Summary

You searched for: Spectrum0=0,1,1,2

Your search produced 482 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 
 361-390  391-420  421-450  451-480  481-482 

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211

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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212

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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213

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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214

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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215

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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216

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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217

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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218

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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219

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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220

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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221

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

Degree: 5

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

Maple   LaTex

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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222

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

Degree: 5

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

Maple   LaTex

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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223

New Number: 5.7 |  AESZ: 27  |  Superseeker: 14/3 910/3  |  Hash: 3671a1760894e9030e36de89070612e8  

Degree: 5

\(3^{2} \theta^4-3 x\left(173\theta^4+340\theta^3+272\theta^2+102\theta+15\right)-2 x^{2}\left(1129\theta^4+5032\theta^3+7597\theta^2+4773\theta+1083\right)+2 x^{3}\left(843\theta^4+2628\theta^3+2353\theta^2+675\theta+6\right)-x^{4}\left(295\theta^4+608\theta^3+478\theta^2+174\theta+26\right)+x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 109, 3317, 121501, ...
--> OEIS
Normalized instanton numbers (n0=1): 14/3, 175/6, 910/3, 14147/3, 265496/3, ... ; Common denominator:...

Discriminant

\((z^3-289z^2-57z+1)(z-3)^2\)

Local exponents

≈\(-0.213297\)\(0\) ≈\(0.016211\)\(3\) ≈\(289.197085\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

A-incarnation: X(1,1,1,1,1,1,1) in G(2,7)
There is a second MUM point at infinity related to
the Pfaffian in P^7, AESZ 243/5.46

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224

New Number: 5.80 |  AESZ: 311  |  Superseeker: 25/13 875/13  |  Hash: 8219f3f4bd56f6c2b2cc3ab9093b65d1  

Degree: 5

\(13^{2} \theta^4-13 x\left(327\theta^4+1038\theta^3+857\theta^2+338\theta+52\right)-2^{4} x^{2}\left(12848\theta^4+42008\theta^3+52082\theta^2+28548\theta+5707\right)-2^{11} x^{3}\left(122\theta^4-1872\theta^3-6341\theta^2-5772\theta-1547\right)+2^{16} x^{4}(2\theta+1)(76\theta^3+426\theta^2+570\theta+227)+2^{23} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 84, 1840, 56980, ...
--> OEIS
Normalized instanton numbers (n0=1): 25/13, 1359/52, 875/13, 36572/13, 256800/13, ... ; Common denominator:...

Discriminant

\((8192z^3-896z^2-35z+1)(13+64z)^2\)

Local exponents

\(-\frac{ 13}{ 64}\) ≈\(-0.045147\)\(0\) ≈\(0.020117\) ≈\(0.134405\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.80" from ...

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225

New Number: 5.81 |  AESZ: 312  |  Superseeker: 5/7 48/7  |  Hash: 767262575f8b1458839c1e9a8beacf0a  

Degree: 5

\(7^{2} \theta^4-7 x\left(39\theta^4+234\theta^3+201\theta^2+84\theta+14\right)-2 x^{2}\left(12073\theta^4+43222\theta^3+57461\theta^2+34328\theta+7756\right)-2^{2} x^{3}\left(28923\theta^4+48426\theta^3-33393\theta^2-80976\theta-32032\right)+2^{3} 13 x^{4}\left(359\theta^4+9790\theta^3+20805\theta^2+15784\theta+4124\right)+2^{5} 3 13^{2} x^{5}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2, 30, 308, 5950, ...
--> OEIS
Normalized instanton numbers (n0=1): 5/7, 239/28, 48/7, 4451/14, 5888/7, ... ; Common denominator:...

Discriminant

\((16z+1)(2z-1)(27z-1)(7+26z)^2\)

Local exponents

\(-\frac{ 7}{ 26}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 7}{ 6}\)

Note:

This is operator "5.81" from ...

