1
New Number: 4.10 | AESZ: | Superseeker: -84 -148820 | Hash: fc2837f1001e57a5cc53749a08d4f2bf
Degree: 4
\(\theta^4-2 3 x\left(216\theta^4+432\theta^3+516\theta^2+300\theta+67\right)+2^{2} 3^{2} x^{2}\left(12312\theta^4+49248\theta^3+76374\theta^2+54252\theta+15017\right)-2^{6} 3^{10} x^{3}(\theta^2+3\theta+3)(2\theta+3)^2+2^{4} 3^{10} x^{4}(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 402, 197010, 104962956, 58311249066, ... --> OEIS Normalized instanton numbers (n0=1): -84, -5271/2, -148820, -41373213/4, -836813460, ... ; Common denominator:...
\((1-648z+11664z^2)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 2}\) | \(\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 2}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
2
New Number: 4.11 | AESZ: | Superseeker: -63 -96866 | Hash: 39ed55f37672c58e7ce182c4c33d4a66
Degree: 4
\(\theta^4-x\left(972\theta^4+1944\theta^3+2322\theta^2+1350\theta+603/2\right)+x^{2}\left(196830\theta^4+787320\theta^3+2110455/2\theta^2+535815\theta+237897/4\right)+3^{14} x^{3}(\theta^2+3\theta+3)(2\theta+3)^2+x^{4}43046721/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 603/2, 1008855/8, 898513875/16, 3331190162475/128, ... --> OEIS Normalized instanton numbers (n0=1): -63, -8757/4, -96866, -6253821, -446217723, ... ; Common denominator:...
\((-1+486z+19683z^2)^2\)
\(-\frac{ 1}{ 81}-\frac{ 2}{ 243}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 81}+\frac{ 2}{ 243}\sqrt{ 3}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
\(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
3
New Number: 4.12 | AESZ: | Superseeker: -45 7080 | Hash: 6c95cb50a57e8a1c96a5a4e3e353cb85
Degree: 4
\(\theta^4-x\left(1188\theta^4+2376\theta^3+2874\theta^2+1686\theta+765/2\right)+x^{2}\left(535086\theta^4+2140344\theta^3+7708527/2\theta^2+3427839\theta+4938345/4\right)-3^{8} 5^{3} x^{3}(33\theta^2+99\theta+100)(2\theta+3)^2+x^{4}922640625/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 765/2, 1009575/8, 627988725/16, 1505754528075/128, ... --> OEIS Normalized instanton numbers (n0=1): -45, -135, 7080, 406035, 17168436, ... ; Common denominator:...
\((1-594z+91125z^2)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 3375}-\frac{ 2}{ 3375}I\) | \(\frac{ 11}{ 3375}+\frac{ 2}{ 3375}I\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
4
New Number: 4.7 | AESZ: | Superseeker: -54 -40552 | Hash: ee8508b4e5567367ca11f74e074e8099
Degree: 4
\(\theta^4-2 3 x\left(180\theta^4+360\theta^3+433\theta^2+253\theta+57\right)+2^{2} 3^{4} 11 x^{2}\left(108\theta^4+432\theta^3+741\theta^2+618\theta+209\right)-2^{5} 3^{8} x^{3}(60\theta^2+180\theta+181)(2\theta+3)^2+2^{8} 3^{10} x^{4}(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 342, 117990, 42901884, 16240501782, ... --> OEIS Normalized instanton numbers (n0=1): -54, -864, -40552, -2192400, -123334380, ... ; Common denominator:...
\((432z-1)^2(108z-1)^2\)
\(0\) | \(\frac{ 1}{ 432}\) | \(\frac{ 1}{ 108}\) | \(\infty\) |
---|---|---|---|
\(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
\(0\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
5
New Number: 4.8 | AESZ: | Superseeker: -135 -417685 | Hash: f5702d0b3fd53e9b80a42c76a335b648
Degree: 4
\(\theta^4-x\left(1836\theta^4+3672\theta^3+4368\theta^2+2532\theta+1125/2\right)+x^{2}\left(844182\theta^4+3376728\theta^3+10153755/2\theta^2+3400299\theta+3426705/4\right)-x^{3}6561/2(2\theta+3)^2(102\theta^2+306\theta+305)+x^{4}59049/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 1125/2, 3219615/8, 5002535925/16, 32404173968475/128, ... --> OEIS Normalized instanton numbers (n0=1): -135, -22815/4, -417685, -78983235/2, -4331084310, ... ; Common denominator:...
\((1-918z+729z^2)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 17}{ 27}-\frac{ 4}{ 9}\sqrt{ 2}\) | \(\frac{ 17}{ 27}+\frac{ 4}{ 9}\sqrt{ 2}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
6
New Number: 4.9 | AESZ: | Superseeker: -33 29693 | Hash: c444fb1a912bd488ee5947b8bc1e2c53
Degree: 4
\(\theta^4-x\left(756\theta^4+1512\theta^3+1824\theta^2+1068\theta+483/2\right)+x^{2}\left(260982\theta^4+1043928\theta^3+3947211/2\theta^2+1859355\theta+2817729/4\right)-x^{3}531441/2(2\theta+3)^2(42\theta^2+126\theta+127)+x^{4}387420489/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 483/2, 300015/8, 32162403/16, -132658029189/128, ... --> OEIS Normalized instanton numbers (n0=1): -33, 1095/2, 29693, 1241103/2, -16117818, ... ; Common denominator:...
\((1-378z+59049z^2)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |