1
New Number: 2.10 | AESZ: 70 | Superseeker: 27 18089 | Hash: 3d2adae6eaf26a56c76b8b67d92cc5df
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(10\theta^2+10\theta+3)+3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 1350, 156240, 22141350, ... --> OEIS Normalized instanton numbers (n0=1): 27, 432, 18089, 997785, 68438142, ... ; Common denominator:...
\((243z-1)(27z-1)\)
\(0\) | \(\frac{ 1}{ 243}\) | \(\frac{ 1}{ 27}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 3}\) |
2
New Number: 2.16 | AESZ: 65 | Superseeker: 240 19105840 | Hash: 13ba368bcbb10731ac8727b510731ff2
Degree: 2
\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{9} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 240, 277200, 457416960, 904864680720, ... --> OEIS Normalized instanton numbers (n0=1): 240, 57102, 19105840, 14810143935, 10017820614480, ... ; Common denominator:...
\((3456z-1)(1728z-1)\)
\(0\) | \(\frac{ 1}{ 3456}\) | \(\frac{ 1}{ 1728}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 6}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 6}\) |
\(0\) | \(2\) | \(2\) | \(\frac{ 11}{ 6}\) |
3
New Number: 2.2 | AESZ: 15 | Superseeker: 21 15894 | Hash: c8053e0e9c05ef468263fafd5e3fc764
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(7\theta^2+7\theta+2)-2^{3} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ... --> OEIS Normalized instanton numbers (n0=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...
\(-(27z+1)(216z-1)\)
\(-\frac{ 1}{ 27}\) | \(0\) | \(\frac{ 1}{ 216}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
\(1\) | \(0\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(1\) | \(0\) | \(1\) | \(\frac{ 4}{ 3}\) |
\(2\) | \(0\) | \(2\) | \(\frac{ 5}{ 3}\) |
4
New Number: 2.5 | AESZ: 25 | Superseeker: 20 8220 | Hash: 93279abcbeeade30c29508de7784e582
Degree: 2
\(\theta^4-2^{2} x(2\theta+1)^2(11\theta^2+11\theta+3)-2^{4} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 684, 58800, 6129900, ... --> OEIS Normalized instanton numbers (n0=1): 20, 277, 8220, 352994, 18651536, ... ; Common denominator:...
\(1-176z-256z^2\)
\(-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}\) | \(0\) | \(-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(\frac{ 3}{ 2}\) |
\(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
5
New Number: 4.42 | AESZ: 222 | Superseeker: 69/5 29081/5 | Hash: aad7a72e711c9c463396d319e0bf7603
Degree: 4
\(5^{2} \theta^4-5 x\left(407\theta^4+1198\theta^3+909\theta^2+310\theta+40\right)-2^{7} x^{2}\left(2103\theta^4+6999\theta^3+8358\theta^2+4050\theta+680\right)-2^{12} x^{3}\left(1387\theta^4+3840\theta^3+3081\theta^2+960\theta+100\right)-2^{21} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 504, 36800, 3518200, ... --> OEIS Normalized instanton numbers (n0=1): 69/5, 1383/4, 29081/5, 346080, 72023607/5, ... ; Common denominator:...
\(-(8192z^2+107z-1)(5+64z)^2\)
\(-\frac{ 5}{ 64}\) | \(-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
6
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:...
\(-(-1+54z)(162z-1)^2(108z-1)^2\)
\(0\) | \(\frac{ 1}{ 162}\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 54}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 5}{ 6}\) |
\(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 7}{ 6}\) |
\(0\) | \(4\) | \(1\) | \(2\) | \(\frac{ 4}{ 3}\) |
7
New Number: 5.35 | AESZ: 218 | Superseeker: 138/7 42984/7 | Hash: a76111af659715caf2c4344eedd9d678
Degree: 5
\(7^{2} \theta^4-2 3 7 x\left(192\theta^4+396\theta^3+303\theta^2+105\theta+14\right)+2^{2} 3 x^{2}\left(1188\theta^4+11736\theta^3+20431\theta^2+12152\theta+2436\right)+2^{2} 3^{3} x^{3}\left(532\theta^4+504\theta^3-3455\theta^2-3829\theta-1036\right)-2^{4} 3^{4} x^{4}(2\theta+1)(36\theta^3+306\theta^2+421\theta+156)-2^{6} 3^{4} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 612, 48000, 4580100, ... --> OEIS Normalized instanton numbers (n0=1): 138/7, 1506/7, 42984/7, 235596, 78950334/7, ... ; Common denominator:...
