Summary

You searched for: Spectrum0=0,1,3,4

Your search produced 381 matches
 1-30  31-60  61-90  91-120  121-150  151-180 
 181-210  211-240  241-270  271-300  301-330  331-360 
 361-381 

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1

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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2

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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3

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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4

New Number: 4.38 |  AESZ: 207  |  Superseeker: -70944 -3707752060576  |  Hash: eadc0882a9bf59840ef2b4a602f586e8  

Degree: 4

\(\theta^4-2^{4} x\left(1072\theta^4-17824\theta^3-10888\theta^2-1976\theta-145\right)-2^{17} x^{2}\left(51088\theta^4+116368\theta^3-45264\theta^2-14228\theta-1397\right)+2^{28} 13 x^{3}\left(73104\theta^4+1536\theta^3-488\theta^2+384\theta+97\right)-2^{44} 13^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2320, 57601296, -2373661139200, 121665506430000400, ...
--> OEIS
Normalized instanton numbers (n0=1): -70944, 107317768, -3707752060576, 66327758316665792, -1970671594871618215520, ... ; Common denominator:...

Discriminant

\(-(16777216z^2-89344z-1)(-1+53248z)^2\)

Local exponents

\(\frac{ 349}{ 131072}-\frac{ 85}{ 131072}\sqrt{ 17}\)\(0\)\(s_2\)\(s_1\)\(\frac{ 1}{ 53248}\)\(\frac{ 349}{ 131072}+\frac{ 85}{ 131072}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator.
There is a further MUM point hidden at infinity.
That operator is AESZ 99/4.34

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5

New Number: 4.39 |  AESZ: 210  |  Superseeker: -444/5 -1501908/5  |  Hash: 155d0198a5b26de08a0c2caf680f0786  

Degree: 4

\(5^{2} \theta^4+2^{2} 5 x\left(688\theta^4+1352\theta^3+981\theta^2+305\theta+35\right)+2^{4} x^{2}\left(5856\theta^4+7008\theta^3+96\theta^2-1260\theta-265\right)+2^{10} x^{3}\left(176\theta^4+120\theta^3+69\theta^2+30\theta+5\right)+2^{12} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -28, 4716, -1226800, 389349100, ...
--> OEIS
Normalized instanton numbers (n0=1): -444/5, 16653/5, -1501908/5, 199965534/5, -6573697776, ... ; Common denominator:...

Discriminant

\((256z^2+544z+1)(5+16z)^2\)

Local exponents

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

Note:

Sporadic operator. There is a second MUM point hidden at infinity; Operator AESZ 211/4.40

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6

New Number: 4.40 |  AESZ: 211  |  Superseeker: -2400 -2956977632  |  Hash: c923c78e33e72a3a2b294bf3f2749298  

Degree: 4

\(\theta^4+2^{4} x\left(704\theta^4+928\theta^3+612\theta^2+148\theta+13\right)+2^{12} x^{2}\left(5856\theta^4+4704\theta^3-1632\theta^2-972\theta-121\right)+2^{20} 5 x^{3}\left(2752\theta^4+96\theta^3-60\theta^2+24\theta+7\right)+2^{28} 5^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -208, 531216, -2168300800, 10900554288400, ...
--> OEIS
Normalized instanton numbers (n0=1): -2400, 1830480, -2956977632, 7117422755016, -21319886408804640, ... ; Common denominator:...

Discriminant

\((65536z^2+8704z+1)(1+1280z)^2\)

Local exponents

\(-\frac{ 17}{ 256}-\frac{ 3}{ 64}\sqrt{ 2}\)\(-\frac{ 1}{ 1280}\)\(-\frac{ 17}{ 256}+\frac{ 3}{ 64}\sqrt{ 2}\)\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM point hidden at infinity. That corresponds to Operator AESZ210/

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7

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   LaTex

Coefficients 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:...

