1
New Number: 14.1 | AESZ: | Superseeker: 0 0 | Hash: a8cf56492aecc07971e82c9104785180
Degree: 14
\(\theta^4-x\left(13\theta^4+14\theta^3+16\theta^2+9\theta+2\right)+x^{2}\left(33\theta^4-88\theta^3-265\theta^2-324\theta-148\right)+x^{3}\left(217\theta^4+2362\theta^3+6403\theta^2+8178\theta+4160\right)-2 x^{4}\left(677\theta^4+4134\theta^3+8089\theta^2+6210\theta+360\right)+2^{2} 3 x^{5}\left(151\theta^4-1266\theta^3-11610\theta^2-28955\theta-25110\right)+2^{2} x^{6}\left(1895\theta^4+37302\theta^3+176991\theta^2+355848\theta+268836\right)-2^{2} x^{7}\left(9635\theta^4+89170\theta^3+185885\theta^2-107394\theta-522464\right)+2^{3} x^{8}\left(5907\theta^4-10636\theta^3-416125\theta^2-1666326\theta-2051920\right)+2^{5} x^{9}\left(2947\theta^4+80284\theta^3+519934\theta^2+1328475\theta+1205150\right)-2^{6} x^{10}\left(6122\theta^4+84852\theta^3+397555\theta^2+722745\theta+356430\right)+2^{6} 3 x^{11}\left(2259\theta^4+13398\theta^3-46549\theta^2-456244\theta-796656\right)+2^{7} 3^{2} x^{12}(\theta+4)(371\theta^3+8580\theta^2+53325\theta+101564)-2^{10} 3^{3} x^{13}(\theta+4)(\theta+5)(51\theta^2+519\theta+1330)+2^{11} 3^{4} 5 x^{14}(\theta+4)(\theta+5)^2(\theta+6)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 2, 16, 48, 264, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/4, 0, -1/2, 0, ... ; Common denominator:...
\((z-1)(6z-1)(4z-1)(3z+1)(4z+1)(5z-1)(2z+1)^2(2z-1)^2(6z^2-2z+1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 1}{ 6}-\frac{ 1}{ 6}\sqrt{ 5}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 6}+\frac{ 1}{ 6}\sqrt{ 5}I\) | \(\frac{ 1}{ 5}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(0\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(5\) |
| \(-1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(5\) |
| \(1\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) | \(2\) | \(6\) |
2
New Number: 6.20 | AESZ: | Superseeker: 0 -1/3 | Hash: 5169c67af7361bf7e6467dabea9612bd
Degree: 6
\(\theta^4+x\left(11\theta+26\theta^3+2+13\theta^4+24\theta^2\right)-x^{2}(141\theta^2+282\theta+296)(\theta+1)^2-2 x^{3}(\theta+2)(\theta+1)(407\theta^2+1221\theta+654)+2^{2} 7 x^{4}(\theta+3)(\theta+1)(389\theta^2+1556\theta+1460)-2^{3} 3 7^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+166)+2^{5} 3 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2, 28, -224, 2464, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...
\((-1+2z)(4z-1)(21z^2-9z+1)(1+14z)^2\)
| \(-\frac{ 1}{ 14}\) | \(0\) | \(\frac{ 3}{ 14}-\frac{ 1}{ 42}\sqrt{ 3}I\) | \(\frac{ 3}{ 14}+\frac{ 1}{ 42}\sqrt{ 3}I\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(1\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(5\) |
3
New Number: 7.17 | AESZ: | Superseeker: 0 18 | Hash: c248fd7c807d0aae71ef687a9ee40c80
Degree: 7
\(\theta^4+3 x\left(87\theta^4+84\theta^3+86\theta^2+44\theta+9\right)+2 3^{3} x^{2}\left(539\theta^4+1076\theta^3+1366\theta^2+880\theta+233\right)+2 3^{5} x^{3}\left(3699\theta^4+11424\theta^3+17579\theta^2+13389\theta+4088\right)+3^{7} x^{4}\left(30367\theta^4+128696\theta^3+235722\theta^2+205070\theta+69226\right)+3^{9} x^{5}\left(74547\theta^4+405660\theta^3+871096\theta^2+848930\theta+310507\right)+2 3^{11} 5 x^{6}(2\theta+3)(5066\theta^3+26325\theta^2+44815\theta+23766)+2^{2} 3^{14} 5^{2} 7^{2} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -27, 783, -23481, 717903, ... --> OEIS Normalized instanton numbers (n0=1): 0, -27/2, 18, -999/2, 1566, ... ; Common denominator:...
\((27z+1)(1323z^2+72z+1)(36z+1)^2(45z+1)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 36}\) | \(-\frac{ 4}{ 147}-\frac{ 1}{ 441}\sqrt{ 3}I\) | \(-\frac{ 4}{ 147}+\frac{ 1}{ 441}\sqrt{ 3}I\) | \(-\frac{ 1}{ 45}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(3\) |
4
New Number: 8.54 | AESZ: | Superseeker: 0 1/3 | Hash: bb80872017d0578a4ae56172666b807c
Degree: 8
\(\theta^4+x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)-2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)+2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)+2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 72, 1296, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/2, 1/3, -1, 2, ... ; Common denominator:...
\((4z+1)(6z+1)(43z^2+13z+1)(2z+1)^2(12z-1)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 6}\) | \(-\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(-\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(0\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(1\) | \(4\) |
5
New Number: 8.64 | AESZ: | Superseeker: 0 -32768 | Hash: 00b5810e4a2d21fec464e4e87169df86
Degree: 8
\(\theta^4-2^{4} x\left(32\theta^4+16\theta^3+14\theta^2+6\theta+1\right)+2^{10} x^{2}\left(86\theta^4+176\theta^3+184\theta^2+76\theta+13\right)-2^{16} x^{3}\left(61\theta^4+510\theta^3+620\theta^2+327\theta+68\right)-2^{22} x^{4}\left(110\theta^4-260\theta^3-942\theta^2-608\theta-141\right)+2^{26} x^{5}\left(708\theta^4+2160\theta^3-666\theta^2-1230\theta-397\right)+2^{32} x^{6}\left(134\theta^4-1536\theta^3-1488\theta^2-492\theta-29\right)-2^{38} 5 x^{7}\left(73\theta^4+170\theta^3+168\theta^2+83\theta+17\right)-2^{44} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 272, -15104, -2814704, ... --> OEIS Normalized instanton numbers (n0=1): 0, -1116, -32768, -2011784, -92274688, ... ; Common denominator:...
\(-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2\)
| ≈\(-0.23168\) | \(-\frac{ 1}{ 160}-\frac{ 1}{ 320}\sqrt{ 14}\) | \(0\) | \(-\frac{ 1}{ 160}+\frac{ 1}{ 320}\sqrt{ 14}\) | ≈\(0.006465-0.004906I\) | ≈\(0.006465+0.004906I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) |
6
New Number: 8.82 | AESZ: | Superseeker: 0 -1/3 | Hash: 8bab1ddc8b31cb2c21f01402f27895ce
Degree: 8
\(\theta^4-x\theta(3\theta^3-6\theta^2-4\theta-1)-x^{2}\left(211\theta^4+856\theta^3+1433\theta^2+1184\theta+384\right)+2 x^{3}\left(761\theta^4+3288\theta^3+6477\theta^2+6654\theta+2700\right)+2^{2} x^{4}(\theta+1)(2013\theta^3+17379\theta^2+40726\theta+28548)-2^{3} x^{5}(\theta+1)(15719\theta^3+126105\theta^2+325408\theta+269508)+2^{5} 3^{2} x^{6}(\theta+1)(\theta+2)(1817\theta^2+11967\theta+19631)-2^{7} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(89\theta+350)+2^{9} 3^{3} 43 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, -72, 1296, ... --> OEIS Normalized instanton numbers (n0=1): 0, 1/2, -1/3, -1, -2, ... ; Common denominator:...
\((6z-1)(4z-1)(43z^2-13z+1)(12z+1)^2(-1+2z)^2\)
| \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 13}{ 86}-\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 13}{ 86}+\frac{ 1}{ 86}\sqrt{ 3}I\) | \(\frac{ 1}{ 6}\) | \(\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) |
7
New Number: 16.1 | AESZ: | Superseeker: 0 0 | Hash: ce5c5b062cf22bc8935e236748d3c341
Degree: 16
\(\theta^4-2 3^{3} x\left(20\theta^4+2\theta^3-2\theta^2-3\theta-1\right)+2^{2} x^{2}\left(151949\theta^4-14254\theta^3-70179\theta^2-42595\theta-6216\right)-2^{3} 3^{3} x^{3}\left(1072962\theta^4-437056\theta^3-954370\theta^2-299161\theta+63015\right)+2^{4} x^{4}\left(4076695248\theta^4-3035262048\theta^3-4506216565\theta^2-507642115\theta+724750374\right)-2^{6} 3^{3} x^{5}\left(8140262160\theta^4-8793595488\theta^3-8101604275\theta^2+976456152\theta+1899621139\right)+2^{8} x^{6}\left(9218034049688\theta^4-12854277745104\theta^3-5970652217281\theta^2+3294754727367\theta+1790401729671\right)-2^{10} 3^{3} x^{7}\left(11107333819640\theta^4-18438103960576\theta^3-2693186543039\theta^2+5732786101958\theta+1009111312972\right)+2^{12} x^{8}\left(7427475217648672\theta^4-13903863079521824\theta^3+549990096918185\theta^2+4264594906566611\theta-196065070315692\right)-2^{14} 3^{3} x^{9}\left(5006788889131248\theta^4-10423307017692208\theta^3+1148559437524935\theta^2+2739247379862508\theta-601863144518181\right)+2^{16} 3^{4} x^{10}\left(20921192499862036\theta^4-51546334623445432\theta^3+3958462764104225\theta^2+10021243264975981\theta-3621545193405921\right)-2^{18} 3^{7} x^{11}\left(5701586950847588\theta^4-21188224783674368\theta^3-757538843568497\theta^2+2746993547213600\theta-1268918638558608\right)+2^{23} 3^{10} x^{12}\left(39160297802908\theta^4-814299201549560\theta^3-95884988762411\theta^2+91861472904467\theta-44237005356800\right)+2^{28} 3^{13} x^{13}\left(5094274414759\theta^4+20214234618156\theta^3-2519812312315\theta^2-4449859616032\theta+1201444818880\right)-2^{35} 3^{16} 5 31 x^{14}\theta(269358010\theta^3+131761607\theta^2-826543489\theta-380205376)-2^{40} 3^{19} 5^{2} 31^{2} x^{15}\theta(\theta+1)(1997\theta^2+119865\theta+91208)+2^{47} 3^{22} 5^{3} 31^{3} x^{16}\theta(\theta+2)(\theta+1)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -54, -1362, -73548, -4170906, ... --> OEIS Normalized instanton numbers (n0=1): 0, 12293/4, 0, -8127101, 0, ... ; Common denominator:...
\(\)
No data for singularities
8
New Number: 6.13 | AESZ: | Superseeker: 0 0 | Hash: b7b28238d79425febad0c26d36cce7ef
Degree: 6
\(3 \theta^4-2 3 5^{2} x\left(8\theta^4+10\theta^3+10\theta^2+5\theta+1\right)+2^{2} 3 5 x^{2}\left(3129\theta^4+7266\theta^3+9285\theta^2+5913\theta+1490\right)-2^{3} 3 5^{3} x^{3}\left(4774\theta^4+15120\theta^3+22026\theta^2+15303\theta+4073\right)+2^{4} 3 5^{5} x^{4}\left(3552\theta^4+13296\theta^3+20195\theta^2+13733\theta+3492\right)-2^{6} 3 5^{7} x^{5}(\theta+1)^2(524\theta^2+1096\theta+611)+2^{10} 5^{9} x^{6}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 50, 3450, 267500, 22029250, ... --> OEIS Normalized instanton numbers (n0=1): 0, 165/4, 0, -44335/8, 0, ... ; Common denominator:...
\(\)
No data for singularities
9
New Number: 2.71 | AESZ: | Superseeker: 0 0 | Hash: 757b011780c5986bd45a5bf434c76c28
Degree: 2
\(\theta^4-2^{5} x(2\theta+1)^2(2\theta^2+2\theta+1)+2^{8} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 2160, 181760, 17021200, ... --> OEIS Normalized instanton numbers (n0=1): 0, -20, 0, -865, 0, ... ; Common denominator:...
\((-1+128z)^2\)
| \(0\) | \(\frac{ 1}{ 128}\) | \(\infty\) |
|---|---|---|
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 4}\) | \(\frac{ 5}{ 4}\) |
| \(0\) | \(1\) | \(\frac{ 3}{ 2}\) |