\(-(1296z^3-864z^2+168z-1)(7+12z)^2\)
\(-\frac{ 7}{ 12}\) | \(0\) | ≈\(0.006145\) | ≈\(0.330261-0.128447I\) | ≈\(0.330261+0.128447I\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 4}{ 3}\) |
\(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
8
New Number: 5.51 | AESZ: 250 | Superseeker: 308/23 70799/23 | Hash: 9c19794a84073d1c6dfd11c8a7c9a740
Degree: 5
\(23^{2} \theta^4-23 x\left(3271\theta^4+5078\theta^3+3896\theta^2+1357\theta+184\right)+x^{2}\left(1357863\theta^4+999924\theta^3-787393\theta^2-850862\theta-205712\right)-2^{3} x^{3}\left(775799\theta^4-272481\theta^3-218821\theta^2+176709\theta+100234\right)-2^{4} 61 x^{4}\left(1005\theta^4-15654\theta^3-36317\theta^2-27938\theta-7304\right)-2^{9} 61^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 324, 19304, 1388260, ... --> OEIS Normalized instanton numbers (n0=1): 308/23, 3526/23, 70799/23, 2148684/23, 81402822/23, ... ; Common denominator:...
\(-(512z^3+113z^2+121z-1)(-23+244z)^2\)
≈\(-0.114451-0.474453I\) | ≈\(-0.114451+0.474453I\) | \(0\) | ≈\(0.008199\) | \(\frac{ 23}{ 244}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
\(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 5}{ 4}\) |
9
New Number: 5.70 | AESZ: 287 | Superseeker: 361/21 120472/21 | Hash: 97932196c46a8712f6dcb11165d698be
Degree: 5
\(3^{2} 7^{2} \theta^4-3 7 x\left(3289\theta^4+6098\theta^3+4645\theta^2+1596\theta+210\right)+2^{2} 5 x^{2}\left(7712\theta^4-46168\theta^3-106885\theta^2-67410\theta-13629\right)+2^{4} x^{3}\left(106636\theta^4+493416\theta^3+420211\theta^2+116361\theta+6090\right)-2^{8} 5 x^{4}(2\theta+1)(1916\theta^3+2622\theta^2+1077\theta+91)-2^{12} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 10, 510, 38260, 3473470, ... --> OEIS Normalized instanton numbers (n0=1): 361/21, 4780/21, 120472/21, 1537864/7, 216261320/21, ... ; Common denominator:...
\(-(64z^3+800z^2+149z-1)(-21+80z)^2\)
≈\(-12.310784\) | ≈\(-0.195701\) | \(0\) | ≈\(0.006485\) | \(\frac{ 21}{ 80}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
\(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
10
New Number: 8.26 | AESZ: 301 | Superseeker: 193/11 48570/11 | Hash: a91db18876a9dfbf42b88f8d64c55d85
Degree: 8
\(11^{2} \theta^4-11 x\left(1517\theta^4+3136\theta^3+2393\theta^2+825\theta+110\right)-x^{2}\left(24266+106953\theta+202166\theta^2+207620\theta^3+90362\theta^4\right)-x^{3}\left(53130+217437\theta+415082\theta^2+507996\theta^3+245714\theta^4\right)-x^{4}\left(15226+183269\theta+564786\theta^2+785972\theta^3+407863\theta^4\right)-x^{5}\left(25160+279826\theta+728323\theta^2+790148\theta^3+434831\theta^4\right)-2^{3} x^{6}\left(36361\theta^4+70281\theta^3+73343\theta^2+37947\theta+7644\right)-2^{4} 5 x^{7}\left(1307\theta^4+3430\theta^3+3877\theta^2+2162\theta+488\right)-2^{9} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 10, 466, 32392, 2727826, ... --> OEIS Normalized instanton numbers (n0=1): 193/11, 1973/11, 48570/11, 1689283/11, 72444183/11, ... ; Common denominator:...
\(-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2\)
\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\) | \(-1\) | \(-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I\) | \(-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I\) | \(0\) | \(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
\(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(3\) | \(0\) | \(1\) | \(1\) |
\(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(2\) | \(1\) |