31
New Number: 5.128 | AESZ: | Superseeker: -50 -20600 | Hash: 5a0123bd26e43e2fd9c7e6c3d21a2a33
Degree: 5
\(\theta^4+2 5 x\left(60\theta^3+45\theta^2+15\theta+2\right)-2^{2} 5^{4} x^{2}\left(8\theta^4+8\theta^3-29\theta^2-20\theta-4\right)-2^{4} 5^{5} x^{3}\left(16\theta^4+216\theta^3+288\theta^2+147\theta+26\right)+2^{6} 5^{7} x^{4}(13\theta^2+37\theta+27)(2\theta+1)^2-2^{8} 5^{9} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 900, -38000, 122500, ... --> OEIS Normalized instanton numbers (n0=1): -50, -1675/2, -20600, -1433000, -408984396/5, ... ; Common denominator:...
\(-(800000z^3-10000z^2-200z-1)(-1+100z)^2\)
| ≈\(-0.006091-0.003681I\) | ≈\(-0.006091+0.003681I\) | \(0\) | \(\frac{ 1}{ 100}\) | ≈\(0.024681\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
32
New Number: 5.129 | AESZ: | Superseeker: -26 -8344 | Hash: 6c96cbe2aa88f7096e6b9f02e290d167
Degree: 5
\(\theta^4+2 x\left(24\theta^4+228\theta^3+181\theta^2+67\theta+10\right)-2^{2} 5 x^{2}\left(584\theta^4+392\theta^3-1717\theta^2-1320\theta-300\right)-2^{4} 3 5^{2} x^{3}\left(128\theta^4+2328\theta^3+3008\theta^2+1563\theta+290\right)+2^{6} 3^{2} 5^{3} x^{4}(2\theta+1)(266\theta^3+831\theta^2+883\theta+315)-2^{8} 3^{3} 5^{4} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 900, -52400, 3482500, ... --> OEIS Normalized instanton numbers (n0=1): -26, -561/2, -8344, -278334, -11536332, ... ; Common denominator:...
\(-(20z-1)(108z+1)(80z+1)(-1+60z)^2\)
| \(-\frac{ 1}{ 80}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\frac{ 1}{ 60}\) | \(\frac{ 1}{ 20}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
33
New Number: 5.12 | AESZ: 74 | Superseeker: -30 -14632 | Hash: e668180adb7c88d4e5fbab5eb7ee61c7
Degree: 5
\(\theta^4-2 3 x\left(99\theta^4+36\theta^3+39\theta^2+21\theta+4\right)+2^{2} 3^{2} x^{2}\left(3807\theta^4+3564\theta^3+3798\theta^2+1683\theta+284\right)-2^{3} 3^{5} x^{3}\left(7857\theta^4+13608\theta^3+14562\theta^2+7317\theta+1444\right)+2^{4} 3^{9} x^{4}\left(2592\theta^4+7128\theta^3+8550\theta^2+4851\theta+1052\right)-2^{5} 3^{13} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1152, 71520, 5101200, ... --> OEIS Normalized instanton numbers (n0=1): -30, -516, -14632, -4227807/8, -22139868, ... ; Common denominator:...
\(-(-1+54z)(162z-1)^2(108z-1)^2\)
| \(0\) | \(\frac{ 1}{ 162}\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 54}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(0\) | \(4\) | \(1\) | \(2\) | \(\frac{ 4}{ 3}\) |
34
New Number: 5.130 | AESZ: | Superseeker: 108 122756 | Hash: 829aca3d7a00547e299bf794c8643162
Degree: 5
\(\theta^4-2^{2} 3 x\left(12\theta^4+96\theta^3+71\theta^2+23\theta+3\right)-2^{4} 3^{3} x^{2}\left(160\theta^4+64\theta^3-544\theta^2-340\theta-65\right)+2^{8} 3^{5} x^{3}\left(32\theta^4+576\theta^3+588\theta^2+240\theta+35\right)+2^{12} 3^{7} x^{4}(28\theta^2+52\theta+31)(2\theta+1)^2+2^{16} 3^{9} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 3780, 558000, 98828100, ... --> OEIS Normalized instanton numbers (n0=1): 108, -1782, 122756, -5930658, 607239072, ... ; Common denominator:...
\((144z-1)(6912z^2+288z-1)(1+144z)^2\)
| \(-\frac{ 1}{ 48}-\frac{ 1}{ 72}\sqrt{ 3}\) | \(-\frac{ 1}{ 144}\) | \(0\) | \(-\frac{ 1}{ 48}+\frac{ 1}{ 72}\sqrt{ 3}\) | \(\frac{ 1}{ 144}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
35
New Number: 5.131 | AESZ: | Superseeker: 325 9106834/3 | Hash: 79657f8be76c1fed5fd1a658989ca15a
Degree: 5
\(\theta^4-x\left(60+460\theta+1565\theta^2+2210\theta^3-623\theta^4\right)-2^{5} 3^{2} x^{2}\left(550\theta^4+2764\theta^3-3581\theta^2-2190\theta-459\right)-2^{8} 3^{4} x^{3}\left(2164\theta^4-17928\theta^3-13315\theta^2-3645\theta-126\right)+2^{14} 3^{8} x^{4}(2\theta+1)(148\theta^3+114\theta^2-35\theta-41)-2^{20} 3^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 60, 5508, 362400, -34621020, ... --> OEIS Normalized instanton numbers (n0=1): 325, -24254, 9106834/3, -514805406, 102077718255, ... ; Common denominator:...
\(-(81z-1)(82944z^2-448z+1)(1+576z)^2\)
| \(-\frac{ 1}{ 576}\) | \(0\) | \(\frac{ 7}{ 2592}-\frac{ 1}{ 648}\sqrt{ 2}I\) | \(\frac{ 7}{ 2592}+\frac{ 1}{ 648}\sqrt{ 2}I\) | \(\frac{ 1}{ 81}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
36
New Number: 5.132 | AESZ: | Superseeker: 388 3446444 | Hash: 55a5cb23b8c035363ff67bcc0d5fd556
Degree: 5
\(\theta^4+2^{2} x\left(92\theta^4-680\theta^3-481\theta^2-141\theta-18\right)-2^{8} 3^{2} x^{2}\left(192\theta^4+456\theta^3-514\theta^2-323\theta-67\right)-2^{14} 3^{4} x^{3}\left(88\theta^4-312\theta^3-248\theta^2-75\theta-5\right)+2^{20} 3^{7} x^{4}(2\theta+1)(8\theta^3+8\theta^2+\theta-1)-2^{26} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 72, 12456, 3202560, 1030375080, ... --> OEIS Normalized instanton numbers (n0=1): 388, -23196, 3446444, -571523888, 119779121440, ... ; Common denominator:...
\(-(144z-1)(576z-1)(64z-1)(1+576z)^2\)
| \(-\frac{ 1}{ 576}\) | \(0\) | \(\frac{ 1}{ 576}\) | \(\frac{ 1}{ 144}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
37
New Number: 5.133 | AESZ: | Superseeker: 192 1016256 | Hash: 0f3cb34d2bc462fbc58cdf15040595d1
Degree: 5
\(\theta^4+2^{4} x\left(24\theta^4-96\theta^3-70\theta^2-22\theta-3\right)-2^{10} x^{2}\left(124\theta^4+496\theta^3-271\theta^2-202\theta-45\right)-2^{17} 3^{2} x^{3}\left(32\theta^4-56\theta^3-66\theta^2-31\theta-5\right)+2^{24} 3^{3} x^{4}(\theta+1)(2\theta+1)(6\theta^2+11\theta+6)+2^{32} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 5136, 710400, 112104720, ... --> OEIS Normalized instanton numbers (n0=1): 192, -9940, 1016256, -134713756, 20854352960, ... ; Common denominator:...
\((256z-1)(64z+1)(192z-1)(1+384z)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 384}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 192}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
38
New Number: 5.134 | AESZ: | Superseeker: 176 1215248/3 | Hash: 5bd656df18dc5d02b2f2a068ba88ab74
Degree: 5
\(\theta^4+2^{2} x\left(4\theta^4-352\theta^3-250\theta^2-74\theta-9\right)-2^{4} 3 x^{2}\left(3168\theta^4+5952\theta^3-3712\theta^2-2648\theta-519\right)-2^{8} 3^{3} x^{3}\left(2912\theta^4-3008\theta^3-3152\theta^2-1160\theta-145\right)+2^{12} 3^{3} 5 x^{4}(2\theta+1)(824\theta^3+1668\theta^2+1342\theta+405)+2^{16} 3^{4} 5^{2} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 4572, 918000, 228519900, ... --> OEIS Normalized instanton numbers (n0=1): 176, -3238, 1215248/3, -18807038, 3651829680, ... ; Common denominator:...
\((48z-1)(432z-1)(16z+1)(1+240z)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 240}\) | \(0\) | \(\frac{ 1}{ 432}\) | \(\frac{ 1}{ 48}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
39
New Number: 5.13 | AESZ: 83 | Superseeker: -80 -174096 | Hash: 171e1251d8e4f7de878d0d07de6f58ab
Degree: 5
\(\theta^4-2^{4} x\left(88\theta^4+32\theta^3+33\theta^2+17\theta+3\right)+2^{9} x^{2}\left(1504\theta^4+1408\theta^3+1436\theta^2+596\theta+93\right)-2^{18} x^{3}\left(776\theta^4+1344\theta^3+1381\theta^2+651\theta+117\right)+2^{23} 3 x^{4}(2\theta+1)(512\theta^3+1152\theta^2+1054\theta+339)-2^{31} 3^{2} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 5328, 779520, 131619600, ... --> OEIS Normalized instanton numbers (n0=1): -80, -2954, -174096, -13270953, -1179175536, ... ; Common denominator:...
\(-(128z-1)(384z-1)^2(256z-1)^2\)
| \(0\) | \(\frac{ 1}{ 384}\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 128}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 5}{ 4}\) |
| \(0\) | \(4\) | \(1\) | \(2\) | \(\frac{ 3}{ 2}\) |
40
New Number: 5.14 | AESZ: 116 | Superseeker: 64 23360 | Hash: 0b366ad8c78b6697205c5a7fff270f5b
Degree: 5
\(\theta^4-2^{5} x\left(10\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(52\theta^4+472\theta^3+832\theta^2+492\theta+103\right)+2^{16} x^{3}\left(14\theta^4+12\theta^3-96\theta^2-105\theta-29\right)-2^{18} x^{4}(2\theta+1)(56\theta^3+468\theta^2+646\theta+249)-2^{24} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 2448, 273920, 38525200, ... --> OEIS Normalized instanton numbers (n0=1): 64, 12, 23360, 654490, 53956288, ... ; Common denominator:...
\(-(-1+256z)(32z+1)^2(64z-1)^2\)
| \(-\frac{ 1}{ 32}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 4}\) |
| \(3\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 5}{ 4}\) |
| \(4\) | \(0\) | \(2\) | \(1\) | \(\frac{ 3}{ 2}\) |
41
New Number: 5.15 | AESZ: 117 | Superseeker: -52/3 -17428 | Hash: 111a4ce3248a309bf6283916fd9f11c4
Degree: 5
\(3^{2} \theta^4+2^{2} 3 x\left(256\theta^4+176\theta^3+133\theta^2+45\theta+6\right)+2^{7} x^{2}\left(2588\theta^4+1952\theta^3+584\theta^2+15\theta-15\right)+2^{12} x^{3}\left(3183\theta^4+2466\theta^3+1801\theta^2+711\theta+111\right)+2^{17} 7 x^{4}\left(134\theta^4+250\theta^3+180\theta^2+55\theta+5\right)-2^{22} 7^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 424, -36224, 3778216, ... --> OEIS Normalized instanton numbers (n0=1): -52/3, 1348/3, -17428, 884000, -163422880/3, ... ; Common denominator:...
\(-(16z+1)(256z^2-176z-1)(3+224z)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 3}{ 224}\) | \(\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}\) | \(0\) | \(\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(1\) |
42
New Number: 5.16 | AESZ: 118 | Superseeker: 55 116555 | Hash: d950d38dab80e3772855675af0cdb950
Degree: 5
\(\theta^4-x\left(465\theta^4+594\theta^3+431\theta^2+134\theta+16\right)+2^{4} x^{2}\left(2625\theta^4+1911\theta^3-946\theta^2-884\theta-176\right)-2^{6} x^{3}\left(16105\theta^4-3624\theta^3-5241\theta^2-1284\theta-36\right)-2^{11} 7 x^{4}\left(155\theta^4+334\theta^3+306\theta^2+139\theta+26\right)+2^{16} 7^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 1816, 310336, 64483576, ... --> OEIS Normalized instanton numbers (n0=1): 55, 1915, 116555, 10661240, 1227998285, ... ; Common denominator:...
\((z-1)(1024z^2+352z-1)(-1+56z)^2\)
| \(-\frac{ 11}{ 64}-\frac{ 5}{ 64}\sqrt{ 5}\) | \(0\) | \(-\frac{ 11}{ 64}+\frac{ 5}{ 64}\sqrt{ 5}\) | \(\frac{ 1}{ 56}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
43
New Number: 5.17 | AESZ: 119 | Superseeker: 28/3 3892/3 | Hash: dc8ec37012f2c92c83e6519935956eeb
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(256\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+2^{7} x^{2}\left(3104\theta^4+7040\theta^3+8012\theta^2+4452\theta+927\right)-2^{15} x^{3}\left(752\theta^4+2304\theta^3+3042\theta^2+1854\theta+405\right)+2^{21} x^{4}(2\theta+1)(176\theta^3+552\theta^2+622\theta+231)-2^{31} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1128, 67200, 4634280, ... --> OEIS Normalized instanton numbers (n0=1): 28/3, 394/3, 3892/3, 108262/3, 1044128, ... ; Common denominator:...
\(-(-1+128z)(64z-1)^2(128z-3)^2\)
| \(0\) | \(\frac{ 1}{ 128}\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 128}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 4}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 3}{ 4}\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(1\) | \(4\) | \(\frac{ 3}{ 2}\) |
44
New Number: 5.18 | AESZ: 124 | Superseeker: 163/61 4795/61 | Hash: 394b401a3162e31c79ede5b46973791d
Degree: 5
\(61^{2} \theta^4-61 x\left(3029\theta^4+5572\theta^3+4677\theta^2+1891\theta+305\right)+x^{2}\left(1215215\theta^4+3428132\theta^3+4267228\theta^2+2572675\theta+611586\right)-3^{4} x^{3}\left(39370\theta^4+140178\theta^3+206807\theta^2+142191\theta+37332\right)+3^{8} x^{4}\left(566\theta^4+2230\theta^3+3356\theta^2+2241\theta+558\right)-3^{13} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 69, 1427, 35749, ... --> OEIS Normalized instanton numbers (n0=1): 163/61, 630/61, 4795/61, 48422/61, 599809/61, ... ; Common denominator:...
