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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121

New Number: 5.52 |  AESZ: 252  |  Superseeker: -232/5 -122168/5  |  Hash: cae57e93a6afb98313f62899d1f75e2e  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(36\theta^4-636\theta^3-488\theta^2-170\theta-25\right)-2^{4} x^{2}\left(21301\theta^4+27148\theta^3-86889\theta^2-63110\theta-14975\right)+2^{8} 5 x^{3}\left(3907\theta^4-58863\theta^3-25285\theta^2+10878\theta+7151\right)+2^{10} 59 x^{4}\left(10981\theta^4-29878\theta^3-89811\theta^2-70372\theta-17759\right)+2^{15} 3 59^{2} x^{5}(4\theta+5)(3\theta+2)(3\theta+4)(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -20, 684, -32240, 1969900, ...
--> OEIS
Normalized instanton numbers (n0=1): -232/5, -7499/10, -122168/5, -4503443/5, -200467616/5, ... ; Common denominator:...

Discriminant

\((108z+1)(2048z^2+52z+1)(-5+472z)^2\)

Local exponents

\(-\frac{ 13}{ 1024}-\frac{ 7}{ 1024}\sqrt{ 7}I\)\(-\frac{ 13}{ 1024}+\frac{ 7}{ 1024}\sqrt{ 7}I\)\(-\frac{ 1}{ 108}\)\(0\)\(\frac{ 5}{ 472}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(1\)\(0\)\(3\)\(\frac{ 5}{ 4}\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.52" from ...

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122

New Number: 5.53 |  AESZ: 259  |  Superseeker: 82450 22323908689400  |  Hash: 8b20756bb52131d41c44fd699c9e3a24  

Degree: 5

\(\theta^4+2 5 x\left(40000\theta^4-17500\theta^3-8125\theta^2+625\theta+238\right)+2^{2} 5^{6} x^{2}\left(835000\theta^4-365000\theta^3+371125\theta^2+58500\theta+2116\right)+2^{4} 5^{11} x^{3}\left(3130000\theta^4+1815000\theta^3+1662000\theta^2+625875\theta+96914\right)+2^{6} 5^{19} 13 x^{4}(625\theta^2+745\theta+351)(2\theta+1)^2+2^{8} 5^{25} 13^{2} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2380, 14400900, -112575082000, 993749164922500, ...
--> OEIS
Normalized instanton numbers (n0=1): 82450, -976323150, 22323908689400, -680892969306394000, 24398212781075814030620, ... ; Common denominator:...

Discriminant

\((1+50000z)(12500z+1)^2(162500z+1)^2\)

Local exponents

\(-\frac{ 1}{ 12500}\)\(-\frac{ 1}{ 50000}\)\(-\frac{ 1}{ 162500}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(2\)\(4\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.53" from ...

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123

New Number: 5.54 |  AESZ: 260  |  Superseeker: -188/5 -450516/5  |  Hash: 03ff8e2e94b897c3891e6981e7fb4ec9  

Degree: 5

\(5^{2} \theta^4+2^{2} 5 x\left(596\theta^4+544\theta^3+397\theta^2+125\theta+15\right)+2^{4} 3 x^{2}\left(30048\theta^4+14784\theta^3-13312\theta^2-10940\theta-2115\right)+2^{8} 3^{3} x^{3}\left(6368\theta^4-6720\theta^3-9052\theta^2-4080\theta-655\right)-2^{12} 3^{6} x^{4}(2\theta+1)^2(76\theta^2+196\theta+139)-2^{16} 3^{9} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 1260, -188400, 34353900, ...
--> OEIS
Normalized instanton numbers (n0=1): -188/5, 7693/5, -450516/5, 37785946/5, -790482672, ... ; Common denominator:...

Discriminant

\(-(16z+1)(6912z^2-288z-1)(5+432z)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 5}{ 432}\)\(\frac{ 1}{ 48}-\frac{ 1}{ 72}\sqrt{ 3}\)\(0\)\(\frac{ 1}{ 48}+\frac{ 1}{ 72}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.54" from ...

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124

New Number: 5.55 |  AESZ: 261  |  Superseeker: -76/5 -24836/5  |  Hash: adadb5e720011482371f48cfa73dab99  

Degree: 5

\(5^{2} \theta^4+2^{2} 5 x\left(292\theta^4+368\theta^3+289\theta^2+105\theta+15\right)+2^{4} x^{2}\left(24736\theta^4+43648\theta^3+38936\theta^2+18980\theta+3735\right)+2^{9} 3^{2} x^{3}\left(2512\theta^4+5760\theta^3+6328\theta^2+3330\theta+655\right)+2^{12} 3^{4} x^{4}(2\theta+1)(232\theta^3+588\theta^2+590\theta+207)+2^{18} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 492, -32880, 2743020, ...
--> OEIS
Normalized instanton numbers (n0=1): -76/5, 1103/5, -24836/5, 847456/5, -36542448/5, ... ; Common denominator:...

Discriminant

\((1+144z)(16z+1)^2(144z+5)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 5}{ 144}\)\(-\frac{ 1}{ 144}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(3\)\(1\)\(0\)\(1\)
\(1\)\(4\)\(2\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.55" from ...

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125

New Number: 5.56 |  AESZ: 262  |  Superseeker: -28/5 -1268/5  |  Hash: 4899f97226a5ec3b1ded2994470e9fdc  

Degree: 5

\(5^{2} \theta^4+2^{2} 5 x\left(136\theta^4+224\theta^3+197\theta^2+85\theta+15\right)+2^{4} x^{2}\left(5584\theta^4+16192\theta^3+21924\theta^2+14800\theta+3955\right)+2^{11} x^{3}\left(608\theta^4+2280\theta^3+3642\theta^2+2745\theta+780\right)+2^{14} x^{4}\left(464\theta^4+1888\theta^3+2956\theta^2+2012\theta+501\right)+2^{24} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 236, -6384, 217836, ...
--> OEIS
Normalized instanton numbers (n0=1): -28/5, 153/5, -1268/5, 18598/5, -320048/5, ... ; Common denominator:...

Discriminant

\((1+64z)(32z+5)^2(16z+1)^2\)

Local exponents

\(-\frac{ 5}{ 32}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(0\)\(1\)
\(3\)\(1\)\(1\)\(0\)\(1\)
\(4\)\(1\)\(2\)\(0\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to the Operator AESZ 263/5.57

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126

New Number: 5.57 |  AESZ: 263  |  Superseeker: 1312 58156704  |  Hash: 2157fe92de97f7b684b3cbd7b8bdf280  

Degree: 5

\(\theta^4+2^{4} x\left(464\theta^4-32\theta^3+76\theta^2+92\theta+21\right)+2^{15} x^{2}\left(608\theta^4+152\theta^3+450\theta^2+131\theta+5\right)+2^{22} x^{3}\left(5584\theta^4+6144\theta^3+6852\theta^2+2808\theta+471\right)+2^{34} 5 x^{4}\left(136\theta^4+320\theta^3+341\theta^2+181\theta+39\right)+2^{46} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -336, 198416, -142318848, 112152177936, ...
--> OEIS
Normalized instanton numbers (n0=1): 1312, -211968, 58156704, -19819112104, 7519377878624, ... ; Common denominator:...

Discriminant

\((1+256z)(1024z+1)^2(2560z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 1024}\)\(-\frac{ 1}{ 2560}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)
\(2\)\(1\)\(4\)\(0\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 262/5.56

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127

New Number: 5.58 |  AESZ: 266  |  Superseeker: -18/5 -642/5  |  Hash: 5d46913a13c5fa5fa6a547d8b5646133  

Degree: 5

\(5^{2} \theta^4-3 5 x\left(27\theta^4+108\theta^3+124\theta^2+70\theta+15\right)-2 3^{2} x^{2}\left(1377\theta^4+4536\theta^3+6507\theta^2+4455\theta+1220\right)+2 3^{5} x^{3}\left(567\theta^4+4860\theta^3+11583\theta^2+10665\theta+3445\right)+3^{8} x^{4}\left(729\theta^4+3888\theta^3+6606\theta^2+4662\theta+1184\right)+3^{15} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 171, 3087, 69579, ...
--> OEIS
Normalized instanton numbers (n0=1): -18/5, 117/10, -642/5, 1197, -76788/5, ... ; Common denominator:...

Discriminant

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

Local exponents

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

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 267/5.59

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128

New Number: 5.59 |  AESZ: 267  |  Superseeker: 1818 467810538  |  Hash: 924287a9ba8517571071ec73d860af7e  

Degree: 5

\(\theta^4+3^{2} x\left(729\theta^4-972\theta^3-684\theta^2-198\theta-31\right)+2 3^{8} x^{2}\left(567\theta^4-2592\theta^3+405\theta^2+189\theta+70\right)-2 3^{14} x^{3}\left(1377\theta^4+972\theta^3+1161\theta^2+459\theta+113\right)-3^{22} 5 x^{4}\left(27\theta^4-38\theta^2-38\theta-12\right)+3^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 279, 124011, 64869777, 36848978379, ...
--> OEIS
Normalized instanton numbers (n0=1): 1818, -681336, 467810538, -422903176767, 446062311232740, ... ; Common denominator:...

Discriminant

\((1+729z)(3645z+1)^2(729z-1)^2\)

Local exponents

\(-\frac{ 1}{ 729}\)\(-\frac{ 1}{ 3645}\)\(0\)\(\frac{ 1}{ 729}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(0\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(1\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 266/5.58

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129

New Number: 5.5 |  AESZ: 22  |  Superseeker: 10/7 295/7  |  Hash: 5b96eae0872756be1130d4b12ffe60a6  

Degree: 5

\(7^{2} \theta^4-7 x\left(155\theta^4+286\theta^3+234\theta^2+91\theta+14\right)-x^{2}\left(16105\theta^4+68044\theta^3+102261\theta^2+66094\theta+15736\right)+2^{3} x^{3}\left(2625\theta^4+8589\theta^3+9071\theta^2+3759\theta+476\right)-2^{4} x^{4}\left(465\theta^4+1266\theta^3+1439\theta^2+806\theta+184\right)+2^{9} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 34, 488, 9826, ...
--> OEIS
Normalized instanton numbers (n0=1): 10/7, 65/7, 295/7, 3065/7, 4245, ... ; Common denominator:...

Discriminant

\((32z-1)(z^2-11z-1)(4z-7)^2\)

Local exponents

\(\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\)\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 7}{ 4}\)\(\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 118/5.16
A-Incarnation: five (1,1) sections in ${\bf P}^4 \times {\bf P}^4$.Quotient by ${\bf Z}/2$ of this:
the Reye congruence Calabi-Yau threefold.

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130

New Number: 5.60 |  AESZ: 268  |  Superseeker: -828/5 -4270932/5  |  Hash: 638e2881183378c7a47b7508d9acc072  

Degree: 5

\(5^{2} \theta^4-2^{2} 3 5 x\left(108\theta^4+432\theta^3+661\theta^2+445\theta+105\right)-2^{4} 3^{2} x^{2}\left(44064\theta^4+145152\theta^3+239004\theta^2+186300\theta+58045\right)+2^{9} 3^{5} x^{3}\left(9072\theta^4+77760\theta^3+180954\theta^2+164970\theta+53965\right)+2^{12} 3^{8} x^{4}\left(11664\theta^4+62208\theta^3+104940\theta^2+73836\theta+18659\right)+2^{20} 3^{15} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 252, 87084, 31502448, 12121584876, ...
--> OEIS
Normalized instanton numbers (n0=1): -828/5, 25533/5, -4270932/5, 598304142/5, -24767201520, ... ; Common denominator:...

Discriminant

\((1+432z)(432z+5)^2(432z-1)^2\)

Local exponents

\(-\frac{ 5}{ 432}\)\(-\frac{ 1}{ 432}\)\(0\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(\frac{ 3}{ 2}\)\(1\)

Note:

There is a second MUM-point at infinity, correspondint to
Operator AESZ 269/5.61

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131

New Number: 5.61 |  AESZ: 269  |  Superseeker: 549216 5134247872650720  |  Hash: f6285c6dd849b8edc6913a248c74c2ac  

Degree: 5

\(\theta^4+2^{4} 3^{2} x\left(11664\theta^4-15552\theta^3-11700\theta^2-3924\theta-781\right)+2^{13} 3^{8} x^{2}\left(9072\theta^4-41472\theta^3+2106\theta^2-54\theta+1261\right)-2^{20} 3^{14} x^{3}\left(44064\theta^4+31104\theta^3+67932\theta^2+32508\theta+9661\right)-2^{30} 3^{22} 5 x^{4}\left(108\theta^4+13\theta^2+13\theta-3\right)+2^{40} 3^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 112464, 16304096016, 2572332025515264, 423329707157060783376, ...
--> OEIS
Normalized instanton numbers (n0=1): 549216, -39437661960, 5134247872650720, -893529522332436373560, 182442495912657901797814560, ... ; Common denominator:...

Discriminant

\((1+186624z)(933120z+1)^2(186624z-1)^2\)

Local exponents

\(-\frac{ 1}{ 186624}\)\(-\frac{ 1}{ 933120}\)\(0\)\(\frac{ 1}{ 186624}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(\frac{ 3}{ 2}\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 268/5.60

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132

New Number: 5.62 |  AESZ: 270  |  Superseeker: -76/5 -2100  |  Hash: 256e3b3a92e3fd332be8b01f71853ea4  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(48\theta^4+192\theta^3+251\theta^2+155\theta+35\right)-2^{4} x^{2}\left(8704\theta^4+28672\theta^3+43664\theta^2+31760\theta+9265\right)+2^{11} x^{3}\left(1792\theta^4+15360\theta^3+36248\theta^2+33240\theta+10795\right)+2^{16} x^{4}\left(2304\theta^4+12288\theta^3+20816\theta^2+14672\theta+3719\right)+2^{30} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 28, 1324, 63856, 3489004, ...
--> OEIS
Normalized instanton numbers (n0=1): -76/5, 367/5, -2100, 43436, -6582256/5, ... ; Common denominator:...

Discriminant

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

Local exponents

\(-\frac{ 5}{ 64}\)\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 4}\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(\frac{ 5}{ 4}\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 271/ 5.63

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133

New Number: 5.63 |  AESZ: 271  |  Superseeker: 10912 71557619232  |  Hash: c20fda7ad02ecc06f9b3f74bf4327d05  

Degree: 5

\(\theta^4+2^{4} x\left(2304\theta^4-3072\theta^3-2224\theta^2-688\theta-121\right)+2^{17} x^{2}\left(1792\theta^4-8192\theta^3+920\theta^2+344\theta+235\right)-2^{28} x^{3}\left(8704\theta^4+6144\theta^3+9872\theta^2+4368\theta+1201\right)-2^{44} 5 x^{4}\left(48\theta^4-37\theta^2-37\theta-13\right)+2^{60} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 1936, 5433616, 17299986688, 58672579116304, ...
--> OEIS
Normalized instanton numbers (n0=1): 10912, -20731504, 71557619232, -326717237089712, 1743820693922321120, ... ; Common denominator:...

Discriminant

\((1+4096z)(20480z+1)^2(4096z-1)^2\)

Local exponents

\(-\frac{ 1}{ 4096}\)\(-\frac{ 1}{ 20480}\)\(0\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(-\frac{ 1}{ 4}\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(\frac{ 5}{ 4}\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 270 /5.62

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134

New Number: 5.64 |  AESZ: 272  |  Superseeker: 468/5 11885484  |  Hash: 467bb784f4bd6e978748e98f6ea4a573  

Degree: 5

\(5^{2} \theta^4-2^{2} 3 5 x\left(1332\theta^4+3528\theta^3+3289\theta^2+1525\theta+285\right)+2^{4} 3^{2} x^{2}\left(331776\theta^4+2602368\theta^3+4533336\theta^2+2996640\theta+724415\right)+2^{8} 3^{5} x^{3}\left(539136\theta^4+622080\theta^3-3024864\theta^2-4008960\theta-1315985\right)-2^{15} 3^{8} x^{4}\left(41472\theta^4+393984\theta^3+735984\theta^2+510912\theta+120811\right)-2^{20} 3^{11} x^{5}(12\theta+7)(12\theta+11)(12\theta+13)(12\theta+17)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 684, 761004, 985011120, 1373164693740, ...
--> OEIS
Normalized instanton numbers (n0=1): 468/5, -315477/5, 11885484, -14354122356/5, 808514230608, ... ; Common denominator:...

Discriminant

\(-(-1+432z)(1728z+5)^2(1728z-1)^2\)

Local exponents

\(-\frac{ 5}{ 1728}\)\(0\)\(\frac{ 1}{ 1728}\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 12}\)
\(1\)\(0\)\(-\frac{ 1}{ 6}\)\(1\)\(\frac{ 11}{ 12}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 13}{ 12}\)
\(4\)\(0\)\(\frac{ 7}{ 6}\)\(2\)\(\frac{ 17}{ 12}\)

Note:

This is operator "5.64" from ...

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135

New Number: 5.65 |  AESZ: 273  |  Superseeker: 63/5 14016/5  |  Hash: cf49bc645cb0404ce7bc9ca1d41d3152  

Degree: 5

\(5^{2} \theta^4-3 5 x\left(333\theta^4+882\theta^3+781\theta^2+340\theta+60\right)+2^{2} 3^{2} x^{2}\left(5184\theta^4+40662\theta^3+71829\theta^2+47700\theta+11540\right)+2^{2} 3^{5} x^{3}\left(8424\theta^4+9720\theta^3-46899\theta^2-63045\theta-21260\right)-2^{4} 3^{8} x^{4}\left(1296\theta^4+12312\theta^3+23094\theta^2+16263\theta+3956\right)-2^{6} 3^{11} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 2196, 161280, 13032900, ...
--> OEIS
Normalized instanton numbers (n0=1): 63/5, -747/4, 14016/5, -55584, 6071598/5, ... ; Common denominator:...

Discriminant

\(-(-1+27z)(108z+5)^2(108z-1)^2\)

Local exponents

\(-\frac{ 5}{ 108}\)\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(0\)\(\frac{ 1}{ 6}\)\(1\)\(\frac{ 5}{ 6}\)
\(3\)\(0\)\(\frac{ 5}{ 6}\)\(1\)\(\frac{ 7}{ 6}\)
\(4\)\(0\)\(1\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.65" from ...

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136

New Number: 5.66 |  AESZ: 274  |  Superseeker: 49/5 6032/15  |  Hash: 729d44a3b7b561b49603f26a25d26069  

Degree: 5

\(5^{2} \theta^4-5 x\left(757\theta^4+1298\theta^3+1049\theta^2+400\theta+60\right)+2^{2} 3^{2} x^{2}\left(5456\theta^4+17498\theta^3+22121\theta^2+11940\theta+2340\right)-2^{2} 3^{4} x^{3}\left(15128\theta^4+68040\theta^3+112171\theta^2+73845\theta+16380\right)+2^{4} 3^{8} x^{4}(2\theta+1)(216\theta^3+864\theta^2+1015\theta+356)-2^{6} 3^{10} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 324, 12000, 548100, ...
--> OEIS
Normalized instanton numbers (n0=1): 49/5, -68/5, 6032/15, 36276/5, 350082/5, ... ; Common denominator:...

Discriminant

\(-(81z-1)(1296z^2-56z+1)(-5+36z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I\)\(\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I\)\(\frac{ 5}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.66" from ...

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137

New Number: 5.67 |  AESZ: 275  |  Superseeker: 116/5 186172/5  |  Hash: f411d346afd4b8ff14b8b4c1836bae77  

Degree: 5

\(5^{2} \theta^4-2^{2} 5 x\left(592\theta^4+1568\theta^3+1419\theta^2+635\theta+115\right)+2^{4} x^{2}\left(65536\theta^4+514048\theta^3+902816\theta^2+598400\theta+144735\right)+2^{10} x^{3}\left(106496\theta^4+122880\theta^3-594816\theta^2-794880\theta-265065\right)-2^{19} x^{4}\left(8192\theta^4+77824\theta^3+145728\theta^2+102016\theta+24527\right)-2^{26} x^{5}(8\theta+5)(8\theta+7)(8\theta+9)(8\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 92, 14124, 2572400, 510577900, ...
--> OEIS
Normalized instanton numbers (n0=1): 116/5, -5993/5, 186172/5, -8039756/5, 384321296/5, ... ; Common denominator:...

Discriminant

\(-(-1+64z)(256z+5)^2(256z-1)^2\)

Local exponents

\(-\frac{ 5}{ 256}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 8}\)
\(1\)\(0\)\(0\)\(1\)\(\frac{ 7}{ 8}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 9}{ 8}\)
\(4\)\(0\)\(1\)\(2\)\(\frac{ 11}{ 8}\)

Note:

This is operator "5.67" from ...

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138

New Number: 5.68 |  AESZ: 279  |  Superseeker: -10/17 10  |  Hash: 06f80606fbeb2b0cc9559df633f1f59d  

Degree: 5

\(17^{2} \theta^4+17 x\left(286\theta^4+734\theta^3+656\theta^2+289\theta+51\right)+3^{2} x^{2}\left(4110\theta^4+22074\theta^3+37209\theta^2+26265\theta+6800\right)-3^{5} x^{3}\left(1521\theta^4+7344\theta^3+12936\theta^2+9945\theta+2822\right)+3^{8} x^{4}\left(123\theta^4+552\theta^3+879\theta^2+603\theta+152\right)-3^{12} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -3, 9, 51, -1431, ...
--> OEIS
Normalized instanton numbers (n0=1): -10/17, -19/17, 10, -369/17, -1413/17, ... ; Common denominator:...

Discriminant

\(-(729z^3-189z^2-20z-1)(-17+27z)^2\)

Local exponents

≈\(-0.044921-0.04372I\) ≈\(-0.044921+0.04372I\)\(0\) ≈\(0.349102\)\(\frac{ 17}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 280/5.69

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139

New Number: 5.69 |  AESZ: 280  |  Superseeker: -117 -844872  |  Hash: 5083c4e9f432302302c564ba554e3bcd  

Degree: 5

\(\theta^4-3^{2} x\left(123\theta^4-60\theta^3-39\theta^2-9\theta-1\right)+3^{5} x^{2}\left(1521\theta^4-1260\theta^3+30\theta^2-21\theta-10\right)-3^{8} x^{3}\left(4110\theta^4-5634\theta^3-4353\theta^2-1629\theta-220\right)-3^{12} 17 x^{4}\left(286\theta^4+410\theta^3+170\theta^2-35\theta-30\right)-3^{18} 17^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -9, 81, 1017, -93231, ...
--> OEIS
Normalized instanton numbers (n0=1): -117, -28899/4, -844872, -131189436, -23932952667, ... ; Common denominator:...

Discriminant

\(-(531441z^3+14580z^2+189z-1)(-1+459z)^2\)

Local exponents

≈\(-0.015682-0.015263I\) ≈\(-0.015682+0.015263I\)\(0\)\(\frac{ 1}{ 459}\) ≈\(0.003929\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 279/5.68

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140

New Number: 5.6 |  AESZ: 23  |  Superseeker: 4/3 44/3  |  Hash: 65760d446ba9c3da587ce5bd9912745e  

Degree: 5

\(3^{2} \theta^4-2^{2} 3 x\left(64\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+2^{7} x^{2}\left(194\theta^4+440\theta^3+527\theta^2+315\theta+75\right)-2^{12} x^{3}\left(94\theta^4+288\theta^3+397\theta^2+261\theta+66\right)+2^{17} x^{4}\left(22\theta^4+80\theta^3+117\theta^2+77\theta+19\right)-2^{23} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 104, 1664, 30376, ...
--> OEIS
Normalized instanton numbers (n0=1): 4/3, 13/3, 44/3, 278/3, 2336/3, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(1\)
\(0\)\(2\)\(1\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,corresponding to Operator AESZ 56/5.9
A-Incarnation: (2,0),(2.0),(0,2),(0,2),(1,1).intersection in $P^4 \times P^4$

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141

New Number: 5.70 |  AESZ: 287  |  Superseeker: 361/21 120472/21  |  Hash: 97932196c46a8712f6dcb11165d698be  

Degree: 5

\(3^{2} 7^{2} \theta^4-3 7 x\left(3289\theta^4+6098\theta^3+4645\theta^2+1596\theta+210\right)+2^{2} 5 x^{2}\left(7712\theta^4-46168\theta^3-106885\theta^2-67410\theta-13629\right)+2^{4} x^{3}\left(106636\theta^4+493416\theta^3+420211\theta^2+116361\theta+6090\right)-2^{8} 5 x^{4}(2\theta+1)(1916\theta^3+2622\theta^2+1077\theta+91)-2^{12} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 510, 38260, 3473470, ...
--> OEIS
Normalized instanton numbers (n0=1): 361/21, 4780/21, 120472/21, 1537864/7, 216261320/21, ... ; Common denominator:...

Discriminant

\(-(64z^3+800z^2+149z-1)(-21+80z)^2\)

Local exponents

≈\(-12.310784\) ≈\(-0.195701\)\(0\) ≈\(0.006485\)\(\frac{ 21}{ 80}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.70" from ...

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142

New Number: 5.71 |  AESZ: 290  |  Superseeker: 162 751026  |  Hash: 5552195a371df176b84ac2c2d791be7e  

Degree: 5

\(\theta^4+3 x\left(279\theta^4-252\theta^3-160\theta^2-34\theta-3\right)+2 3^{5} x^{2}\left(423\theta^4-468\theta^3+457\theta^2+215\theta+37\right)+2 3^{9} x^{3}\left(531\theta^4+1296\theta^3+1243\theta^2+567\theta+104\right)+3^{15} 5 x^{4}\left(51\theta^4+120\theta^3+126\theta^2+66\theta+14\right)+3^{20} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, -837, -32553, 4787019, ...
--> OEIS
Normalized instanton numbers (n0=1): 162, -8829, 751026, -163125009/2, 10343901204, ... ; Common denominator:...

Discriminant

\((27z+1)(19683z^2+1)(1+405z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(-\frac{ 1}{ 405}\)\(0-\frac{ 1}{ 243}\sqrt{ 3}I\)\(0\)\(0+\frac{ 1}{ 243}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 17/5.1

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143

New Number: 5.72 |  AESZ: 291  |  Superseeker: -28 -37768  |  Hash: cbc8242a8fecc72056e6e36b4864b868  

Degree: 5

\(\theta^4-x\left(566\theta^4+34\theta^3+62\theta^2+45\theta+9\right)+3 x^{2}\left(39370\theta^4+17302\theta^3+22493\theta^2+8369\theta+1140\right)-3^{2} x^{3}\left(1215215\theta^4+1432728\theta^3+1274122\theta^2+538245\theta+93222\right)+3^{7} 61 x^{4}\left(3029\theta^4+6544\theta^3+6135\theta^2+2863\theta+548\right)-3^{12} 61^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 9, 189, 3375, -159651, ...
--> OEIS
Normalized instanton numbers (n0=1): -28, -809, -37768, -2185213, -143204777, ... ; Common denominator:...

Discriminant

\(-(59049z^3-11421z^2+200z-1)(-1+183z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 183}\) ≈\(0.009423-0.002866I\) ≈\(0.009423+0.002866I\) ≈\(0.174569\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(4\)\(2\)\(2\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 124/5.18

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144

New Number: 5.73 |  AESZ: 293  |  Superseeker: 20 13188  |  Hash: f19eeaee48396d15d7cf7be47d7d48a7  

Degree: 5

\(\theta^4-2^{2} x\left(54\theta^4+66\theta^3+49\theta^2+16\theta+2\right)+2^{4} x^{2}\left(417\theta^4-306\theta^3-1219\theta^2-776\theta-154\right)+2^{8} x^{3}\left(166\theta^4+1920\theta^3+1589\theta^2+432\theta+23\right)-2^{12} 7 x^{4}(2\theta+1)(38\theta^3+45\theta^2+12\theta-2)-2^{14} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 528, 45440, 4763920, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 867/2, 13188, 609734, 35512476, ... ; Common denominator:...

Discriminant

\(-(16z+1)(256z^2+176z-1)(-1+28z)^2\)

Local exponents

\(-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}\)\(-\frac{ 1}{ 16}\)\(0\)\(-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 28}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.73" from ...

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145

New Number: 5.74 |  AESZ: 297  |  Superseeker: 26/7 55644/7  |  Hash: cd0b6008fa6b70d89e004100b5698063  

Degree: 5

\(7^{2} \theta^4-2 7 x\theta(520\theta^3+68\theta^2+41\theta+7)-2^{2} 3 x^{2}\left(9480\theta^4+153912\theta^3+212893\theta^2+108080\theta+18816\right)+2^{4} 3^{3} 7 x^{3}\left(13424\theta^4+48792\theta^3+45656\theta^2+17979\theta+2606\right)-2^{6} 3^{7} x^{4}(2\theta+1)^2(2257\theta^2+3601\theta+1942)+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 288, 7200, 1058400, ...
--> OEIS
Normalized instanton numbers (n0=1): 26/7, 2594/7, 55644/7, 2996576/7, 135364470/7, ... ; Common denominator:...

Discriminant

\((128z-1)(432z^2-72z-1)(-7+324z)^2\)

Local exponents

\(\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 7}{ 324}\)\(\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.74" from ...

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146

New Number: 5.75 |  AESZ: 298  |  Superseeker: 205/9 97622/9  |  Hash: e52d50673ec5c795512e2bc3e1017b12  

Degree: 5

\(3^{4} \theta^4-3^{2} x\left(1993\theta^4+3218\theta^3+2437\theta^2+828\theta+108\right)+2^{5} x^{2}\left(17486\theta^4+25184\theta^3+12239\theta^2+2790\theta+297\right)-2^{8} x^{3}\left(23620\theta^4+34776\theta^3+28905\theta^2+12447\theta+2106\right)+2^{15} x^{4}(2\theta+1)(340\theta^3+618\theta^2+455\theta+129)-2^{22} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 708, 63840, 6989220, ...
--> OEIS
Normalized instanton numbers (n0=1): 205/9, 3206/9, 97622/9, 496806, 254037095/9, ... ; Common denominator:...

Discriminant

\(-(z-1)(1024z^2-192z+1)(-9+128z)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 32}-\frac{ 1}{ 16}\sqrt{ 2}\)\(\frac{ 9}{ 128}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 16}\sqrt{ 2}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.75" from ...

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147

New Number: 5.76 |  AESZ: 306  |  Superseeker: 73/3 11119  |  Hash: d14307aa38b16c728ee31e5936937c44  

Degree: 5

\(3^{2} \theta^4-3 x\left(592\theta^4+1100\theta^3+829\theta^2+279\theta+36\right)+x^{2}\left(13801\theta^4+6652\theta^3-18041\theta^2-14904\theta-3312\right)-2 x^{3}\theta(8461\theta^3-29160\theta^2-28365\theta-7236)-2^{2} 3 7 x^{4}\left(513\theta^4+864\theta^3+487\theta^2+64\theta-16\right)-2^{3} 3 7^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 732, 67080, 7456140, ...
--> OEIS
Normalized instanton numbers (n0=1): 73/3, 2131/6, 11119, 518671, 29749701, ... ; Common denominator:...

Discriminant

\(-(z+1)(54z^2+189z-1)(-3+14z)^2\)

Local exponents

\(-\frac{ 7}{ 4}-\frac{ 11}{ 36}\sqrt{ 33}\)\(-1\)\(0\)\(-\frac{ 7}{ 4}+\frac{ 11}{ 36}\sqrt{ 33}\)\(\frac{ 3}{ 14}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.76" from ...

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148

New Number: 5.77 |  AESZ: 307  |  Superseeker: 69/11 8883/11  |  Hash: 3a2dcd4c59d8fa5b7c57250efeecba62  

Degree: 5

\(11^{2} \theta^4-3 11 x\left(361\theta^4+530\theta^3+419\theta^2+154\theta+22\right)+2^{2} x^{2}\left(47008\theta^4+45904\theta^3-3251\theta^2-17094\theta-4851\right)-2^{4} 3 x^{3}\left(31436\theta^4+86856\theta^3+160363\theta^2+122133\theta+30294\right)+2^{9} 3^{2} x^{4}(2\theta+1)(1252\theta^3+5442\theta^2+6767\theta+2625)-2^{14} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 162, 6540, 314370, ...
--> OEIS
Normalized instanton numbers (n0=1): 69/11, 620/11, 8883/11, 171916/11, 4334406/11, ... ; Common denominator:...

Discriminant

\(-(81z-1)(64z^2+1)(-11+96z)^2\)

Local exponents

\(0-\frac{ 1}{ 8}I\)\(0\)\(0+\frac{ 1}{ 8}I\)\(\frac{ 1}{ 81}\)\(\frac{ 11}{ 96}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.77" from ...

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149

New Number: 5.78 |  AESZ: 308  |  Superseeker: 248/29 38708/29  |  Hash: 94e96c5d238b2d22a633f4e05ec1ae9f  

Degree: 5

\(29^{2} \theta^4-2 29 x\left(1318\theta^4+2336\theta^3+1806\theta^2+638\theta+87\right)-2^{2} x^{2}\left(90996\theta^4+744384\theta^3+1267526\theta^2+791584\theta+168345\right)+2^{2} 5^{2} x^{3}\left(34172\theta^4+77256\theta^3-46701\theta^2-110403\theta-36540\right)+2^{4} 5^{4} x^{4}(2\theta+1)(68\theta^3+1842\theta^2+2899\theta+1215)-2^{6} 5^{7} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 6, 210, 9780, 551250, ...
--> OEIS
Normalized instanton numbers (n0=1): 248/29, 2476/29, 38708/29, 940480/29, 27926248/29, ... ; Common denominator:...

Discriminant

\(-(2000z^3+1024z^2+84z-1)(-29+100z)^2\)

Local exponents

≈\(-0.40534\) ≈\(-0.117186\)\(0\) ≈\(0.010526\)\(\frac{ 29}{ 100}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.78" from ...

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150

New Number: 5.79 |  AESZ: 310  |  Superseeker: 181/11 47171/11  |  Hash: 2b9b103b1c8f0d3175cd1fb9ef5aacc2  

Degree: 5

\(11^{2} \theta^4-11 x\left(1673\theta^4+3046\theta^3+2337\theta^2+814\theta+110\right)+2 5 x^{2}\left(19247\theta^4+28298\theta^3+13285\theta^2+3454\theta+660\right)-2^{2} x^{3}\left(167497\theta^4+245982\theta^3+227451\theta^2+115434\theta+22968\right)+2^{3} 5^{2} x^{4}\left(4079\theta^4+10270\theta^3+11427\theta^2+6226\theta+1340\right)-2^{5} 5^{4} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

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Coefficients of the holomorphic solution: 1, 10, 450, 30772, 2551810, ...
--> OEIS
Normalized instanton numbers (n0=1): 181/11, 2018/11, 47171/11, 3261479/22, 69313270/11, ... ; Common denominator:...

Discriminant

\(-(z-1)(128z^2-142z+1)(-11+50z)^2\)

Local exponents

\(0\)\(\frac{ 71}{ 128}-\frac{ 17}{ 128}\sqrt{ 17}\)\(\frac{ 11}{ 50}\)\(1\)\(\frac{ 71}{ 128}+\frac{ 17}{ 128}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.79" from ...

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