Summary

You searched for: sol=68

1

New Number: 3.14 |  AESZ:  |  Superseeker: 444 19050964  |  Hash: dc96aa2da269d989ee90c49dab6a9c5a

Degree: 3

$\theta^4-2^{2} x\left(452\theta^4+920\theta^3+633\theta^2+173\theta+17\right)-2^{4} x^{2}(4\theta+3)(3808\theta^3+10504\theta^2+8884\theta+1635)-2^{8} 11^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

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Coefficients of the holomorphic solution: 1, 68, 42220, 38866320, 43812369900, ...
--> OEIS
Normalized instanton numbers (n0=1): 444, 57104, 19050964, 9432910668, 5781274591408, ... ; Common denominator:...

Discriminant

$-(1936z-1)(1+64z)^2$

Local exponents

$-\frac{ 1}{ 64}$$0$$\frac{ 1}{ 1936}$$\infty$
$0$$0$$0$$\frac{ 1}{ 4}$
$\frac{ 1}{ 2}$$0$$1$$\frac{ 3}{ 4}$
$1$$0$$1$$\frac{ 7}{ 4}$
$\frac{ 3}{ 2}$$0$$2$$\frac{ 9}{ 4}$

Note:

This is operator Pi = 3.14 (approx.), equivalent to AESZ 238.

2

New Number: 7.19 |  AESZ:  |  Superseeker: 4/3 -124/81  |  Hash: f7f0f5d883101c38ed22cb74c80c8f5c

Degree: 7

$3^{3} \theta^4-2^{2} 3^{2} x\left(12\theta^4-16\theta^3-21\theta^2-13\theta-3\right)-2^{4} 3 x^{2}\left(240\theta^4+1280\theta^3+2068\theta^2+1636\theta+489\right)+2^{10} x^{3}\left(212\theta^4+592\theta^3+490\theta^2-34\theta-129\right)+2^{13} x^{4}\left(72\theta^4+1536\theta^3+4804\theta^2+5468\theta+2031\right)-2^{18} x^{5}\left(100\theta^4+720\theta^3+1535\theta^2+1155\theta+276\right)+2^{20} x^{6}\left(144\theta^4+768\theta^3+1268\theta^2+884\theta+229\right)-2^{28} x^{7}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, -4, 68, -496, 9796, ...
--> OEIS
Normalized instanton numbers (n0=1): 4/3, -14/9, -124/81, -4498/243, 37024/729, ... ; Common denominator:...

Discriminant

$-(16z-1)^2(16z+1)^2(16z-3)^3$

Local exponents

$-\frac{ 1}{ 16}$$0$$\frac{ 1}{ 16}$$\frac{ 3}{ 16}$$\infty$
$0$$0$$0$$0$$1$
$0$$0$$\frac{ 1}{ 2}$$2$$1$
$1$$0$$\frac{ 1}{ 2}$$3$$1$
$1$$0$$1$$5$$1$

Note:

This is operator "7.19" from ...

3

New Number: 8.18 |  AESZ: 197  |  Superseeker: 3 1621/13  |  Hash: 4cc8bdba73e5fa6cb4089fa5296429de

Degree: 8

$13^{2} \theta^4-13^{2} x\left(41\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-2^{3} 13 x^{2}\left(471\theta^4+1788\theta^3+2555\theta^2+1534\theta+338\right)+2^{6} 13 x^{3}\left(251\theta^4+1014\theta^3+1798\theta^2+1413\theta+405\right)+2^{9} x^{4}\left(749\theta^4+436\theta^3-4908\theta^2-6266\theta-2145\right)-2^{12} x^{5}\left(379\theta^4+1270\theta^3+967\theta^2-42\theta-178\right)-2^{15} x^{6}\left(9\theta^4-156\theta^3-273\theta^2-156\theta-28\right)+2^{18} x^{7}\left(13\theta^4+26\theta^3+20\theta^2+7\theta+1\right)-2^{21} x^{8}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 4, 68, 1552, 43156, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 226/13, 1621/13, 20666/13, 289056/13, ... ; Common denominator:...

Discriminant

$-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2$

Local exponents

$-\frac{ 1}{ 8}\sqrt{ 13}$$-\frac{ 1}{ 8}$$0$$\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}$$\frac{ 1}{ 8}\sqrt{ 13}$$\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}$$1$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$0$$1$$1$$1$$1$$1$
$3$$1$$0$$1$$3$$1$$1$$1$
$4$$2$$0$$2$$4$$2$$2$$1$

Note:

The operator has a second MUM-point at infinity, corresponding to operator 8.19.