\(-(243z^3-200z^2+47z-1)(-61+81z)^2\)
| \(0\) | ≈\(0.023574\) | ≈\(0.399736-0.121575I\) | ≈\(0.399736+0.121575I\) | \(\frac{ 61}{ 81}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |
45
New Number: 5.19 | AESZ: 180 | Superseeker: -624 -43406256 | Hash: c174fb2dfd87730e48b4ae8b57ac66df
Degree: 5
\(\theta^4-2^{4} 3 x\left(198\theta^4+72\theta^3+69\theta^2+33\theta+5\right)+2^{9} 3^{2} x^{2}\left(7614\theta^4+7128\theta^3+6813\theta^2+2529\theta+340\right)-2^{14} 3^{5} x^{3}\left(15714\theta^4+27216\theta^3+26343\theta^2+11151\theta+1685\right)+2^{19} 3^{9} x^{4}(3\theta+1)(3\theta+2)(576\theta^2+1008\theta+605)-2^{27} 3^{13} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 240, 173520, 170016000, 193451504400, ... --> OEIS Normalized instanton numbers (n0=1): -624, -137190, -43406256, -18281817141, -9083828410320, ... ; Common denominator:...
\(-(-1+864z)(2592z-1)^2(1728z-1)^2\)
| \(0\) | \(\frac{ 1}{ 2592}\) | \(\frac{ 1}{ 1728}\) | \(\frac{ 1}{ 864}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 4}{ 3}\) |
| \(0\) | \(4\) | \(1\) | \(2\) | \(\frac{ 5}{ 3}\) |
46
New Number: 5.1 | AESZ: 17 | Superseeker: 6/5 118/5 | Hash: 370d10edbf5900002f79cf6163e106a5
Degree: 5
\(5^{2} \theta^4-3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2 3 x^{2}\left(531\theta^4+828\theta^3+541\theta^2+155\theta+15\right)-2 3^{3} x^{3}\left(423\theta^4+2160\theta^3+4399\theta^2+3795\theta+1170\right)+3^{5} x^{4}\left(279\theta^4+1368\theta^3+2270\theta^2+1586\theta+402\right)-3^{10} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, 27, 381, 6219, ... --> OEIS Normalized instanton numbers (n0=1): 6/5, 39/10, 118/5, 1443/10, 6108/5, ... ; Common denominator:...
\(-(27z-1)(27z^2+1)(-5+9z)^2\)
| \(0-\frac{ 1}{ 9}\sqrt{ 3}I\) | \(0\) | \(0+\frac{ 1}{ 9}\sqrt{ 3}I\) | \(\frac{ 1}{ 27}\) | \(\frac{ 5}{ 9}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(1\) |
47
New Number: 5.20 | AESZ: 186 | Superseeker: 49/19 1761/19 | Hash: b3d164f22d02de1efcd62d3aa9ab5ce4
Degree: 5
\(19^{2} \theta^4-19 x\left(700\theta^4+1238\theta^3+999\theta^2+380\theta+57\right)-x^{2}\left(64745\theta^4+368006\theta^3+609133\theta^2+412756\theta+102258\right)+3^{3} x^{3}\left(6397\theta^4+12198\theta^3-11923\theta^2-27360\theta-11286\right)+3^{6} x^{4}\left(64\theta^4+1154\theta^3+2425\theta^2+1848\theta+486\right)-3^{11} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, 51, 1029, 25299, ... --> OEIS Normalized instanton numbers (n0=1): 49/19, 252/19, 1761/19, 18990/19, 246159/19, ... ; Common denominator:...
