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You searched for: inst=237/2

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1

New Number: 12.14 |  AESZ:  |  Superseeker: 7/2 237/2  |  Hash: 614b95fc4275078df0800c7546870e7f  

Degree: 12

\(2^{2} \theta^4+2 x\left(74\theta^4+22\theta^3+77\theta^2+66\theta+18\right)+3^{2} x^{2}\left(97\theta^4+1206\theta^3+2235\theta^2+1750\theta+642\right)+3^{4} x^{3}\left(126\theta^4+3910\theta^3+7341\theta^2+8588\theta+3750\right)+3^{6} x^{4}\left(832\theta^4+6078\theta^3+26372\theta^2+37719\theta+21825\right)+3^{8} x^{5}\left(442\theta^4+12544\theta^3+62654\theta^2+116087\theta+78828\right)-3^{10} x^{6}\left(1032\theta^4-5126\theta^3-73629\theta^2-192529\theta-165306\right)-2 3^{12} x^{7}\left(1432\theta^4+11737\theta^3+11907\theta^2-41634\theta-71496\right)-3^{14} x^{8}\left(1871\theta^4+35422\theta^3+145979\theta^2+220752\theta+99504\right)+2 3^{17} x^{9}\left(151\theta^4-2094\theta^3-20341\theta^2-54972\theta-48672\right)+2^{3} 3^{19} x^{10}(\theta+3)(86\theta^3+414\theta^2+181\theta-936)+2^{3} 3^{22} x^{11}(\theta+4)(\theta+3)(21\theta^2+137\theta+224)+2^{4} 3^{24} x^{12}(\theta+3)(\theta+5)(\theta+4)^2\)

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Coefficients of the holomorphic solution: 1, -9, -18, 747, -5751, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...

Discriminant

\((9z+1)(z+1)(324z^2-18z+1)(81z^2+9z+1)^2(486z^2-27z-2)^2\)

Local exponents

\(-1\)\(-\frac{ 1}{ 9}\)\(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 3}I\)\(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 3}I\)\(\frac{ 1}{ 36}-\frac{ 1}{ 108}\sqrt{ 57}\)\(0\)\(\frac{ 1}{ 36}-\frac{ 1}{ 36}\sqrt{ 3}I\)\(\frac{ 1}{ 36}+\frac{ 1}{ 36}\sqrt{ 3}I\)\(\frac{ 1}{ 36}+\frac{ 1}{ 108}\sqrt{ 57}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(3\)
\(1\)\(1\)\(0\)\(0\)\(1\)\(0\)\(1\)\(1\)\(1\)\(4\)
\(1\)\(1\)\(-1\)\(-1\)\(3\)\(0\)\(1\)\(1\)\(3\)\(4\)
\(2\)\(2\)\(1\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(5\)

Note:

This is operator "12.14" from ...

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2

New Number: 15.1 |  AESZ:  |  Superseeker: 7/2 237/2  |  Hash: df146e1b37d7a257f905c6707b923620  

Degree: 15

\(2^{2} 5^{30} \theta^4-2 5^{28} x\left(3640\theta^4+11006\theta^3+13879\theta^2+8376\theta+1980\right)+3^{2} 5^{26} x^{2}\left(538345\theta^4+4434106\theta^3+9865547\theta^2+10318472\theta+4308060\right)-3^{4} 5^{24} x^{3}\left(6742465\theta^4+323187588\theta^3+1293374270\theta^2+2006832192\theta+1174440960\right)-3^{7} 5^{22} x^{4}\left(526873995\theta^4-1668961078\theta^3-24223747379\theta^2-58879161136\theta-47787749580\right)+3^{8} 5^{20} x^{5}\left(112183726219\theta^4+702881575498\theta^3-655695079267\theta^2-6796301255992\theta-8645676874410\right)-3^{10} 5^{18} x^{6}\left(2728176480430\theta^4+50098509218682\theta^3+140700841079393\theta^2+45277394357802\theta-187513884611415\right)-3^{12} 5^{16} x^{7}\left(34762414267630\theta^4-1334642903889766\theta^3-8286651788306957\theta^2-15990739837380612\theta-8287376192342010\right)+3^{15} 5^{14} x^{8}\left(1629579653924345\theta^4+954388085050194\theta^3-55618872802839705\theta^2-207693840516161754\theta-214442659712419520\right)-3^{17} 5^{12} x^{9}\left(65369060331963795\theta^4+512595644471686042\theta^3+992825405643594911\theta^2-1201538784520100286\theta-4009291166039086080\right)+3^{20} 5^{10} x^{10}\left(534261782717034863\theta^4+6643553399420804992\theta^3+30007608488826895812\theta^2+55818610344670779952\theta+32009410686899411085\right)-3^{22} 5^{8} x^{11}\left(8440215529571954655\theta^4+138165063547130806682\theta^3+847930452008770373373\theta^2+2305208800672476166582\theta+2332526675705017692360\right)+2^{2} 3^{25} 5^{6} x^{12}(\theta+5)(6822457746356194860\theta^3+105594221828043028718\theta^2+542119266560031019991\theta+926555809752183305931)-2^{2} 3^{27} 5^{4} x^{13}(\theta+5)(\theta+6)(15337273149232082245\theta^2+289665397258229241319\theta+1092956642701689252996)-2^{5} 3^{30} 5^{2} 7 163 4447 x^{14}(\theta+5)(\theta+6)(\theta+7)(4612345059685\theta+22748051972446)+2^{12} 3^{33} 7^{2} 17 163^{2} 1213 4447^{2} x^{15}(\theta+5)(\theta+6)(\theta+7)(\theta+8)\)

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Coefficients of the holomorphic solution: 1, 198/5, 119412/125, 59226669/3125, 27037427724/78125, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/2, -193/8, 237/2, -6119/4, 16307, ... ; Common denominator:...

Discriminant

\((128z-25)(72z+25)(153z-25)(294759z^2-18900z+625)(378z-25)^2(39609z^2-2025z+625)^2(360207z^2-1575z-1250)^2\)

Local exponents

\(-\frac{ 25}{ 72}\)\(\frac{ 175}{ 80046}-\frac{ 625}{ 80046}\sqrt{ 57}\)\(0\)\(\frac{ 25}{ 978}-\frac{ 625}{ 8802}\sqrt{ 3}I\)\(\frac{ 25}{ 978}+\frac{ 625}{ 8802}\sqrt{ 3}I\)\(\frac{ 350}{ 10917}-\frac{ 625}{ 32751}\sqrt{ 3}I\)\(\frac{ 350}{ 10917}+\frac{ 625}{ 32751}\sqrt{ 3}I\)\(\frac{ 175}{ 80046}+\frac{ 625}{ 80046}\sqrt{ 57}\)\(\frac{ 25}{ 378}\)\(\frac{ 25}{ 153}\)\(\frac{ 25}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(5\)
\(1\)\(1\)\(0\)\(0\)\(0\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(6\)
\(1\)\(3\)\(0\)\(-1\)\(-1\)\(1\)\(1\)\(3\)\(1\)\(1\)\(1\)\(7\)
\(2\)\(4\)\(0\)\(1\)\(1\)\(2\)\(2\)\(4\)\(-2\)\(2\)\(2\)\(8\)

Note:

This is operator "15.1" from ...

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