Discriminant

\(-(8192z^2+107z-1)(5+64z)^2\)

Local exponents

\(-\frac{ 5}{ 64}\)\(-\frac{ 107}{ 16384}-\frac{ 51}{ 16384}\sqrt{ 17}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 107}{ 16384}+\frac{ 51}{ 16384}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ225/4.43

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8

New Number: 4.43 |  AESZ: 225  |  Superseeker: 93984 25265152551072  |  Hash: 5993002ccf811247be9232b089dd8e3a  

Degree: 4

\(\theta^4+2^{4} x\left(22192\theta^4-17056\theta^3-9576\theta^2-1048\theta-49\right)+2^{20} x^{2}\left(33648\theta^4-44688\theta^3+16224\theta^2+1764\theta+17\right)+2^{34} 5 x^{3}\left(6512\theta^4-6144\theta^3-4440\theta^2-1536\theta-193\right)-2^{55} 5^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 784, 3226896, 20413907200, 157477179235600, ...
--> OEIS
Normalized instanton numbers (n0=1): 93984, -1084521600, 25265152551072, -787700706860008320, 28889437619654310485088, ... ; Common denominator:...

Discriminant

\(-(536870912z^2-27392z-1)(1+163840z)^2\)

Local exponents

≈\(-2.5e-05\)\(-\frac{ 1}{ 163840}\)\(0\)\(s_2\)\(s_1\) ≈\(7.6e-05\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point
hiding at infinity, corresponding to Operator
AESZ 222/4.42

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9

New Number: 4.44 |  AESZ: 232  |  Superseeker: 379/5 1364199/5  |  Hash: 8d5ff690c87757ed51a092dee764eede  

Degree: 4

\(5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ...
--> OEIS
Normalized instanton numbers (n0=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...

Discriminant

\(-(27z+1)(512z-1)(-5+96z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 512}\)\(\frac{ 5}{ 96}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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10

New Number: 4.45 |  AESZ: 233  |  Superseeker: 80 104976  |  Hash: 03f67459f6d678669f766c99281b1e79  

Degree: 4

\(\theta^4-2^{4} x\left(83\theta^4+94\theta^3+71\theta^2+24\theta+3\right)+2^{11} 3 x^{2}\left(101\theta^4+191\theta^3+174\theta^2+71\theta+10\right)-2^{16} 3^{2} x^{3}\left(203\theta^4+432\theta^3+333\theta^2+102\theta+11\right)+2^{23} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 9360, 2553600, 813027600, ...
--> OEIS
Normalized instanton numbers (n0=1): 80, 2794, 104976, 5367454, 508265072, ... ; Common denominator:...

Discriminant

\((512z-1)(432z-1)(-1+192z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 512}\)\(\frac{ 1}{ 432}\)\(\frac{ 1}{ 192}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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11

New Number: 4.46 |  AESZ: 237  |  Superseeker: 208 1218192  |  Hash: 52c18dd4477f6548dd3b185e97b94c20  

Degree: 4

\(\theta^4-2^{4} x\left(46\theta^4+128\theta^3+91\theta^2+27\theta+3\right)-2^{9} 3 x^{2}\left(74\theta^4-16\theta^3-231\theta^2-127\theta-20\right)+2^{14} 3^{2} x^{3}\left(14\theta^4+216\theta^3+175\theta^2+51\theta+5\right)+2^{19} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 12240, 4972800, 2489533200, ...
--> OEIS
Normalized instanton numbers (n0=1): 208, 5874, 1218192, 220754467, 56417503216, ... ; Common denominator:...

Discriminant

\((864z-1)(64z-1)(1+96z)^2\)

Local exponents

\(-\frac{ 1}{ 96}\)\(0\)\(\frac{ 1}{ 864}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

This is operator "4.46" from ...

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12

New Number: 4.47 |  AESZ: 239  |  Superseeker: 1584 171534960  |  Hash: 8e610c3437d7f38e552038bc55399495  

Degree: 4

\(\theta^4+2^{4} 3 x\left(9\theta^4-198\theta^3-131\theta^2-32\theta-3\right)-2^{11} 3^{2} x^{2}\left(486\theta^4+1215\theta^3+81\theta^2-27\theta-5\right)-2^{16} 3^{5} x^{3}\left(891\theta^4+972\theta^3+675\theta^2+216\theta+25\right)-2^{23} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 144, 147600, 239904000, 479672701200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1584, -17874, 171534960, 30012731550, 105934107802896, ... ; Common denominator:...

Discriminant

\(-(432z+1)(3456z-1)(1+1728z)^2\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 1}{ 1728}\)\(0\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 3}\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(2\)\(4\)\(0\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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13

New Number: 4.48 |  AESZ: 241  |  Superseeker: 320 19748928  |  Hash: b4d16d8dd1eb7839630ecf8e8d242023  

Degree: 4

\(\theta^4-2^{4} x\left(152\theta^4+160\theta^3+110\theta^2+30\theta+3\right)+2^{10} 3 x^{2}\left(428\theta^4+176\theta^3-299\theta^2-170\theta-25\right)-2^{17} 3^{2} x^{3}\left(136\theta^4-216\theta^3-180\theta^2-51\theta-5\right)-2^{24} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 26640, 21907200, 22048765200, ...
--> OEIS
Normalized instanton numbers (n0=1): 320, 61084, 19748928, 9428973876, 5618509433280, ... ; Common denominator:...

Discriminant

\(-(64z+1)(1728z-1)(-1+384z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 1728}\)\(\frac{ 1}{ 384}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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14

New Number: 4.49 |  AESZ: 254  |  Superseeker: -5408 -22147077792  |  Hash: 2539c1ff260271c9f7de53e267e2e8cf  

Degree: 4

\(\theta^4-2^{4} x\left(2608\theta^4-544\theta^3-200\theta^2+72\theta+15\right)+2^{15} 3 x^{2}\left(6128\theta^4-208\theta^3+2328\theta^2+452\theta+25\right)-2^{24} 3^{2} 5 x^{3}\left(4592\theta^4+3456\theta^3+2632\theta^2+816\theta+95\right)+2^{38} 3^{3} 5^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 314640, 627244800, 1516001533200, ...
--> OEIS
Normalized instanton numbers (n0=1): -5408, -8033784, -22147077792, -80392290665536, -341267541912723040, ... ; Common denominator:...

Discriminant

\((6912z-1)(4096z-1)(-1+15360z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 15360}\)\(\frac{ 1}{ 6912}\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(3\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(4\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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15

New Number: 4.50 |  AESZ: 256  |  Superseeker: -128 -800384  |  Hash: 05e172cfdecc836685981a2b01b75d1d  

Degree: 4

\(\theta^4+2^{5} x\left(24\theta^4+42\theta^3+30\theta^2+9\theta+1\right)+2^{8} x^{2}\left(164\theta^4+104\theta^3-144\theta^2-100\theta-17\right)+2^{14} x^{3}\left(28\theta^4-48\theta^3-44\theta^2-12\theta-1\right)-2^{18} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -32, 7056, -2393600, 991152400, ...
--> OEIS
Normalized instanton numbers (n0=1): -128, 6884, -800384, 143245314, -31691939200, ... ; Common denominator:...

Discriminant

\(-(4096z^2-704z-1)(1+32z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity, corresponding to Operator AESZ 257/4.51
B-Incarnation:
Fibre product 4*11-- x 25311,
Double octic; D.O.257

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16

New Number: 4.51 |  AESZ:  |  Superseeker: 992 63721056  |  Hash: 1d45a05c9bcf007b5042b0f7a5672551  

Degree: 4

\(\theta^4-2^{4} x\left(112\theta^4+416\theta^3+280\theta^2+72\theta+7\right)-2^{12} x^{2}\left(656\theta^4+896\theta^3-216\theta^2-160\theta-23\right)-2^{23} x^{3}\left(96\theta^4+24\theta^3+12\theta^2+6\theta+1\right)-2^{30} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 112, 93456, 124614400, 204621667600, ...
--> OEIS
Normalized instanton numbers (n0=1): 992, 98792, 63721056, 40943244128, 36122052633760, ... ; Common denominator:...

Discriminant

\(-(65536z^2+2816z-1)(1+512z)^2\)

Local exponents

\(-\frac{ 11}{ 512}-\frac{ 5}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 512}\)\(0\)\(s_2\)\(s_1\)\(-\frac{ 11}{ 512}+\frac{ 5}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point
hiding at infinity, corresponding to Operator
AESZ 256/4.50

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17

New Number: 4.52 |  AESZ: 258  |  Superseeker: 480 4215904  |  Hash: bfb9f01124fd9980817cbf1b50f789c3  

Degree: 4

\(\theta^4-2^{4} x\left(16\theta^4+224\theta^3+156\theta^2+44\theta+5\right)-2^{14} x^{2}\left(48\theta^4+48\theta^3-120\theta^2-66\theta-11\right)-2^{22} x^{3}\left(16\theta^4-192\theta^3-156\theta^2-48\theta-5\right)+2^{32} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 80, 24336, 11398400, 6632189200, ...
--> OEIS
Normalized instanton numbers (n0=1): 480, -16536, 4215904, -242723592, 151800032928, ... ; Common denominator:...

Discriminant

\((1024z-1)(256z-1)(1+512z)^2\)

Local exponents

\(-\frac{ 1}{ 512}\)\(0\)\(\frac{ 1}{ 1024}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator.

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18

New Number: 4.53 |  AESZ: 264  |  Superseeker: 37216 464865119712  |  Hash: 625990ef22ba977bc3dd247ccc791780  

Degree: 4

\(\theta^4+2^{4} x\left(3392\theta^4-9344\theta^3-5764\theta^2-1092\theta-93\right)-2^{17} 3 x^{2}\left(1952\theta^4+15200\theta^3-7758\theta^2-2593\theta-323\right)-2^{26} 3^{2} 7 x^{3}\left(11584\theta^4-6912\theta^3-5364\theta^2-1632\theta-167\right)+2^{42} 3^{3} 7^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1488, 11258640, 139962144000, 2191135140810000, ...
--> OEIS
Normalized instanton numbers (n0=1): 37216, -75619080, 464865119712, -2749454414283384, 24030314100181942560, ... ; Common denominator:...

Discriminant

\((27648z-1)(4096z-1)(1+43008z)^2\)

Local exponents

\(-\frac{ 1}{ 43008}\)\(0\)\(\frac{ 1}{ 27648}\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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19

New Number: 4.54 |  AESZ: 265  |  Superseeker: 1056 138459552  |  Hash: fad89ac60b7ab4118edfed4cf6350d0c  

Degree: 4

\(\theta^4+2^{4} 3 x\left(96\theta^4-96\theta^3-60\theta^2-12\theta-1\right)+2^{13} 3 x^{2}\left(288\theta^4-144\theta^3+526\theta^2+206\theta+27\right)+2^{20} 3^{3} x^{3}\left(288\theta^4+864\theta^3+652\theta^2+204\theta+23\right)+2^{30} 3^{5} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, -30960, -11961600, 15342742800, ...
--> OEIS
Normalized instanton numbers (n0=1): 1056, -360672, 138459552, -50965971720, 20236543243104, ... ; Common denominator:...

Discriminant

\((1769472z^2+1)(1+2304z)^2\)

Local exponents

\(-\frac{ 1}{ 2304}\)\(0-\frac{ 1}{ 2304}\sqrt{ 3}I\)\(0\)\(s_1\)\(s_2\)\(0+\frac{ 1}{ 2304}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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20

New Number: 4.55 |  AESZ: 276  |  Superseeker: -188832 -101990911789344  |  Hash: 797e27181bf0a060708a3d221ec79699  

Degree: 4

\(\theta^4-2^{4} 3 x\left(18432\theta^4-4608\theta^3-1024\theta^2+1280\theta+221\right)+2^{17} 3^{4} x^{2}\left(25344\theta^4-2304\theta^3+11680\theta^2+1472\theta-33\right)-2^{28} 3^{8} x^{3}\left(18432\theta^4+13824\theta^3+11392\theta^2+3264\theta+359\right)+2^{46} 3^{12} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10608, 477012240, 30101658720000, 2213759644568010000, ...
--> OEIS
Normalized instanton numbers (n0=1): -188832, -3134817768, -101990911789344, -4414817659429205136, -223930278487379610386400, ... ; Common denominator:...

Discriminant

\((331776z-1)^2(110592z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 331776}\)\(\frac{ 1}{ 110592}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(\frac{ 1}{ 2}\)
\(0\)\(4\)\(1\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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21

New Number: 4.56 |  AESZ: 277  |  Superseeker: 4192 2124587232  |  Hash: 9d905a8d31566f4976cbeb2d3bf0624c  

Degree: 4

\(\theta^4+2^{4} x\left(576\theta^4-1152\theta^3-724\theta^2-148\theta-13\right)-2^{17} x^{2}\left(32\theta^4+992\theta^3-166\theta^2-57\theta-6\right)-2^{26} 3 x^{3}\left(832\theta^4+768\theta^3+556\theta^2+192\theta+25\right)-2^{40} 3^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 208, 254736, 490988800, 1163138813200, ...
--> OEIS
Normalized instanton numbers (n0=1): 4192, -1708008, 2124587232, -2777042329304, 4857272052090400, ... ; Common denominator:...

Discriminant

\(-(1024z+1)(4096z-1)(1+6144z)^2\)

Local exponents

\(-\frac{ 1}{ 1024}\)\(-\frac{ 1}{ 6144}\)\(0\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(4\)\(0\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to Operator 4.33, reducible to 3.35.

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22

New Number: 4.57 |  AESZ: 278  |  Superseeker: 243 513936  |  Hash: b30f6ac0da69cf91ab39089e6bf1ac8c  

Degree: 4

\(\theta^4-3 x\left(279\theta^4+882\theta^3+641\theta^2+200\theta+24\right)-2 3^{5} x^{2}\left(72\theta^4-1710\theta^3-3665\theta^2-1864\theta-296\right)+2^{2} 3^{9} x^{3}\left(909\theta^4+3888\theta^3+3082\theta^2+918\theta+92\right)+2^{4} 3^{15} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 72, 18360, 6552000, 2767980600, ...
--> OEIS
Normalized instanton numbers (n0=1): 243, -3402, 513936, 2470824, 6888345300, ... ; Common denominator:...

Discriminant

\((729z-1)(432z-1)(1+162z)^2\)

Local exponents

\(-\frac{ 1}{ 162}\)\(0\)\(\frac{ 1}{ 729}\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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23

New Number: 4.58 |  AESZ: 282  |  Superseeker: 364/5 1264916  |  Hash: 582c9abe0a0b8176a2a06ec6c223bef4  

Degree: 4

\(5^{2} \theta^4-2^{2} 5 x\left(1348\theta^4+752\theta^3+521\theta^2+145\theta+15\right)+2^{4} 3^{4} x^{2}\left(5696\theta^4-1792\theta^3-7304\theta^2-3740\theta-585\right)-2^{10} 3^{8} x^{3}\left(20\theta^4-360\theta^3-289\theta^2-90\theta-10\right)-2^{12} 3^{13} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 3564, 1081200, 418200300, ...
--> OEIS
Normalized instanton numbers (n0=1): 364/5, 43384/5, 1264916, 1297643028/5, 323354425968/5, ... ; Common denominator:...

Discriminant

\(-(62208z^2+560z-1)(-5+1296z)^2\)

Local exponents

\(-\frac{ 35}{ 7776}-\frac{ 13}{ 7776}\sqrt{ 13}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 35}{ 7776}+\frac{ 13}{ 7776}\sqrt{ 13}\)\(\frac{ 5}{ 1296}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity,corresponding to the Operator AESZ 283/4.59

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24

New Number: 4.59 |  AESZ: 283  |  Superseeker: -188 -807540  |  Hash: 987222cb05e8a3d02c76c47abefbb9f4  

Degree: 4

\(\theta^4+2^{2} x\left(20\theta^4+400\theta^3+281\theta^2+81\theta+9\right)-2^{4} 3 x^{2}\left(5696\theta^4+13184\theta^3+3928\theta^2+628\theta+39\right)+2^{10} 3^{2} 5 x^{3}\left(1348\theta^4+1944\theta^3+1415\theta^2+486\theta+63\right)-2^{12} 3^{7} 5^{2} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -36, 7236, -2257200, 860876100, ...
--> OEIS
Normalized instanton numbers (n0=1): -188, 831, -807540, 39235244, -18812436256, ... ; Common denominator:...

Discriminant

\(-(62208z^2-560z-1)(-1+240z)^2\)

Local exponents

\(\frac{ 35}{ 7776}-\frac{ 13}{ 7776}\sqrt{ 13}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 240}\)\(\frac{ 35}{ 7776}+\frac{ 13}{ 7776}\sqrt{ 13}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to AESZ 282/4.58

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25

New Number: 4.60 |  AESZ: 288  |  Superseeker: 3616 264403872  |  Hash: 3373ebdbe30d220b5562cfd77d4e8f96  

Degree: 4

\(\theta^4-2^{4} x\left(496\theta^4+1568\theta^3+1060\theta^2+276\theta+27\right)-2^{15} 3 x^{2}\left(32\theta^4-760\theta^3-1570\theta^2-651\theta-81\right)+2^{22} 3^{2} x^{3}\left(1616\theta^4+6912\theta^3+5092\theta^2+1416\theta+135\right)+2^{34} 3^{3} x^{4}(4\theta+1)(3\theta+1)(3\theta+2)(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 432, 982800, 3259872000, 12958462717200, ...
--> OEIS
Normalized instanton numbers (n0=1): 3616, 114144, 264403872, 424149521656, 710239010095456, ... ; Common denominator:...

Discriminant

\((6912z-1)(4096z-1)(1+1536z)^2\)

Local exponents

\(-\frac{ 1}{ 1536}\)\(0\)\(\frac{ 1}{ 6912}\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 3}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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26

New Number: 4.61 |  AESZ: 289  |  Superseeker: 8224 15542388128  |  Hash: 673413653f5554d4f0cc1a8af33e8bbe  

Degree: 4

\(\theta^4-2^{4} x\left(400\theta^4+2720\theta^3+1752\theta^2+392\theta+33\right)-2^{15} x^{2}\left(4272\theta^4+6288\theta^3-3184\theta^2-1484\theta-177\right)-2^{24} 5 x^{3}\left(4688\theta^4-1536\theta^3-1384\theta^2-336\theta-27\right)+2^{36} 5^{2} x^{4}(4\theta+1)(2\theta+1)^2(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 528, 2434320, 18496262400, 174225386134800, ...
--> OEIS
Normalized instanton numbers (n0=1): 8224, 3407456, 15542388128, 54609260446560, 282477571639256928, ... ; Common denominator:...

Discriminant

\((16384z-1)(256z-1)(1+5120z)^2\)

Local exponents

\(-\frac{ 1}{ 5120}\)\(0\)\(\frac{ 1}{ 16384}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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27

New Number: 4.62 |  AESZ: 292  |  Superseeker: 4300/3 1701817028/3  |  Hash: bce26f214ee56f65c7a275cd8fdcc0c7  

Degree: 4

\(3^{2} \theta^4-2^{2} 3 x\left(4636\theta^4+7928\theta^3+5347\theta^2+1383\theta+126\right)+2^{9} x^{2}\left(59048\theta^4+50888\theta^3-26248\theta^2-16827\theta-2205\right)-2^{16} 7 x^{3}\left(9004\theta^4-2304\theta^3-2511\theta^2-504\theta-27\right)-2^{24} 7^{2} x^{4}(4\theta+1)(2\theta+1)^2(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 168, 279720, 737721600, 2391487698600, ...
--> OEIS
Normalized instanton numbers (n0=1): 4300/3, 1768292/3, 1701817028/3, 2484553593752/3, 1500880129466144, ... ; Common denominator:...

