1
New Number: 5.23 | AESZ: 194 | Superseeker: 126/17 11700/17 | Hash: 6bf19665aa6705f30ef88df42bc4eac4
Degree: 5
\(17^{2} \theta^4-17 x\left(1465\theta^4+2768\theta^3+2200\theta^2+816\theta+119\right)+2 x^{2}\left(62015\theta^4+131582\theta^3+125017\theta^2+65926\theta+15300\right)-2 3^{3} x^{3}\left(4325\theta^4+10914\theta^3+12803\theta^2+7446\theta+1700\right)+3^{6} x^{4}\left(265\theta^4+836\theta^3+1118\theta^2+700\theta+168\right)-3^{10} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 183, 7225, 345079, ... --> OEIS Normalized instanton numbers (n0=1): 126/17, 848/17, 11700/17, 229808/17, 5539258/17, ... ; Common denominator:...
\(-(-1+81z)(27z-17)^2(z-1)^2\)
| \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 17}{ 27}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(1\) | \(1\) |
2
New Number: 5.84 | AESZ: 318 | Superseeker: 46/5 1126 | Hash: 3fa38f629ecd5f39b585ce0c1bd88463
Degree: 5
\(5^{2} \theta^4-5 x\left(473\theta^4+892\theta^3+696\theta^2+250\theta+35\right)+2 x^{2}\left(1973\theta^4-4636\theta^3-14417\theta^2-10895\theta-2745\right)+2 3^{2} x^{3}\left(343\theta^4+1920\theta^3+1147\theta^2-345\theta-320\right)-3^{4} x^{4}\left(83\theta^4-104\theta^3-458\theta^2-406\theta-114\right)-3^{8} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 219, 9961, 546379, ... --> OEIS Normalized instanton numbers (n0=1): 46/5, 717/10, 1126, 51481/2, 3609772/5, ... ; Common denominator:...
\(-(z+1)(81z^2+92z-1)(-5+9z)^2\)
| \(-\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\) | \(-1\) | \(0\) | \(-\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\) | \(\frac{ 5}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
3
New Number: 11.14 | AESZ: | Superseeker: 10 13958/9 | Hash: 0a4e6572e1bb29d996fd62dc404c2446
Degree: 11
\(3^{6} \theta^4-3^{6} x\left(111\theta^4+180\theta^3+140\theta^2+50\theta+7\right)+3^{3} x^{2}\left(31925\theta^4+11480\theta^3-42466\theta^2-34182\theta-7560\right)+3^{3} x^{3}\left(4877\theta^4+370644\theta^3+409430\theta^2+199476\theta+42297\right)-2 x^{4}\left(10348339\theta^4+26540048\theta^3+42009388\theta^2+29955528\theta+7880058\right)+2 x^{5}\left(9831565\theta^4+67438924\theta^3+143690304\theta^2+116711926\theta+33599143\right)+2 x^{6}\left(14540887\theta^4-5897448\theta^3-129216202\theta^2-158647410\theta-56400514\right)-2 x^{7}\left(20947985\theta^4+93882580\theta^3+71337738\theta^2-9343940\theta-17269525\right)+x^{8}\left(1325117\theta^4+114002144\theta^3+209338120\theta^2+141064960\theta+32960772\right)+3^{4} x^{9}\left(254941\theta^4+471612\theta^3+445052\theta^2+300870\theta+101457\right)-3^{8} x^{10}\left(1621\theta^4+5816\theta^3+8326\theta^2+5418\theta+1332\right)+3^{13} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 231, 11185, 654199, ... --> OEIS Normalized instanton numbers (n0=1): 10, 2591/27, 13958/9, 1037839/27, 3535478/3, ... ; Common denominator:...
\((z-1)(243z^4-520z^3+310z^2+96z-1)(27-189z-143z^2+81z^3)^2\)
| ≈\(-0.97581\) | \(0\) | ≈\(0.130861\) | \(1\) | ≈\(2.610381\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(4\) | \(2\) | \(4\) | \(2\) | \(1\) |
4
New Number: 8.22 | AESZ: 284 | Superseeker: 241/38 8729/19 | Hash: dbe506beab1f66a0b331f15c91b7fcde
Degree: 8
\(2^{2} 19^{2} \theta^4-2 19 x\left(3014\theta^4+5878\theta^3+4725\theta^2+1786\theta+266\right)+x^{2}\left(402002+1810054\theta+3057079\theta^2+2305502\theta^3+689717\theta^4\right)-x^{3}\left(1576582+6295992\theta+9142457\theta^2+5812350\theta^3+1438808\theta^4\right)+x^{4}\left(663471+3375833\theta+6297445\theta^2+5075392\theta^3+1395491\theta^4\right)+x^{5}\left(52928-604005\theta-2407768\theta^2-2657224\theta^3-834163\theta^4\right)-x^{6}\left(4832-148359\theta-572576\theta^2-692484\theta^3-277543\theta^4\right)-11 x^{7}\left(4625\theta^4+9100\theta^3+6395\theta^2+1845\theta+178\right)-11^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 163, 5767, 247651, ... --> OEIS Normalized instanton numbers (n0=1): 241/38, 1353/38, 8729/19, 150334/19, 6399445/38, ... ; Common denominator:...
\(-(-1+78z-374z^2+425z^3+z^4)(38-25z+11z^2)^2\)
| \(0\) | \(\frac{ 25}{ 22}-\frac{ 1}{ 22}\sqrt{ 1047}I\) | \(\frac{ 25}{ 22}+\frac{ 1}{ 22}\sqrt{ 1047}I\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |
5
New Number: 9.10 | AESZ: | Superseeker: 307/31 30366/31 | Hash: 7a61ae3114ae9cdc48f662244260cd65
Degree: 9
\(31^{2} \theta^4-31 x\left(2424\theta^4+5574\theta^3+4337\theta^2+1550\theta+217\right)-x^{2}\left(184202+713186\theta+1382715\theta^2+1756478\theta^3+914057\theta^4\right)-x^{3}\left(2273850+8903076\theta+13251149\theta^2+8635710\theta^3+3075537\theta^4\right)-x^{4}\left(11927218+37908836\theta+46269935\theta^2+23766918\theta^3+2064696\theta^4\right)-x^{5}\left(30324779+80902562\theta+70842936\theta^2+13913564\theta^3-3177385\theta^4\right)+2 x^{6}\left(2606232\theta^4+10916676\theta^3-6409705\theta^2-26416695\theta-14341608\right)+2^{2} 7 x^{7}\left(74376\theta^4+1138248\theta^3+2184799\theta^2+1451482\theta+280295\right)-2^{4} 5 7^{2} x^{8}(\theta+1)(592\theta^3-1128\theta^2-5448\theta-4091)-2^{6} 5^{2} 7^{3} x^{9}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 211, 9217, 485611, ... --> OEIS Normalized instanton numbers (n0=1): 307/31, 1814/31, 30366/31, 639686/31, 17126962/31, ... ; Common denominator:...
\(-(z+1)(z^2+z+1)(112z^2+88z-1)(-31-121z+140z^2)^2\)
| \(-1\) | \(-\frac{ 11}{ 28}-\frac{ 2}{ 7}\sqrt{ 2}\) | \(-\frac{ 1}{ 2}-\frac{ 1}{ 2}\sqrt{ 3}I\) | \(-\frac{ 1}{ 2}+\frac{ 1}{ 2}\sqrt{ 3}I\) | \(\frac{ 121}{ 280}-\frac{ 1}{ 280}\sqrt{ 32001}\) | \(0\) | \(-\frac{ 11}{ 28}+\frac{ 2}{ 7}\sqrt{ 2}\) | \(\frac{ 121}{ 280}+\frac{ 1}{ 280}\sqrt{ 32001}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) |
6
New Number: 24.3 | AESZ: | Superseeker: 52/5 5899/5 | Hash: d0e287eaa4fef980c189e2ff531cfe15
Degree: 24
\(5^{2} \theta^4-5 x\left(491\theta^4+934\theta^3+722\theta^2+255\theta+35\right)+x^{2}\left(7159\theta^4+6232\theta^3-12151\theta^2-20470\theta-7105\right)+x^{3}\left(18758\theta^4+85536\theta^3+125256\theta^2+44940\theta+9625\right)+x^{4}\left(107306\theta^4-465824\theta^3-1781630\theta^2-1509010\theta-420741\right)-x^{5}\left(740094\theta^4-1297608\theta^3-5441440\theta^2+261976\theta+1419015\right)-x^{6}\left(425070\theta^4+2630928\theta^3-1828778\theta^2-9227454\theta-5729271\right)+x^{7}\left(2418550\theta^4+20716304\theta^3-31322144\theta^2-45688692\theta-18761303\right)+x^{8}\left(12130172\theta^4-80918752\theta^3+123192250\theta^2+111390334\theta+20525227\right)-x^{9}\left(17292844\theta^4-87187836\theta^3+258415980\theta^2+122394558\theta-28117691\right)-x^{10}\left(77350272\theta^4-52258560\theta^3-209801740\theta^2+35556398\theta+112842235\right)+x^{11}\left(169708186\theta^4-275075696\theta^3-61487240\theta^2+173105868\theta+132064403\right)+x^{12}\left(10381942\theta^4+721961664\theta^3+662207782\theta^2+449099274\theta+145105369\right)-x^{13}\left(297104050\theta^4+976538840\theta^3+1274259392\theta^2+987704752\theta+327432741\right)+x^{14}\left(221581518\theta^4+18861264\theta^3-741766394\theta^2-1393177990\theta-797694603\right)+x^{15}\left(114705522\theta^4+1320217008\theta^3+3568249520\theta^2+4492131828\theta+2173936059\right)-x^{16}\left(224356709\theta^4+1230081376\theta^3+2802678530\theta^2+3051898566\theta+1307246399\right)+x^{17}\left(65530931\theta^4+95408210\theta^3-252661082\theta^2-914043647\theta-686884832\right)+x^{18}\left(56745577\theta^4+512911848\theta^3+1706476923\theta^2+2593842540\theta+1461946064\right)-2^{3} x^{19}\left(5403673\theta^4+39411950\theta^3+129809978\theta^2+200689723\theta+116245602\right)+2^{4} x^{20}\left(169515\theta^4+1407570\theta^3+7987370\theta^2+18253981\theta+13483356\right)+2^{6} x^{21}\left(97217\theta^4+692142\theta^3+1820686\theta^2+1961919\theta+708018\right)-2^{6} 3 x^{22}\left(8565\theta^4+73588\theta^3+231589\theta^2+312066\theta+153136\right)-2^{9} 3^{2} x^{23}\left(51\theta^4+242\theta^3+354\theta^2+101\theta-88\right)+2^{12} 3^{3} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 231, 10787, 606497, ... --> OEIS Normalized instanton numbers (n0=1): 52/5, 677/10, 5899/5, 273031/10, 3873518/5, ... ; Common denominator:...
\((z-1)(z^2+z-1)(64z^6-328z^5+603z^4-336z^3-82z^2+96z-1)(z+1)^2(8z^5+8z^4-37z^3+47z^2+17z+5)^2(3z-1)^3\)
No data for singularities
7
New Number: 24.6 | AESZ: | Superseeker: 22/3 -2493289/4374 | Hash: 97e76a6ce607bb4fccacf27108605ba7
Degree: 24
\(3^{3} \theta^4-3^{2} x\left(219\theta^4+446\theta^3+360\theta^2+137\theta+21\right)+3 x^{2}\left(15627\theta^4+62272\theta^3+87089\theta^2+4898\theta+9723\right)+x^{3}\left(87074\theta^4+751000\theta^3+1683376\theta^2+1419752\theta+477111\right)+x^{4}\left(1075878\theta^4+4128600\theta^3+1741490\theta^2-1627922\theta-880575\right)+x^{5}\left(20429470\theta^4+32622816\theta^3-100269124\theta^2-119243256\theta-38585541\right)+x^{6}\left(52275790\theta^4+137259464\theta^3-203637486\theta^2-370722394\theta-179832543\right)+x^{7}\left(273436034\theta^4-125542744\theta^3-803761016\theta^2-566839232\theta-164572889\right)+x^{8}\left(2111185276\theta^4-2958667464\theta^3-2052772526\theta^2+693402126\theta+563121065\right)+x^{9}\left(3487867272\theta^4-3567208236\theta^3-4453342156\theta^2-584255458\theta+1162144961\right)-x^{10}\left(2826802128\theta^4+10637991096\theta^3+17173705808\theta^2+12603066166\theta+2809918629\right)-x^{11}\left(8467877458\theta^4+22469569032\theta^3+37357510304\theta^2+30751477632\theta+9486012867\right)-x^{12}\left(47261798\theta^4-11482116968\theta^3-37739757574\theta^2-52237237770\theta-27215392395\right)+x^{13}\left(6972931522\theta^4+37972250992\theta^3+97327664068\theta^2+121840259280\theta+59059397729\right)+x^{14}\left(1229738322\theta^4-3456117864\theta^3-29388044354\theta^2-59103053358\theta-39073746749\right)-x^{15}\left(2875813642\theta^4+21430553672\theta^3+6570307164\theta^2+95717791808\theta+52198669355\right)-x^{16}\left(701991271\theta^4-20262056\theta^3-13732371862\theta^2-37536315274\theta-28587938635\right)+x^{17}\left(698255755\theta^4+5749394442\theta^3+16419399796\theta^2+20814436635\theta+9550138208\right)+x^{18}\left(206408655\theta^4+630883992\theta^3-382921555\theta^2-4052942572\theta-3878369584\right)-2^{3} x^{19}\left(15011337\theta^4+134546526\theta^3+382469296\theta^2+404733725\theta+122967534\right)-2^{4} x^{20}\left(1704271\theta^4+4092810\theta^3-2114254\theta^2-16703895\theta-13745412\right)+2^{6} x^{21}\left(186905\theta^4+1413862\theta^3+4086240\theta^2+4999141\theta+2192118\right)+2^{6} x^{22}\left(38911\theta^4+168220\theta^3+172367\theta^2-75610\theta-133744\right)-2^{9} 5 x^{23}\left(463\theta^4+3162\theta^3+8236\theta^2+9711\theta+4376\right)+2^{12} 5^{2} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 105, 452635/243, 14933417/576, ... --> OEIS Normalized instanton numbers (n0=1): 22/3, -11327/36, -2493289/4374, 115727987299/1492992, 607258502821/3499200, ... ; Common denominator:...
\((z-1)(64z^6-600z^5+1279z^4+84z^3-1926z^2+76z-1)(z^2-z-1)(z+1)^2(40z^5+136z^4+187z^3+19z^2+z+1)^2(z-3)^3\)
No data for singularities
8
New Number: 18.4 | AESZ: | Superseeker: 247/36 4444/9 | Hash: 32fa46e290b3c9bee37ffb7a8fd9f4a9
Degree: 18
\(2^{4} 3^{4} \theta^4-2^{2} 3^{2} x\left(3682\theta^4+5390\theta^3+4351\theta^2+1656\theta+252\right)+x^{2}\left(649332+6404206\theta^3+6069697\theta^2+3305113\theta^4+3016440\theta\right)-x^{3}\left(38636254\theta^4+15489180+108265181\theta^2+63679392\theta+93415794\theta^3\right)+x^{4}\left(764158344\theta^3+1036668572\theta^2+689221538\theta+184349683+256670733\theta^4\right)-x^{5}\left(3757797824\theta^3+5722058716\theta^2+4199976622\theta+1217504498+1069676441\theta^4\right)+x^{6}\left(14417904540\theta+4453297047+18342984749\theta^2+11509059738\theta^3+3046889312\theta^4\right)-x^{7}\left(6642155473\theta^4+24242800968\theta+7538554014+23131598018\theta^3+32019404863\theta^2\right)+2 x^{8}\left(6215749063\theta^4+17569348834\theta^3+11741029033\theta^2+1346877246\theta-1108958294\right)-2 x^{9}\left(10076009995\theta^4+24440563356\theta^3-1322218878\theta^2-28555856598\theta-15696067310\right)-x^{10}\left(49102102354-26413304169\theta^4-56670410178\theta^3+1614281629\theta^2+82337880208\theta\right)+x^{11}\left(47360089904\theta-39036891766\theta^3-6364831971\theta^2+31465171724-28479483424\theta^4\right)-x^{12}\left(43718118390\theta+18381816153+26430580224\theta^2-14524633248\theta^3-26803569313\theta^4\right)-x^{13}\left(18753392101\theta^4-62656633898\theta-24930556682+10542306176\theta^3-41804612332\theta^2\right)-x^{14}\left(20759304217+48901375684\theta+32921264817\theta^2-554448182\theta^3-6038807150\theta^4\right)+x^{15}\left(54976569672\theta+20722418334+2052372607\theta^4+51517404847\theta^2+19282089834\theta^3\right)-2 13 x^{16}\left(90710726\theta^4+669539662\theta^3+1753919819\theta^2+1925558652\theta+749345011\right)+2^{2} 7 13^{2} x^{17}(\theta+1)(100405\theta^3+577503\theta^2+1023193\theta+571997)-2^{4} 7^{2} 13^{3} x^{18}(\theta+1)(\theta+2)(4\theta+5)(4\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 155, 5389, 228523, ... --> OEIS Normalized instanton numbers (n0=1): 247/36, 1427/36, 4444/9, 306173/36, 2193041/12, ... ; Common denominator:...
\(-(z-1)(832z^7-355z^6-2395z^5+4723z^4-3034z^3+823z^2-83z+1)(-36+329z-457z^2+269z^3-1439z^4+182z^5)^2\)
No data for singularities