\(-(z+1)(243z^2+35z-1)(-19+27z)^2\)
| \(-1\) | \(-\frac{ 35}{ 486}-\frac{ 13}{ 486}\sqrt{ 13}\) | \(0\) | \(-\frac{ 35}{ 486}+\frac{ 13}{ 486}\sqrt{ 13}\) | \(\frac{ 19}{ 27}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
48
New Number: 5.21 | AESZ: 187 | Superseeker: -107 -121311 | Hash: 9a367922f464a13fa56d1c2e238faa34
Degree: 5
\(\theta^4-x\left(64\theta^4-898\theta^3-653\theta^2-204\theta-27\right)-3^{2} x^{2}\left(6397\theta^4+13390\theta^3-10135\theta^2-7492\theta-1650\right)+3^{4} x^{3}\left(64745\theta^4-109026\theta^3-106415\theta^2-39528\theta-4626\right)+3^{9} 19 x^{4}\left(700\theta^4+1562\theta^3+1485\theta^2+704\theta+138\right)-3^{14} 19^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -27, 1971, -220941, 30762099, ... --> OEIS Normalized instanton numbers (n0=1): -107, -7701/4, -121311, -6204874, -518204863, ... ; Common denominator:...
\(-(243z+1)(243z^2-35z-1)(-1+171z)^2\)
| \(\frac{ 35}{ 486}-\frac{ 13}{ 486}\sqrt{ 13}\) | \(-\frac{ 1}{ 243}\) | \(0\) | \(\frac{ 1}{ 171}\) | \(\frac{ 35}{ 486}+\frac{ 13}{ 486}\sqrt{ 13}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
49
New Number: 5.22 | AESZ: 193 | Superseeker: 129/7 41441/7 | Hash: 44e6fc2823d5ff31e66059ba6b37f2ae
Degree: 5
\(7^{2} \theta^4-7 x\left(1135\theta^4+2204\theta^3+1683\theta^2+581\theta+77\right)+x^{2}\left(28723\theta^4+40708\theta^3+13260\theta^2-1337\theta-896\right)-x^{3}\left(32126\theta^4+38514\theta^3+26511\theta^2+10731\theta+1806\right)+7 11 x^{4}\left(130\theta^4+254\theta^3+192\theta^2+65\theta+8\right)+11^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 11, 559, 42923, 3996751, ... --> OEIS Normalized instanton numbers (n0=1): 129/7, 1557/7, 41441/7, 1594332/7, 75470601/7, ... ; Common denominator:...
\((z^3+84z^2-159z+1)(-7+11z)^2\)
| ≈\(-85.852157\) | \(0\) | ≈\(0.00631\) | \(\frac{ 7}{ 11}\) | ≈\(1.845846\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
50
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:...
\(-(-1+81z)(27z-17)^2(z-1)^2\)
| \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 17}{ 27}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(1\) | \(1\) |
51
New Number: 5.24 | AESZ: 195 | Superseeker: 285/29 40626/29 | Hash: 49a600431b3e9aaa9d9d6947f8df7d2b
Degree: 5
\(29^{2} \theta^4-29 x\left(3026\theta^4+5848\theta^3+4577\theta^2+1653\theta+232\right)+x^{2}\left(5568+57768\theta+239159\theta^2+424220\theta^3+258647\theta^4\right)-x^{3}\left(76560+336864\theta+581647\theta^2+532614\theta^3+272743\theta^4\right)+2^{2} 17 x^{4}\left(1922\theta^4+6193\theta^3+8121\theta^2+4894\theta+1112\right)-2^{2} 3 17^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 264, 13040, 778840, ... --> OEIS Normalized instanton numbers (n0=1): 285/29, 2362/29, 40626/29, 997476/29, 30096841/29, ... ; Common denominator:...
\(-(27z^3-67z^2+102z-1)(-29+34z)^2\)
| \(0\) | ≈\(0.009868\) | \(\frac{ 29}{ 34}\) | ≈\(1.235807-1.492036I\) | ≈\(1.235807+1.492036I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |
52
New Number: 5.25 | AESZ: 198 | Superseeker: -84/11 -9052/11 | Hash: a1f924763b047c2720d99cfca5ca63db
Degree: 5
\(11^{2} \theta^4+7 11 x\left(130\theta^4+266\theta^3+210\theta^2+77\theta+11\right)-x^{2}\left(11198+55253\theta+103725\theta^2+89990\theta^3+32126\theta^4\right)+x^{3}\left(1716+20625\theta+63474\theta^2+74184\theta^3+28723\theta^4\right)-7 x^{4}\left(1135\theta^4+2336\theta^3+1881\theta^2+713\theta+110\right)+7^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -7, 199, -8359, 423751, ... --> OEIS Normalized instanton numbers (n0=1): -84/11, 639/11, -9052/11, 189021/11, -4838013/11, ... ; Common denominator:...
\((z^3-159z^2+84z+1)(-11+7z)^2\)
| ≈\(-0.011648\) | \(0\) | ≈\(0.541757\) | \(\frac{ 11}{ 7}\) | ≈\(158.469891\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
53
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:...
\(-(z-1)(81z-1)^2(51z-1)^2\)
| \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 1}{ 51}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(4\) | \(2\) | \(1\) |
54
New Number: 5.27 | AESZ: 202 | Superseeker: -113/19 -8515/19 | Hash: 3bf3c283277de7b3808ad309fac9b7a1
Degree: 5
\(19^{2} \theta^4+19 x\left(1370\theta^4+2620\theta^3+2089\theta^2+779\theta+114\right)+x^{2}\left(39521\theta^4-3916\theta^3-106779\theta^2-95266\theta-25384\right)-2^{3} x^{3}\left(1649\theta^4+19779\theta^3+29667\theta^2+17613\theta+3876\right)-2^{4} 5 x^{4}(\theta+1)(499\theta^3+1411\theta^2+1378\theta+456)-2^{9} 5^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 142, -4920, 205326, ... --> OEIS Normalized instanton numbers (n0=1): -113/19, 2921/76, -8515/19, 146869/19, -3105422/19, ... ; Common denominator:...
\(-(z-1)(32z^2+71z+1)(19+20z)^2\)
| \(-\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | \(-\frac{ 19}{ 20}\) | \(-\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | \(0\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(1\) |
55
New Number: 5.28 | AESZ: 203 | Superseeker: -13/5 -6729/5 | Hash: dfab012366b4bc6f7af83dc79f28b802
Degree: 5
\(5^{2} \theta^4+5 x\theta(499\theta^3+86\theta^2+53\theta+10)+2^{4} x^{2}\left(1649\theta^4-13183\theta^3-19776\theta^2-11020\theta-2200\right)-2^{6} x^{3}\left(39521\theta^4+162000\theta^3+142095\theta^2+51540\theta+6540\right)-2^{11} 19 x^{4}\left(1370\theta^4+2860\theta^3+2449\theta^2+1019\theta+174\right)-2^{16} 19^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 88, -1728, 99576, ... --> OEIS Normalized instanton numbers (n0=1): -13/5, 427/5, -6729/5, 173044/5, -952275, ... ; Common denominator:...
\(-(32z-1)(32z^2+71z+1)(5+152z)^2\)
| \(-\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\) | \(-\frac{ 5}{ 152}\) | \(-\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\) | \(0\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(1\) |
56
New Number: 5.29 | AESZ: 208 | Superseeker: 274/7 281388/7 | Hash: f1d6dfa8a5cdcc2513dfca4243565b2f
Degree: 5
\(7^{2} \theta^4-2 7 x\left(1056\theta^4+1884\theta^3+1397\theta^2+455\theta+56\right)+2^{2} 3 x^{2}\left(22760\theta^4+13672\theta^3-22537\theta^2-18116\theta-3584\right)-2^{4} x^{3}\left(53312\theta^4-162120\theta^3-195172\theta^2-78561\theta-11130\right)-2^{6} 19 x^{4}(1189\theta^2+2533\theta+1646)(2\theta+1)^2+2^{11} 19^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 1440, 196000, 32418400, ... --> OEIS Normalized instanton numbers (n0=1): 274/7, 6115/7, 281388/7, 2815228, 1699166270/7, ... ; Common denominator:...