Discriminant

\(-(65536z^2+5584z-1)(-3+896z)^2\)

Local exponents

\(-\frac{ 349}{ 8192}-\frac{ 85}{ 8192}\sqrt{ 17}\)\(0\)\(s_1\)\(s_2\)\(-\frac{ 349}{ 8192}+\frac{ 85}{ 8192}\sqrt{ 17}\)\(\frac{ 3}{ 896}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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28

New Number: 4.63 |  AESZ: 294  |  Superseeker: -80416 -15561562691488  |  Hash: f6b5a258285779facb6702e1a2a891bb  

Degree: 4

\(\theta^4-2^{4} x\left(18800\theta^4-14624\theta^3-8184\theta^2-872\theta-33\right)+2^{18} x^{2}\left(101744\theta^4-107920\theta^3+74968\theta^2+15100\theta+1191\right)-2^{30} 17 x^{3}\left(40048\theta^4+49152\theta^3+35848\theta^2+10752\theta+1143\right)+2^{50} 17^{2} x^{4}(4\theta+1)(2\theta+1)^2(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -528, -16919280, -95988076800, 3707387171888400, ...
--> OEIS
Normalized instanton numbers (n0=1): -80416, -872844376, -15561562691488, -341695175348542432, -8482586861983707669856, ... ; Common denominator:...

Discriminant

\((1073741824z^2-22272z+1)(-1+139264z)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 139264}\)\(\frac{ 87}{ 8388608}-\frac{ 91}{ 8388608}\sqrt{ 7}I\)\(\frac{ 87}{ 8388608}+\frac{ 91}{ 8388608}\sqrt{ 7}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 4}\)

Note:

Sporadic Operator.

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29

New Number: 4.64 |  AESZ: 295  |  Superseeker: -5408 -4296119968  |  Hash: e40629f953a095a2a764c68394321139  

Degree: 4

\(\theta^4-2^{4} x\left(816\theta^4-1440\theta^3-904\theta^2-184\theta-17\right)+2^{18} x^{2}\left(80\theta^4-592\theta^3+432\theta^2+164\theta+23\right)+2^{30} x^{3}\left(80\theta^4-384\theta^3-296\theta^2-96\theta-11\right)+2^{45} x^{4}\left((2\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -272, 93456, 194502400, -587215823600, ...
--> OEIS
Normalized instanton numbers (n0=1): -5408, -3839480, -4296119968, -6482749129792, -11816577914904160, ... ; Common denominator:...

Discriminant

\((8388608z^2+3328z+1)(-1+8192z)^2\)

Local exponents

\(-\frac{ 13}{ 65536}-\frac{ 7}{ 65536}\sqrt{ 7}I\)\(-\frac{ 13}{ 65536}+\frac{ 7}{ 65536}\sqrt{ 7}I\)\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 8192}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(2\)\(0\)\(2\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to Operator AESZ 296/4.65

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30

New Number: 4.65 |  AESZ:  |  Superseeker: 48 -9104  |  Hash: 5ec2790b5eda514313634b7aeb0a295c  

Degree: 4

\(\theta^4-2^{4} x\left(5\theta^4+34\theta^3+25\theta^2+8\theta+1\right)+2^{11} x^{2}\left(5\theta^4+47\theta^3+90\theta^2+47\theta+8\right)+2^{16} x^{3}\left(51\theta^4+192\theta^3+155\theta^2+48\theta+5\right)+2^{23} x^{4}\left((2\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 16, 144, -70400, -9858800, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, -1298, -9104, 387230, 102374160, ... ; Common denominator:...

Discriminant

\((32768z^2-208z+1)(1+64z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 13}{ 4096}-\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\frac{ 13}{ 4096}+\frac{ 7}{ 4096}\sqrt{ 7}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at infinity,
corresponding to Operator AESZ 295/4.64

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