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: 4.14 | AESZ: | Superseeker: -340 -15174100/3 | Hash: a961869d91c2f73091913e8f8c4b5fa0
Degree: 4
\(\theta^4-2^{2} x\left(1088\theta^4+2176\theta^3+2579\theta^2+1491\theta+330\right)+2^{7} 3 x^{2}\left(12352\theta^4+49408\theta^3+74070\theta^2+49324\theta+12325\right)-2^{12} x^{3}(1088\theta^2+3264\theta+3225)(2\theta+3)^2+2^{18} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 1320, 2233320, 4108451200, 7880762169000, ... --> OEIS Normalized instanton numbers (n0=1): -340, -31985, -15174100/3, -1036481610, -246612212640, ... ; Common denominator:...
\((1-2176z+4096z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 17}{ 64}-\frac{ 3}{ 16}\sqrt{ 2}\) | \(\frac{ 17}{ 64}+\frac{ 3}{ 16}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
5
New Number: 4.15 | AESZ: | Superseeker: -76 415420 | Hash: d8c866a60b2b4edb0c88e03315fa2a7b
Degree: 4
\(\theta^4-2^{2} x\left(448\theta^4+896\theta^3+1077\theta^2+629\theta+142\right)+2^{7} x^{2}\left(11456\theta^4+45824\theta^3+86434\theta^2+81220\theta+30693\right)-2^{12} 3^{4} x^{3}(448\theta^2+1344\theta+1343)(2\theta+3)^2+2^{18} 3^{8} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 568, 207720, 25669504, -32774007128, ... --> OEIS Normalized instanton numbers (n0=1): -76, 2958, 415420, 17891650, -1211214176, ... ; Common denominator:...
\((331776z^2-896z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 5184}-\frac{ 1}{ 1296}\sqrt{ 2}I\) | \(\frac{ 7}{ 5184}+\frac{ 1}{ 1296}\sqrt{ 2}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
6
New Number: 4.16 | AESZ: | Superseeker: -208 -1863312 | Hash: ff22b96c1af3d06292a97d4dee085628
Degree: 4
\(\theta^4-2^{4} x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{9} x^{2}\left(4864\theta^4+19456\theta^3+30088\theta^2+21264\theta+5849\right)-2^{18} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{26} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 944, 1093840, 1379945728, 1816122981136, ... --> OEIS Normalized instanton numbers (n0=1): -208, -15098, -1863312, -284211001, -50414626800, ... ; Common denominator:...
\((1-1536z+65536z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 3}{ 256}-\frac{ 1}{ 128}\sqrt{ 2}\) | \(\frac{ 3}{ 256}+\frac{ 1}{ 128}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
7
New Number: 4.17 | AESZ: | Superseeker: -156 -1229332 | Hash: 245e2566c8da93abbfc4296923ccba12
Degree: 4
\(\theta^4-2^{2} 3 x\left(192\theta^4+384\theta^3+457\theta^2+265\theta+59\right)+2^{4} 3^{2} x^{2}\left(7680\theta^4+30720\theta^3+41040\theta^2+20640\theta+2203\right)+2^{12} 3^{4} x^{3}(192\theta^2+576\theta+571)(2\theta+3)^2+2^{18} 3^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 708, 700740, 738956400, 811309522500, ... --> OEIS Normalized instanton numbers (n0=1): -156, -12549, -1229332, -175559052, -27542017056, ... ; Common denominator:...
\((-1+1152z+110592z^2)^2\)
| \(-\frac{ 1}{ 192}-\frac{ 1}{ 288}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 192}+\frac{ 1}{ 288}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
8
New Number: 4.18 | AESZ: | Superseeker: -100 126580 | Hash: 3ab4956c5da76dad5e104e338e7c0128
Degree: 4
\(\theta^4-2^{2} x\left(704\theta^4+1408\theta^3+1697\theta^2+993\theta+225\right)+2^{4} x^{2}\left(187904\theta^4+751616\theta^3+1350224\theta^2+1197216\theta+429975\right)-2^{12} 5^{3} x^{3}(704\theta^2+2112\theta+2115)(2\theta+3)^2+2^{18} 5^{6} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 900, 701100, 515510800, 365497137900, ... --> OEIS Normalized instanton numbers (n0=1): -100, -1260, 126580, 12033300, 1211646512, ... ; Common denominator:...
\((512000z^2-1408z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 8000}-\frac{ 1}{ 4000}I\) | \(\frac{ 11}{ 8000}+\frac{ 1}{ 4000}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 9}{ 4}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
9
New Number: 4.20 | AESZ: | Superseeker: -2484 -1327731388 | Hash: 80035e90a6f24cd6da3d4c5adc98379f
Degree: 4
\(\theta^4-2^{2} 3 x\left(2448\theta^4+4896\theta^3+5773\theta^2+3325\theta+732\right)+2^{6} 3^{4} x^{2}\left(41688\theta^4+166752\theta^3+248973\theta^2+164442\theta+40616\right)-2^{8} 3^{8} x^{3}(816\theta^2+2448\theta+2389)(2\theta+3)^2+2^{14} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8784, 99982728, 1239742123200, 16039070549564328, ... --> OEIS Normalized instanton numbers (n0=1): -2484, -1446309, -1327731388, -1580284433106, -2187358898922144, ... ; Common denominator:...
\((1-14688z+186624z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 17}{ 432}-\frac{ 1}{ 36}\sqrt{ 2}\) | \(\frac{ 17}{ 432}+\frac{ 1}{ 36}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
10
New Number: 4.21 | AESZ: | Superseeker: -492 136094428 | Hash: 595707be6cb20abc1dfeecf72492ae5f
Degree: 4
\(\theta^4-2^{2} 3 x\left(1008\theta^4+2016\theta^3+2411\theta^2+1403\theta+316\right)+2^{6} 3^{2} x^{2}\left(115992\theta^4+463968\theta^3+872325\theta^2+816714\theta+307516\right)-2^{8} 3^{12} x^{3}(336\theta^2+1008\theta+995)(2\theta+3)^2+2^{14} 3^{18} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3792, 9275400, 7430606400, -68166524583000, ... --> OEIS Normalized instanton numbers (n0=1): -492, 128514, 136094428, 32416215738, -16919954920032, ... ; Common denominator:...
\((15116544z^2-6048z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 34992}-\frac{ 1}{ 8748}\sqrt{ 2}I\) | \(\frac{ 7}{ 34992}+\frac{ 1}{ 8748}\sqrt{ 2}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
11
New Number: 4.22 | AESZ: | Superseeker: -1488 -517984144 | Hash: 7d70f749f0fd6381c088f4c1fac4d6df
Degree: 4
\(\theta^4-2^{4} 3 x\left(432\theta^4+864\theta^3+1023\theta^2+591\theta+131\right)+2^{9} 3^{2} x^{2}\left(24624\theta^4+98496\theta^3+151722\theta^2+106452\theta+29023\right)-2^{14} 3^{10} x^{3}(16\theta^2+48\theta+47)(2\theta+3)^2+2^{22} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6288, 49006800, 416705452800, 3698851729136400, ... --> OEIS Normalized instanton numbers (n0=1): -1488, -704730, -517984144, -469396561641, -493072108113648, ... ; Common denominator:...
\((2985984z^2-10368z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 1}{ 576}-\frac{ 1}{ 864}\sqrt{ 2}\) | \(\frac{ 1}{ 576}+\frac{ 1}{ 864}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
12
New Number: 4.23 | AESZ: | Superseeker: -1116 -349462868 | Hash: 4cde44ecce8658b2c2ca6b3c279f4e62
Degree: 4
\(\theta^4-2^{2} 3^{2} x\left(432\theta^4+864\theta^3+1023\theta^2+591\theta+131\right)+2^{4} 3^{5} 5 x^{2}\left(2592\theta^4+10368\theta^3+13788\theta^2+6840\theta+689\right)+2^{8} 3^{14} x^{3}(16\theta^2+48\theta+47)(2\theta+3)^2+2^{14} 3^{16} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4716, 31430916, 223425214992, 1654537886846532, ... --> OEIS Normalized instanton numbers (n0=1): -1116, -586989, -349462868, -300569202144, -280354383814176, ... ; Common denominator:...
\((5038848z^2+7776z-1)^2\)
| \(-\frac{ 1}{ 1296}-\frac{ 1}{ 1944}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 1296}+\frac{ 1}{ 1944}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
13
New Number: 4.24 | AESZ: | Superseeker: -612 51318900 | Hash: dc90e303db3462d0c0bd472762000ad5
Degree: 4
\(\theta^4-2^{2} 3 x\left(1584\theta^4+3168\theta^3+3799\theta^2+2215\theta+501\right)+2^{4} 3^{2} x^{2}\left(951264\theta^4+3805056\theta^3+6812388\theta^2+6014664\theta+2151443\right)-2^{8} 3^{8} 5^{3} x^{3}(528\theta^2+1584\theta+1567)(2\theta+3)^2+2^{14} 3^{10} 5^{6} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6012, 31439916, 155468925360, 741919701370860, ... --> OEIS Normalized instanton numbers (n0=1): -612, -87372, 51318900, 24336059400, 14111081636400, ... ; Common denominator:...
\((23328000z^2-9504z+1)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 54000}-\frac{ 1}{ 27000}I\) | \(\frac{ 11}{ 54000}+\frac{ 1}{ 27000}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
14
New Number: 4.25 | AESZ: 32 | Superseeker: -33 -13051 | Hash: bf53401dcbe0436fb67761f590ee3295
Degree: 4
\(\theta^4-x\left(540\theta^4+1080\theta^3+1296\theta^2+756\theta+339/2\right)+x^{2}\left(72846\theta^4+291384\theta^3+881067/2\theta^2+298299\theta+305217/4\right)+x^{3}\left(14580\theta^4+87480\theta^3+209547\theta^2+234981\theta+205497/2\right)+x^{4}9/16(6\theta+11)^2(6\theta+13)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 339/2, 287415/8, 131845323/16, 251852894379/128, ... --> OEIS Normalized instanton numbers (n0=1): -33, -1995/4, -13051, -435975, -16838124, ... ; Common denominator:...
\((-1+270z+27z^2)^2\)
| \(-5-\frac{ 26}{ 9}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-5+\frac{ 26}{ 9}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 11}{ 6}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 13}{ 6}\) |
15
New Number: 4.2 | AESZ: ~44 | Superseeker: -76 -92996 | Hash: 79f5f70bb79e740c1cd7e835ff99a64c
Degree: 4
\(\theta^4-2^{2} x\left(272\theta^4+544\theta^3+649\theta^2+377\theta+84\right)+2^{6} 3 x^{2}\left(1544\theta^4+6176\theta^3+9307\theta^2+6262\theta+1588\right)-2^{8} x^{3}(272\theta^2+816\theta+819)(2\theta+3)^2+2^{14} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 336, 142728, 65762368, 31568339880, ... --> OEIS Normalized instanton numbers (n0=1): -76, -2002, -92996, -5555506, -384650592, ... ; Common denominator:...
\((1-544z+256z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 17}{ 16}-\frac{ 3}{ 4}\sqrt{ 2}\) | \(\frac{ 17}{ 16}+\frac{ 3}{ 4}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
16
New Number: 4.30 | AESZ: 281 | Superseeker: 5 -420 | Hash: d24d5f19c8a8bf23ea9abd62ea9242b2
Degree: 4
\(\theta^4+x\left(164\theta^4+328\theta^3+402\theta^2+238\theta+109/2\right)+x^{2}\left(12974\theta^4+51896\theta^3+200863/2\theta^2+97071\theta+151081/4\right)+5 x^{3}\left(102500\theta^4+615000\theta^3+1476125\theta^2+1660875\theta+728918\right)+x^{4}15625/16(10\theta+17)(10\theta+19)(10\theta+21)(10\theta+23)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -109/2, 13447/8, 58747/16, -556301557/128, ... --> OEIS Normalized instanton numbers (n0=1): 5, 95/4, -420, 2555, 19930, ... ; Common denominator:...
\((1+82z+3125z^2)^2\)
| \(-\frac{ 41}{ 3125}-\frac{ 38}{ 3125}I\) | \(-\frac{ 41}{ 3125}+\frac{ 38}{ 3125}I\) | \(0\) | \(s_1\) | \(s_2\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 17}{ 10}\) |
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(\frac{ 19}{ 10}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 21}{ 10}\) |
| \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 23}{ 10}\) |
17
New Number: 4.3 | AESZ: | Superseeker: -20 5924 | Hash: 4163e7dfeb4b46f62bda072d071020fc
Degree: 4
\(\theta^4-2^{2} x\left(112\theta^4+224\theta^3+271\theta^2+159\theta+36\right)+2^{6} x^{2}\left(1432\theta^4+5728\theta^3+10849\theta^2+10242\theta+3888\right)-2^{8} 3^{4} x^{3}(112\theta^2+336\theta+341)(2\theta+3)^2+2^{14} 3^{8} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 144, 13320, 432320, -127603800, ... --> OEIS Normalized instanton numbers (n0=1): -20, 199, 5924, 82010, -1170848, ... ; Common denominator:...
\((1-224z+20736z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 1296}-\frac{ 1}{ 324}\sqrt{ 2}I\) | \(\frac{ 7}{ 1296}+\frac{ 1}{ 324}\sqrt{ 2}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
18
New Number: 4.4 | AESZ: | Superseeker: -48 -32368 | Hash: a0903e578f379289d79849a566639775
Degree: 4
\(\theta^4-2^{4} x\left(48\theta^4+96\theta^3+115\theta^2+67\theta+15\right)+2^{9} x^{2}\left(304\theta^4+1216\theta^3+1890\theta^2+1348\theta+375\right)-2^{14} x^{3}(48\theta^2+144\theta+145)(2\theta+3)^2+2^{22} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 240, 69840, 22068480, 7268490000, ... --> OEIS Normalized instanton numbers (n0=1): -48, -910, -32368, -1409193, -71439120, ... ; Common denominator:...
\((1-384z+4096z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\) | \(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
19
New Number: 4.5 | AESZ: | Superseeker: -36 -62596/3 | Hash: f5b4785eb6dd46eea771050179115d33
Degree: 4
\(\theta^4-2^{2} 3 x\left(48\theta^4+96\theta^3+115\theta^2+67\theta+15\right)+2^{4} 3^{2} x^{2}\left(480\theta^4+1920\theta^3+2580\theta^2+1320\theta+151\right)+2^{8} 3^{4} x^{3}(48\theta^2+144\theta+145)(2\theta+3)^2+2^{14} 3^{6} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 180, 44676, 11798640, 3241596996, ... --> OEIS Normalized instanton numbers (n0=1): -36, -756, -62596/3, -839088, -37432800, ... ; Common denominator:...
\((-1+288z+6912z^2)^2\)
| \(-\frac{ 1}{ 48}-\frac{ 1}{ 72}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 48}+\frac{ 1}{ 72}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
20
New Number: 4.6 | AESZ: | Superseeker: -28 1036 | Hash: e42780ff25b428328423d5eea814a37a
Degree: 4
\(\theta^4-2^{2} x\left(176\theta^4+352\theta^3+427\theta^2+251\theta+57\right)+2^{4} x^{2}\left(11744\theta^4+46976\theta^3+84756\theta^2+75560\theta+27275\right)-2^{8} 5^{3} x^{3}(176\theta^2+528\theta+537)(2\theta+3)^2+2^{14} 5^{6} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 228, 44716, 8258768, 1469227500, ... --> OEIS Normalized instanton numbers (n0=1): -28, -21, 1036, 53976, 1260496, ... ; Common denominator:...
\((1-352z+32000z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 2000}-\frac{ 1}{ 1000}I\) | \(\frac{ 11}{ 2000}+\frac{ 1}{ 1000}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
21
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:...
\((1-918z+729z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 17}{ 27}-\frac{ 4}{ 9}\sqrt{ 2}\) | \(\frac{ 17}{ 27}+\frac{ 4}{ 9}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
22
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:...
\((1-378z+59049z^2)^2\)
| \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |