Summary

You searched for: degz=4

Your search produced 77 matches
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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   LaTex

Coefficients of the holomorphic solution: 1, 402, 197010, 104962956, 58311249066, ...
--> OEIS
Normalized instanton numbers (n0=1): -84, -5271/2, -148820, -41373213/4, -836813460, ... ; Common denominator:...

Discriminant

\((1-648z+11664z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 2}\)\(\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 170=$d \ast h \tilde B \ast \epsilon$

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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   LaTex

Coefficients 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:...

Discriminant

\((-1+486z+19683z^2)^2\)

Local exponents

\(-\frac{ 1}{ 81}-\frac{ 2}{ 243}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 1}{ 81}+\frac{ 2}{ 243}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

This is operator "4.11" from ...

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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   LaTex

Coefficients 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:...

Discriminant

\((1-594z+91125z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 3375}-\frac{ 2}{ 3375}I\)\(\frac{ 11}{ 3375}+\frac{ 2}{ 3375}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-operator equivalent to AESZ $=b \ast h ~B \ast \eta$

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4

New Number: 4.13 |  AESZ: ~37  |  Superseeker: -128 -1546624/3  |  Hash: c03e4e4ca58f9f1f76c98c8616bc2cbd  

Degree: 4

\(\theta^4-2^{2} x\left(640\theta^4+1280\theta^3+1534\theta^2+894\theta+201\right)+2^{4} 3 x^{2}\left(45056\theta^4+180224\theta^3+308352\theta^2+256256\theta+86363\right)-2^{19} x^{3}(320\theta^2+960\theta+957)(2\theta+3)^2+2^{30} x^{4}(2\theta+3)(2\theta+5)(4\theta+7)(4\theta+9)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 804, 655260, 563879792, 505573095132, ...
--> OEIS
Normalized instanton numbers (n0=1): -128, -5232, -1546624/3, -64705008, -7960717440, ... ; Common denominator:...

Discriminant

\((1024z-1)^2(256z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 1024}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 37$=C \ast \alpha ~tilde c \ast i$

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5

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   LaTex

Coefficients of the holomorphic solution: 1, 1320, 2233320, 4108451200, 7880762169000, ...
--> OEIS
Normalized instanton numbers (n0=1): -340, -31985, -15174100/3, -1036481610, -246612212640, ... ; Common denominator:...

Discriminant

\((1-2176z+4096z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 17}{ 64}-\frac{ 3}{ 16}\sqrt{ 2}\)\(\frac{ 17}{ 64}+\frac{ 3}{ 16}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 52 $=C \ast \gamma \tilde g \ast i$

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6

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   LaTex

Coefficients of the holomorphic solution: 1, 568, 207720, 25669504, -32774007128, ...
--> OEIS
Normalized instanton numbers (n0=1): -76, 2958, 415420, 17891650, -1211214176, ... ; Common denominator:...

Discriminant

\((331776z^2-896z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 7}{ 5184}-\frac{ 1}{ 1296}\sqrt{ 2}I\)\(\frac{ 7}{ 5184}+\frac{ 1}{ 1296}\sqrt{ 2}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 152 $=C \ast \delta ~tilde \alpha \ast i$

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7

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   LaTex

Coefficients of the holomorphic solution: 1, 944, 1093840, 1379945728, 1816122981136, ...
--> OEIS
Normalized instanton numbers (n0=1): -208, -15098, -1863312, -284211001, -50414626800, ... ; Common denominator:...

Discriminant

\((1-1536z+65536z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 3}{ 256}-\frac{ 1}{ 128}\sqrt{ 2}\)\(\frac{ 3}{ 256}+\frac{ 1}{ 128}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \epsilon ~d \ast i$

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8

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   LaTex

Coefficients of the holomorphic solution: 1, 708, 700740, 738956400, 811309522500, ...
--> OEIS
Normalized instanton numbers (n0=1): -156, -12549, -1229332, -175559052, -27542017056, ... ; Common denominator:...

Discriminant

\((-1+1152z+110592z^2)^2\)

Local exponents

\(-\frac{ 1}{ 192}-\frac{ 1}{ 288}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 1}{ 192}+\frac{ 1}{ 288}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \zeta ~tilde f \ast i$

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9

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   LaTex

Coefficients of the holomorphic solution: 1, 900, 701100, 515510800, 365497137900, ...
--> OEIS
Normalized instanton numbers (n0=1): -100, -1260, 126580, 12033300, 1211646512, ... ; Common denominator:...

Discriminant

\((512000z^2-1408z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 8000}-\frac{ 1}{ 4000}I\)\(\frac{ 11}{ 8000}+\frac{ 1}{ 4000}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 7}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 9}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $C \ast \eta ~b \ast i$

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10

New Number: 4.19 |  AESZ: ~66  |  Superseeker: -864 -147560800  |  Hash: b9b85f803521c6af3b5f7572d309f89a  

Degree: 4

\(\theta^4-2^{2} 3 x\left(1440\theta^4+2880\theta^3+3434\theta^2+1994\theta+447\right)+2^{4} 3^{4} x^{2}\left(76032\theta^4+304128\theta^3+518496\theta^2+428736\theta+143785\right)-2^{15} 3^{8} x^{3}(240\theta^2+720\theta+709)(2\theta+3)^2+2^{26} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5364, 29367900, 170217457200, 1029027458497500, ...
--> OEIS
Normalized instanton numbers (n0=1): -864, -261684, -147560800, -120568926924, -88009904955744, ... ; Common denominator:...

Discriminant

\((6912z-1)^2(1728z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 6912}\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $AESZ 66 =$D \ast \alpha \tilde c \ast j$

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11

New Number: 4.1 |  AESZ: ~39  |  Superseeker: -32 -8736  |  Hash: 462066f711fc3742db1ea9befa2fe01b  

Degree: 4

\(\theta^4-2^{2} x\left(160\theta^4+320\theta^3+386\theta^2+226\theta+51\right)+2^{4} 3 x^{2}\left(2816\theta^4+11264\theta^3+19360\theta^2+16192\theta+5491\right)-2^{15} x^{3}(80\theta^2+240\theta+243)(2\theta+3)^2+2^{26} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 204, 41820, 9022160, 2025179100, ...
--> OEIS
Normalized instanton numbers (n0=1): -32, -284, -8736, -283900, -10041888, ... ; Common denominator:...

Discriminant

\((256z-1)^2(64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(2\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 39=$A \ast \alpha$.

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12

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   LaTex

Coefficients of the holomorphic solution: 1, 8784, 99982728, 1239742123200, 16039070549564328, ...
--> OEIS
Normalized instanton numbers (n0=1): -2484, -1446309, -1327731388, -1580284433106, -2187358898922144, ... ; Common denominator:...

Discriminant

\((1-14688z+186624z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 17}{ 432}-\frac{ 1}{ 36}\sqrt{ 2}\)\(\frac{ 17}{ 432}+\frac{ 1}{ 36}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 149=$D \ast \gamma ~tilde g \ast j$

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13

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   LaTex

Coefficients of the holomorphic solution: 1, 3792, 9275400, 7430606400, -68166524583000, ...
--> OEIS
Normalized instanton numbers (n0=1): -492, 128514, 136094428, 32416215738, -16919954920032, ... ; Common denominator:...

Discriminant

\((15116544z^2-6048z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 7}{ 34992}-\frac{ 1}{ 8748}\sqrt{ 2}I\)\(\frac{ 7}{ 34992}+\frac{ 1}{ 8748}\sqrt{ 2}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

This is operator "4.21" from ...

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14

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   LaTex

Coefficients of the holomorphic solution: 1, 6288, 49006800, 416705452800, 3698851729136400, ...
--> OEIS
Normalized instanton numbers (n0=1): -1488, -704730, -517984144, -469396561641, -493072108113648, ... ; Common denominator:...

Discriminant

\((2985984z^2-10368z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 576}-\frac{ 1}{ 864}\sqrt{ 2}\)\(\frac{ 1}{ 576}+\frac{ 1}{ 864}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $D \ast \epsilon \tilde d \ast j$

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15

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   LaTex

Coefficients of the holomorphic solution: 1, 4716, 31430916, 223425214992, 1654537886846532, ...
--> OEIS
Normalized instanton numbers (n0=1): -1116, -586989, -349462868, -300569202144, -280354383814176, ... ; Common denominator:...

Discriminant

\((5038848z^2+7776z-1)^2\)

Local exponents

\(-\frac{ 1}{ 1296}-\frac{ 1}{ 1944}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 1}{ 1296}+\frac{ 1}{ 1944}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

This is operator "4.23" from ...

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16

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   LaTex

Coefficients of the holomorphic solution: 1, 6012, 31439916, 155468925360, 741919701370860, ...
--> OEIS
Normalized instanton numbers (n0=1): -612, -87372, 51318900, 24336059400, 14111081636400, ... ; Common denominator:...

Discriminant

\((23328000z^2-9504z+1)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 54000}-\frac{ 1}{ 27000}I\)\(\frac{ 11}{ 54000}+\frac{ 1}{ 27000}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 5}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 3}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $D \ast \eta ~b \ast j$

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17

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   LaTex

Coefficients 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:...

Discriminant

\((-1+270z+27z^2)^2\)

Local exponents

\(-5-\frac{ 26}{ 9}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-5+\frac{ 26}{ 9}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 11}{ 6}\)
\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 13}{ 6}\)

Note:

Sporadic YY-Operator

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18

New Number: 4.26 |  AESZ: 60  |  Superseeker: -10 -870  |  Hash: 033b6632bf7cbbfe2a70e1f1eee4bf04  

Degree: 4

\(\theta^4-x\left(248\theta^4+496\theta^3+604\theta^2+356\theta+81\right)+x^{2}\left(18832\theta^4+75328\theta^3+126798\theta^2+102940\theta+33889\right)-2^{3} 3 x^{3}\left(17856\theta^4+107136\theta^3+256985\theta^2+288843\theta+126617\right)+3^{2} x^{4}(24\theta+41)(24\theta+47)(24\theta+49)(24\theta+55)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 81, 13837/2, 1263327/2, 480917043/8, ...
--> OEIS
Normalized instanton numbers (n0=1): -10, -65, -870, -13905, -248910, ... ; Common denominator:...

Discriminant

\((108z-1)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 41}{ 24}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 47}{ 24}\)
\(0\)\(1\)\(1\)\(\frac{ 49}{ 24}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 55}{ 24}\)

Note:

Sporadic YY-Operator

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19

New Number: 4.27 |  AESZ: 189  |  Superseeker: -30 -11360  |  Hash: 2ce243b7535bf4eefb88252a3c164466  

Degree: 4

\(\theta^4-2 x\left(260\theta^4+520\theta^3+625\theta^2+365\theta+82\right)+2^{2} x^{2}\left(17412\theta^4+69648\theta^3+107199\theta^2+75102\theta+20320\right)-2^{4} x^{3}\left(33280\theta^4+199680\theta^3+476760\theta^2+531720\theta+230741\right)+2^{8} x^{4}(8\theta+13)(8\theta+15)(8\theta+17)(8\theta+19)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 164, 32886, 7144704, 1616497596, ...
--> OEIS
Normalized instanton numbers (n0=1): -30, -885/2, -11360, -365910, -13641180, ... ; Common denominator:...

Discriminant

\((256z-1)^2(4z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 13}{ 8}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 15}{ 8}\)
\(0\)\(1\)\(1\)\(\frac{ 17}{ 8}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 19}{ 8}\)

Note:

Sporadic YY-Operator

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20

New Number: 4.28 |  AESZ: 244  |  Superseeker: 10 1018  |  Hash: 6bf8549841e32615ff2b7798191c0de3  

Degree: 4

\(\theta^4+x\left(208\theta^4+416\theta^3+504\theta^2+296\theta+67\right)+x^{2}\left(9952\theta^4+39808\theta^3+57734\theta^2+35852\theta+7665\right)-2^{3} 3 x^{3}\left(3744\theta^4+22464\theta^3+53974\theta^2+60834\theta+26775\right)+3^{2} x^{4}(12\theta+23)^2(12\theta+25)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -67, 11529/2, -1062425/2, 406816235/8, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -167/2, 1018, -16457, 304664, ... ; Common denominator:...

Discriminant

\((108z+1)^2(4z-1)^2\)

No data for singularities

Note:

Sporadic YY-Operator

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21

New Number: 4.29 |  AESZ: 255  |  Superseeker: -20 -28820/3  |  Hash: 86173b300ea0aef95c3f2b60ce5ecf91  

Degree: 4

\(\theta^4+2^{2} x\left(256\theta^4+512\theta^3+653\theta^2+397\theta+94\right)+2^{7} x^{2}\left(3072\theta^4+12288\theta^3+22696\theta^2+20816\theta+7749\right)+2^{12} x^{3}\left(16384\theta^4+98304\theta^3+237760\theta^2+270912\theta+120731\right)+2^{22} x^{4}(4\theta+7)(4\theta+9)(8\theta+15)(8\theta+17)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -376, 117736, -34499456, 9771980456, ...
--> OEIS
Normalized instanton numbers (n0=1): -20, 295, -28820/3, 454190, -26517920, ... ; Common denominator:...

Discriminant

\((256z+1)^4\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0\)\(\infty\)
\(-\frac{ 3}{ 8}\)\(0\)\(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 8}\)\(0\)\(\frac{ 15}{ 8}\)
\(-\frac{ 5}{ 8}\)\(0\)\(\frac{ 17}{ 8}\)
\(-\frac{ 11}{ 8}\)\(0\)\(\frac{ 9}{ 4}\)

Note:

Sporadic YY-Operator.
Can be reduced to 2.70, so not primary operator.

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22

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   LaTex

Coefficients of the holomorphic solution: 1, 336, 142728, 65762368, 31568339880, ...
--> OEIS
Normalized instanton numbers (n0=1): -76, -2002, -92996, -5555506, -384650592, ... ; Common denominator:...

Discriminant

\((1-544z+256z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 17}{ 16}-\frac{ 3}{ 4}\sqrt{ 2}\)\(\frac{ 17}{ 16}+\frac{ 3}{ 4}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 44=$ A \ast \gamma$

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23

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   LaTex

Coefficients 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:...

Discriminant

\((1+82z+3125z^2)^2\)

Local exponents

\(-\frac{ 41}{ 3125}-\frac{ 38}{ 3125}I\)\(-\frac{ 41}{ 3125}+\frac{ 38}{ 3125}I\)\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 17}{ 10}\)
\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(\frac{ 19}{ 10}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 21}{ 10}\)
\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 23}{ 10}\)

Note:

Sporadic YY-Operator

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24

New Number: 4.31 |  AESZ:  |  Superseeker: -10 -340  |  Hash: dc534a2a8e7bca49a87c29d9ed4e3ae8  

Degree: 4

\(\theta^4-2 x\left(172\theta^4+344\theta^3+421\theta^2+249\theta+57\right)+2^{2} x^{2}\left(10852\theta^4+43408\theta^3+78043\theta^2+69270\theta+24987\right)-2^{4} 3 x^{3}\left(49536\theta^4+297216\theta^3+712240\theta^2+799248\theta+349521\right)+2^{14} 3^{2} x^{4}(3\theta+5)(3\theta+7)(6\theta+11)(6\theta+13)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 114, 11466, 1123804, 109952106, ...
--> OEIS
Normalized instanton numbers (n0=1): -10, -40, -340, -5820, -114610, ... ; Common denominator:...

Discriminant

\((108z-1)^2(64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 5}{ 3}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 7}{ 3}\)

Note:

This is operator "4.31" from ...

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25

New Number: 4.32 |  AESZ: 356  |  Superseeker: -14 -196  |  Hash: e73c971c3ed3a4fd581234510642c285  

Degree: 4

\(\theta^4-2 x\left(236\theta^4+472\theta^3+577\theta^2+341\theta+78\right)+2^{2} x^{2}\left(20836\theta^4+83344\theta^3+150531\theta^2+134374\theta+48664\right)-2^{6} 3 x^{3}\left(33984\theta^4+203904\theta^3+487828\theta^2+545916\theta+237757\right)+2^{10} 3^{2} x^{4}(12\theta+19)(12\theta+23)(12\theta+25)(12\theta+29)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 156, 21062, 2714208, 342489420, ...
--> OEIS
Normalized instanton numbers (n0=1): -14, -42, -196, -1218, -208446/5, ... ; Common denominator:...

Discriminant

\((128z-1)^2(108z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 19}{ 12}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 23}{ 12}\)
\(0\)\(1\)\(1\)\(\frac{ 25}{ 12}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 29}{ 12}\)

Note:

Sporadic YY-Operator.

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26

New Number: 4.33 |  AESZ: 55  |  Superseeker: 76/3 144196/3  |  Hash: 7e88cd5b7dc1c51022b66ac6f009218f  

Degree: 4

\(3^{2} \theta^4-2^{2} 3 x\left(208\theta^4+224\theta^3+163\theta^2+51\theta+6\right)+2^{9} x^{2}\left(32\theta^4-928\theta^3-1606\theta^2-837\theta-141\right)+2^{16} x^{3}\left(144\theta^4+576\theta^3+467\theta^2+144\theta+15\right)-2^{24} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 936, 108800, 16748200, ...
--> OEIS
Normalized instanton numbers (n0=1): 76/3, 3476/3, 144196/3, 3563196, 309069600, ... ; Common denominator:...