\((4z+1)(512z^2-284z+1)(-7+76z)^2\)
| \(-\frac{ 1}{ 4}\) | \(0\) | \(\frac{ 71}{ 256}-\frac{ 17}{ 256}\sqrt{ 17}\) | \(\frac{ 7}{ 76}\) | \(\frac{ 71}{ 256}+\frac{ 17}{ 256}\sqrt{ 17}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
57
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:...
\((54z-1)(z^2-11z-1)(23+34z)^2\)
| \(-\frac{ 23}{ 34}\) | \(\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(0\) | \(\frac{ 1}{ 54}\) | \(\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |
58
New Number: 5.30 | AESZ: 209 | Superseeker: 478/17 285760/17 | Hash: a03a0a18a8b2a4926d11e4e42b958f98
Degree: 5
\(17^{2} \theta^4-2 17 x\left(1902\theta^4+3708\theta^3+2789\theta^2+935\theta+119\right)+2^{2} x^{2}\left(62408\theta^4+68576\theta^3-10029\theta^2-24106\theta-5661\right)-2^{2} x^{3}\left(66180\theta^4+33048\theta^3+20785\theta^2+17799\theta+4794\right)+2^{7} x^{4}(2\theta+1)(196\theta^3+498\theta^2+487\theta+169)-2^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 14, 978, 103820, 13387570, ... --> OEIS Normalized instanton numbers (n0=1): 478/17, 7784/17, 285760/17, 15280156/17, 1006004774/17, ... ; Common denominator:...
\(-(16z^3-32z^2+220z-1)(-17+32z)^2\)
| \(0\) | ≈\(0.004548\) | \(\frac{ 17}{ 32}\) | ≈\(0.997726-3.570079I\) | ≈\(0.997726+3.570079I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
59
New Number: 5.31 | AESZ: 212 | Superseeker: -20/7 -104 | Hash: f72aa947ba945355102b3fef56e0af0f
Degree: 5
\(7^{2} \theta^4+2 7 x\left(134\theta^4+286\theta^3+234\theta^2+91\theta+14\right)-2^{2} x^{2}\left(3183\theta^4+10266\theta^3+13501\theta^2+8225\theta+1918\right)+2^{3} x^{3}\left(2588\theta^4+8400\theta^3+10256\theta^2+5649\theta+1190\right)-2^{4} 3 x^{4}\left(256\theta^4+848\theta^3+1141\theta^2+717\theta+174\right)+2^{8} 3^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 64, -1408, 37216, ... --> OEIS Normalized instanton numbers (n0=1): -20/7, 57/4, -104, 16385/14, -110508/7, ... ; Common denominator:...
\((4z-1)(16z^2-44z-1)(6z-7)^2\)
| \(\frac{ 11}{ 8}-\frac{ 5}{ 8}\sqrt{ 5}\) | \(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 7}{ 6}\) | \(\frac{ 11}{ 8}+\frac{ 5}{ 8}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
60
New Number: 5.32 | AESZ: 215 | Superseeker: 220/3 89212 | Hash: ced61f5675491a3c4446c0e55e7bc36b
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(268\theta^4+632\theta^3+463\theta^2+147\theta+18\right)-2^{7} x^{2}\left(448\theta^4-1616\theta^3-4280\theta^2-2418\theta-441\right)+2^{12} x^{3}\left(416\theta^4+2016\theta^3+756\theta^2-288\theta-135\right)+2^{19} x^{4}(8\theta^2-28\theta-33)(2\theta+1)^2-2^{24} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 2664, 470400, 102047400, ... --> OEIS Normalized instanton numbers (n0=1): 220/3, 3538/3, 89212, 7484350, 2459418080/3, ... ; Common denominator:...
\(-(16z-1)(4096z^2-384z+1)(3+64z)^2\)
| \(-\frac{ 3}{ 64}\) | \(0\) | \(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |