Summary

You searched for: Spectrum0=1/2,3/4,5/4,3/2

Your search produced 10 matches

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1

New Number: 2.60 |  AESZ: 18  |  Superseeker: 4 364  |  Hash: bb479f8a4185bf4a943dba2d433e13e5  

Degree: 2

\(\theta^4-2^{2} x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{4} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 4, 108, 3280, 126700, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 39, 364, 6800, 662416/5, ... ; Common denominator:...

Discriminant

\(-(16z+1)(64z-1)\)

Local exponents

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

Note:

A-Incarnation: (1,1) and (2,2) intersection in $P^3 \times P^3$

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2

New Number: 2.65 |  AESZ: 183  |  Superseeker: -4 -556/9  |  Hash: 04a3788c3f9ed53281ae824deb33d833  

Degree: 2

\(\theta^4+2^{2} x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{4} 3 x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 324, -11280, 447300, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, 8, -556/9, 624, -8928, ... ; Common denominator:...

Discriminant

\((48z+1)(64z+1)\)

Local exponents

\(-\frac{ 1}{ 48}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(0\)\(\frac{ 5}{ 4}\)
\(2\)\(2\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "2.65" from ...

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3

New Number: 5.13 |  AESZ: 83  |  Superseeker: -80 -174096  |  Hash: 171e1251d8e4f7de878d0d07de6f58ab  

Degree: 5

\(\theta^4-2^{4} x\left(88\theta^4+32\theta^3+33\theta^2+17\theta+3\right)+2^{9} x^{2}\left(1504\theta^4+1408\theta^3+1436\theta^2+596\theta+93\right)-2^{18} x^{3}\left(776\theta^4+1344\theta^3+1381\theta^2+651\theta+117\right)+2^{23} 3 x^{4}(2\theta+1)(512\theta^3+1152\theta^2+1054\theta+339)-2^{31} 3^{2} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 5328, 779520, 131619600, ...
--> OEIS
Normalized instanton numbers (n0=1): -80, -2954, -174096, -13270953, -1179175536, ... ; Common denominator:...

Discriminant

\(-(128z-1)(384z-1)^2(256z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 384}\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(4\)\(1\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.13" from ...

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4

New Number: 5.14 |  AESZ: 116  |  Superseeker: 64 23360  |  Hash: 0b366ad8c78b6697205c5a7fff270f5b  

Degree: 5

\(\theta^4-2^{5} x\left(10\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(52\theta^4+472\theta^3+832\theta^2+492\theta+103\right)+2^{16} x^{3}\left(14\theta^4+12\theta^3-96\theta^2-105\theta-29\right)-2^{18} x^{4}(2\theta+1)(56\theta^3+468\theta^2+646\theta+249)-2^{24} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 32, 2448, 273920, 38525200, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, 12, 23360, 654490, 53956288, ... ; Common denominator:...

Discriminant

\(-(-1+256z)(32z+1)^2(64z-1)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 4}\)
\(3\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 4}\)
\(4\)\(0\)\(2\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.14" from ...

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5

New Number: 5.44 |  AESZ: 240  |  Superseeker: 231/13 38037/13  |  Hash: 8f46cd6968b3b676e251a9d8635637fc  

Degree: 5

\(13^{2} \theta^4-13 x\left(1449\theta^4+4050\theta^3+3143\theta^2+1118\theta+156\right)-2^{4} x^{2}\left(22760\theta^4-27112\theta^3-121046\theta^2-82316\theta-17589\right)+2^{8} x^{3}\left(3824\theta^4+39936\theta^3-34292\theta^2-63492\theta-19539\right)-2^{16} 3 x^{4}(2\theta+1)(40\theta^3+684\theta^2+1013\theta+399)-2^{20} 3^{2} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 468, 28560, 2135700, ...
--> OEIS
Normalized instanton numbers (n0=1): 231/13, 826/13, 38037/13, 786076/13, 32662752/13, ... ; Common denominator:...

Discriminant

\(-(128z-1)(128z^2-13z+1)(13+192z)^2\)

Local exponents

\(-\frac{ 13}{ 192}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.44" from ...

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6

New Number: 5.88 |  AESZ: 324  |  Superseeker: 148/11 44108/11  |  Hash: 7f84d776cf00ff399b20865542185f87  

Degree: 5

\(11^{2} \theta^4-2^{2} 11 x\left(432\theta^4+624\theta^3+477\theta^2+165\theta+22\right)+2^{5} x^{2}\left(12944\theta^4+4736\theta^3-15491\theta^2-12914\theta-2860\right)-2^{4} 5 x^{3}\left(10688\theta^4-114048\theta^3-159132\theta^2-83028\theta-15455\right)-2^{11} 5^{2} x^{4}(2\theta+1)(4\theta+3)(76\theta^2+189\theta+125)+2^{14} 5^{3} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 360, 23120, 1796200, ...
--> OEIS
Normalized instanton numbers (n0=1): 148/11, 2044/11, 44108/11, 1459636/11, 60212712/11, ... ; Common denominator:...

Discriminant

\((5120z^3-512z^2-128z+1)(-11+160z)^2\)

Local exponents

≈\(-0.120643\)\(0\) ≈\(0.007599\)\(\frac{ 11}{ 160}\) ≈\(0.213044\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.88" from ...