Discriminant

\(-(64z+1)(256z-1)(-3+128z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 3}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic operator. There is a second MUM-point
hiding at infinity, corresponding to Operator 4.56

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27

New Number: 4.34 |  AESZ: 99  |  Superseeker: 647/13 942613/13  |  Hash: f6c6b846edc829f336d8e4ae1dcb5618  

Degree: 4

\(13^{2} \theta^4-13 x\left(4569\theta^4+9042\theta^3+6679\theta^2+2158\theta+260\right)+2^{4} x^{2}\left(6386\theta^4-1774\theta^3-17898\theta^2-11596\theta-2119\right)+2^{8} x^{3}\left(67\theta^4+1248\theta^3+1091\theta^2+312\theta+26\right)-2^{12} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 20, 2196, 369200, 75562900, ...
--> OEIS
Normalized instanton numbers (n0=1): 647/13, 16166/13, 942613/13, 80218296/13, 8418215008/13, ... ; Common denominator:...

Discriminant

\(-(256z^2+349z-1)(-13+16z)^2\)

Local exponents

\(-\frac{ 349}{ 512}-\frac{ 85}{ 512}\sqrt{ 17}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 349}{ 512}+\frac{ 85}{ 512}\sqrt{ 17}\)\(\frac{ 13}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator.
There is a second MUM point hidden at infinity. That is operator AESZ 207/4.38
A-Incarnation: $5 \times 5$-Pfaffian in P^5

A-Incarnation: 5 \times 5 Pfaffian in P^5

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28

New Number: 4.35 |  AESZ:  |  Superseeker: -16 -1744  |  Hash: cd392ce4c33f242f5d17e59976d0ea4f  

Degree: 4

\(\theta^4-2^{4} x\left(23\theta^4+14\theta^3+13\theta^2+6\theta+1\right)+2^{11} x^{2}\theta(21\theta^3+24\theta^2+18\theta+4)-2^{16} x^{3}(2\theta+1)(10\theta^3+7\theta^2-5\theta-4)-2^{23} x^{4}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 912, 67840, 5839120, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -106, -1744, -29526, -644016, ... ; Common denominator:...

Discriminant

\(-(16z+1)(128z-1)^3\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)
\(1\)\(0\)\(\frac{ 3}{ 2}\)\(1\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Operator equivalent to 3.34, equivalent to
AESZ 107 $=d \ast d$.

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29

New Number: 4.36 |  AESZ: 109  |  Superseeker: 1434/7 18676572/7  |  Hash: bca2938ac7fa09f5bdc395cab75caf82  

Degree: 4

\(7^{2} \theta^4-2 3 7 x\left(1272\theta^4+2508\theta^3+1779\theta^2+525\theta+56\right)+2^{2} 3 x^{2}\left(43704\theta^4+38088\theta^3-25757\theta^2-20608\theta-3360\right)-2^{4} 3^{3} x^{3}\left(2736\theta^4-1512\theta^3-1672\theta^2-357\theta-14\right)-2^{6} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 15840, 8148000, 5126536800, ...
--> OEIS
Normalized instanton numbers (n0=1): 1434/7, 14718, 18676572/7, 4988009280/7, 1646787631350/7, ... ; Common denominator:...

Discriminant

\(-(432z^2+1080z-1)(-7+36z)^2\)

Local exponents

\(-\frac{ 5}{ 4}-\frac{ 13}{ 18}\sqrt{ 3}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 5}{ 4}+\frac{ 13}{ 18}\sqrt{ 3}\)\(\frac{ 7}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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30

New Number: 4.37 |  AESZ: 206  |  Superseeker: 4 284  |  Hash: bd5dae321e1369e7fae153775f84a351  

Degree: 4

\(\theta^4-2^{2} x\theta(\theta+1)(2\theta+1)^2-2^{5} x^{2}(2\theta+1)(2\theta+3)(11\theta^2+22\theta+12)-2^{4} 3 5^{2} x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)-2^{8} 19 x^{4}(2\theta+1)(2\theta+3)(2\theta+5)(2\theta+7)\)

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Coefficients of the holomorphic solution: 1, 0, 72, 1200, 44520, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 27, 284, 4368, 80968, ... ; Common denominator:...

Discriminant

\(-(16z+1)(4864z^3+896z^2+32z-1)\)

Local exponents

≈\(-0.10185-0.013248I\) ≈\(-0.10185+0.013248I\)\(-\frac{ 1}{ 16}\)\(0\)\(s_1\)\(s_3\)\(s_2\) ≈\(0.019489\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(2\)\(2\)\(2\)\(0\)\(2\)\(2\)\(2\)\(2\)\(\frac{ 7}{ 2}\)

Note:

Sporadic Operator.

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