\theta^4+7399434\theta^3+14543734\theta^2+8831609\theta-443286\right)-3^{34} x^{21}\left(15470\theta^4-742908\theta^3-2759711\theta^2-3300309\theta-1216344\right)+3^{37} x^{22}\left(19299\theta^4+100277\theta^2+123674\theta+5048\right)-3^{40} x^{23}(12\theta^2+37\theta+29)(20\theta^2+59\theta+46)+3^{43} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 15, 48296/27, 23854513/240, ... --> OEIS Normalized instanton numbers (n0=1): 53/5, 53/10, -309836/1215, -73952369/345600, 209793337409497/1687500000, ... ; Common denominator:...
\(25-3900z+8690029099790358108537z^22-2917839710173662912240z^23+328256967394537077627z^24+21993834501z^6-514004941296z^7-7243232876343z^8+185155393079160z^9+1160551250535366z^10+1013769054901630165059z^16-2331282727106618378796z^17+29459z^2-1538478z^3-32326992z^4+1083058938z^5+751358943012059239959z^18-39535980639598476z^11-12430142917311024z^12+4064712829864708788z^13-16215634451558943342z^14-121627779796976720976z^15+5920637101748069219946z^19-8436786095680921258272z^20-257996000893841822430z^21\)
No data for singularities
5
New Number: 24.9 | AESZ: | Superseeker: -28/5 -2059/5 | Hash: df5798b125b79096c20bb76424736f4f
Degree: 24
\(5^{2} \theta^4+5 x\left(19\theta^4-394\theta^3-422\theta^2-225\theta-45\right)-x^{2}\left(37321\theta^4-66392\theta^3-158089\theta^2-146890\theta-42015\right)+3^{2} x^{3}\left(56362\theta^4+272064\theta^3-263800\theta^2-863100\theta-344265\right)+3^{3} x^{4}\left(753758\theta^4-3721952\theta^3-1612522\theta^2+7875882\theta+3789297\right)-3^{4} x^{5}\left(8666834\theta^4+4922312\theta^3-16890032\theta^2+62390344\theta+36295089\right)+2 3^{6} x^{6}\left(729905\theta^4+30855384\theta^3-25952555\theta^2+45786327\theta+3503895\right)+3^{7} x^{7}\left(134822030\theta^4-93224048\theta^3+625210544\theta^2+316465212\theta+17277309\right)-3^{8} x^{8}\left(706556068\theta^4+1136401312\theta^3+3007159670\theta^2+4193639906\theta+1801612197\right)-3^{10} x^{9}\left(377925716\theta^4+160172796\theta^3+2877742996\theta^2+5024274\theta-495055029\right)+3^{12} x^{10}\left(2448319808\theta^4+5232688960\theta^3+15324605244\theta^2+13824742642\theta+5444471349\right)-3^{14} x^{11}\left(2193574746\theta^4+3668054544\theta^3+11367751208\theta^2+11767214572\theta+4999425971\right)-3^{16} x^{12}\left(1682795498\theta^4+11062016256\theta^3+23629355050\theta^2+26296819542\theta+11746671063\right)+3^{18} x^{13}\left(4763496210\theta^4+22286693400\theta^3+51380463088\theta^2+59266252624\theta+27350967461\right)-3^{20} x^{14}\left(3043951122\theta^4+11179411056\theta^3+23645335946\theta^2+26971875430\theta+12853203483\right)-3^{22} x^{15}\left(953791122\theta^4+11590574448\theta^3+37576565088\theta^2+50793592500\theta+25331154139\right)+3^{24} x^{16}\left(2663679451\theta^4+21556674144\theta^3+67973830382\theta^2+94609426202\theta+49302346577\right)-3^{26} x^{17}\left(1688667811\theta^4+14622262450\theta^3+50242859262\theta^2+75169980505\theta+41538667624\right)+3^{28} x^{18}\left(373177657\theta^4+4454210088\theta^3+19022887355\theta^2+32625784812\theta+19779621968\right)+2^{3} 3^{30} x^{19}\left(13128703\theta^4+20169890\theta^3-263358082\theta^2-784811675\theta-603783258\right)-2^{4} 3^{32} x^{20}\left(5205555\theta^4+36545250\theta^3+75119194\theta^2+46359749\theta-5105268\right)+2^{6} 3^{37} x^{21}\left(239743\theta^4+2547858\theta^3+7737962\theta^2+9377577\theta+3933030\right)+2^{6} 3^{37} x^{22}\left(8715\theta^4-13108\theta^3-174133\theta^2-329058\theta-187552\right)-2^{9} 3^{40} x^{23}\left(219\theta^4+1378\theta^3+3354\theta^2+3733\theta+1600\right)+2^{12} 3^{43} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 15, 45, -3159, ... --> OEIS Normalized instanton numbers (n0=1): -28/5, 233/10, -2059/5, 70897/10, -784822/5, ... ; Common denominator:...
\(25+95z+251150351349762689186880z^22-1363214712593135312598528z^23+1344540538448023869960192z^24+1064201490z^6+294855779610z^7-4635714362148z^8-22316135604084z^9+1301137527083328z^10+752301752679894551931z^16-4292367004180034217819z^17-37321z^2+507258z^3+20351466z^4-702013554z^5+8537107808017624006377z^18-10491800009300874z^11-72438828302462058z^12+1845476031027846690z^13-10613601289596047922z^14-29930976054016991298z^15+21624668188835316881976z^19-154335976146858322828080z^20+6908954524801624371053376z^21\)
No data for singularities