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7

New Number: 5.92 |  AESZ: 332  |  Superseeker: -16/3 208/3  |  Hash: f788b099648b78746af9d38e85874401  

Degree: 5

\(3^{2} \theta^4+2^{2} 3 x\left(67\theta^4+122\theta^3+100\theta^2+39\theta+6\right)+2^{5} x^{2}\left(1172\theta^4+4298\theta^3+5831\theta^2+3315\theta+678\right)+2^{8} x^{3}\left(3021\theta^4+15912\theta^3+29314\theta^2+20925\theta+4926\right)+2^{11} x^{4}(2\theta+1)(826\theta^3+3543\theta^2+4321\theta+1594)+2^{16} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 72, 640, -51800, ...
--> OEIS
Normalized instanton numbers (n0=1): -16/3, -257/6, 208/3, 10444/3, -116608/3, ... ; Common denominator:...

Discriminant

\((32z+1)(2048z^2+52z+1)(8z+3)^2\)

Local exponents

\(-\frac{ 3}{ 8}\)\(-\frac{ 1}{ 32}\)\(-\frac{ 13}{ 1024}-\frac{ 7}{ 1024}\sqrt{ 7}I\)\(-\frac{ 13}{ 1024}+\frac{ 7}{ 1024}\sqrt{ 7}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 3}{ 4}\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(\frac{ 5}{ 4}\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.92" from ...

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8

New Number: 8.78 |  AESZ:  |  Superseeker: 52 48732  |  Hash: 2fb524ad6efb19e0117ae7acbd9f67b9  

Degree: 8

\(\theta^4-2^{2} x\left(184\theta^4+224\theta^3+175\theta^2+63\theta+9\right)+2^{4} 3 x^{2}\left(3472\theta^4+9664\theta^3+9864\theta^2+4264\theta+705\right)-2^{8} 3^{2} x^{3}\left(1936\theta^4+27936\theta^3+43336\theta^2+21528\theta+3933\right)-2^{16} 3^{3} x^{4}\left(1384\theta^4+524\theta^3-4555\theta^2-3404\theta-753\right)+2^{19} 3^{4} x^{5}\left(3440\theta^4+13712\theta^3-58\theta^2-3774\theta-1161\right)+2^{22} 3^{5} x^{6}\left(11312\theta^4-9888\theta^3-10808\theta^2-1608\theta+459\right)-2^{26} 3^{7} x^{7}(2\theta+1)(1336\theta^3+2772\theta^2+2234\theta+663)-2^{32} 3^{9} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 555120, 95199300, ...
--> OEIS
Normalized instanton numbers (n0=1): 52, -399, 48732, -992750, 98106208, ... ; Common denominator:...

Discriminant

\(-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2\)

Local exponents

≈\(-0.091906\)\(-\frac{ 1}{ 288}-\frac{ 1}{ 288}\sqrt{ 7}\)\(0\) ≈\(0.00385\)\(\frac{ 1}{ 256}\)\(-\frac{ 1}{ 288}+\frac{ 1}{ 288}\sqrt{ 7}\) ≈\(0.025556\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "8.78" from ...

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9

New Number: 2.71 |  AESZ:  |  Superseeker: 0 0  |  Hash: 757b011780c5986bd45a5bf434c76c28  

Degree: 2

\(\theta^4-2^{5} x(2\theta+1)^2(2\theta^2+2\theta+1)+2^{8} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 32, 2160, 181760, 17021200, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, -20, 0, -865, 0, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 3}{ 4}\)
\(0\)\(\frac{ 3}{ 4}\)\(\frac{ 5}{ 4}\)
\(0\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator is equivalent to [2.33]. Transformation:.....

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10

New Number: 8.88 |  AESZ:  |  Superseeker: 571/15 394769/15  |  Hash: 96ea6b0b71373481f874100af7f89d67  

Degree: 8

\(3^{2} 5^{2} \theta^4-3 5 x\left(4063\theta^4+7682\theta^3+5731\theta^2+1890\theta+240\right)+2 x^{2}\left(605228\theta^4+1651274\theta^3+1743713\theta^2+827790\theta+149520\right)-2^{2} x^{3}\left(122453\theta^4+9232248\theta^3+20066474\theta^2+11895930\theta+2347980\right)-2^{3} x^{4}\left(14154736\theta^4-3374404\theta^3-69996921\theta^2-57156850\theta-13566428\right)+2^{4} x^{5}\left(30476536\theta^4+168961384\theta^3-11782973\theta^2-90041748\theta-28710648\right)+2^{6} 23 x^{6}\left(1194624\theta^4-7988712\theta^3-9497764\theta^2-3726021\theta-451296\right)-2^{8} 7 23^{2} x^{7}(2\theta+1)(8454\theta^3+5577\theta^2-4303\theta-3155)+2^{10} 7^{2} 23^{3} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1224, 146320, 21334600, ...
--> OEIS
Normalized instanton numbers (n0=1): 571/15, 3038/5, 394769/15, 23541584/15, 352406944/3, ... ; Common denominator:...

Discriminant

\((1-261z+2952z^2-12368z^3+23552z^4)(-15+74z+1288z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_3\)\(s_2\)\(s_5\)\(s_4\)\(s_6\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(3\)\(1\)\(3\)\(1\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(4\)\(2\)\(4\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "8.88" from ...

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