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226

New Number: 5.82 |  AESZ: 313  |  Superseeker: 45 43531  |  Hash: f8bfe82988e14680bdb775a3ce956216  

Degree: 5

\(\theta^4-x(\theta+1)(285\theta^3+321\theta^2+128\theta+18)-2 x^{2}\left(1640\theta^4+1322\theta^3-1337\theta^2-1178\theta-240\right)-2^{2} 3^{2} x^{3}\left(213\theta^4-256\theta^3-286\theta^2-80\theta-5\right)+2^{3} 3^{3} x^{4}(2\theta+1)(22\theta^3+37\theta^2+24\theta+6)+2^{4} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1662, 236340, 40943070, ...
--> OEIS
Normalized instanton numbers (n0=1): 45, 845, 43531, 3091112, 273471538, ... ; Common denominator:...

Discriminant

\((z-1)(48z^2+296z-1)(6z+1)^2\)

Local exponents

\(-\frac{ 37}{ 12}-\frac{ 7}{ 6}\sqrt{ 7}\)\(-\frac{ 1}{ 6}\)\(0\)\(-\frac{ 37}{ 12}+\frac{ 7}{ 6}\sqrt{ 7}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.82" from ...

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227

New Number: 5.83 |  AESZ: 316  |  Superseeker: 852/11 1678156/11  |  Hash: b8201d587a016cc013e2477aadb5c1ff  

Degree: 5

\(11^{2} \theta^4-2^{2} 3 11 x\left(364\theta^4+824\theta^3+599\theta^2+187\theta+22\right)-2^{5} x^{2}\left(62164\theta^4+84496\theta^3+12499\theta^2-6402\theta-1584\right)-2^{4} 3 x^{3}\left(484016\theta^4+474144\theta^3+366952\theta^2+161832\theta+27027\right)-2^{11} 3^{2} x^{4}(964\theta^2+1360\theta+669)(2\theta+1)^2-2^{16} 3^{4} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 3240, 675600, 171901800, ...
--> OEIS
Normalized instanton numbers (n0=1): 852/11, 21572/11, 1678156/11, 15912512, 22956446184/11, ... ; Common denominator:...

Discriminant

\(-(2304z^3+1664z^2+432z-1)(11+192z)^2\)

Local exponents

≈\(-0.362258-0.240689I\) ≈\(-0.362258+0.240689I\)\(-\frac{ 11}{ 192}\)\(0\) ≈\(0.002294\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.83" from ...

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228

New Number: 5.84 |  AESZ: 318  |  Superseeker: 46/5 1126  |  Hash: 3fa38f629ecd5f39b585ce0c1bd88463  

Degree: 5

\(5^{2} \theta^4-5 x\left(473\theta^4+892\theta^3+696\theta^2+250\theta+35\right)+2 x^{2}\left(1973\theta^4-4636\theta^3-14417\theta^2-10895\theta-2745\right)+2 3^{2} x^{3}\left(343\theta^4+1920\theta^3+1147\theta^2-345\theta-320\right)-3^{4} x^{4}\left(83\theta^4-104\theta^3-458\theta^2-406\theta-114\right)-3^{8} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 7, 219, 9961, 546379, ...
--> OEIS
Normalized instanton numbers (n0=1): 46/5, 717/10, 1126, 51481/2, 3609772/5, ... ; Common denominator:...

Discriminant

\(-(z+1)(81z^2+92z-1)(-5+9z)^2\)

Local exponents

\(-\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\)\(-1\)\(0\)\(-\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\)\(\frac{ 5}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 319/5.85
Fibre product: 53211- x 632--1(1)

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229

New Number: 5.85 |  AESZ: 319  |  Superseeker: -26 -14942/3  |  Hash: 40a034330b9ad40ec865803f0a601932  

Degree: 5

\(\theta^4+x\left(83\theta^4+436\theta^3+352\theta^2+134\theta+21\right)-2 3^{2} x^{2}\left(343\theta^4-548\theta^3-2555\theta^2-1749\theta-405\right)-2 3^{4} x^{3}\left(1973\theta^4+12528\theta^3+11329\theta^2+3861\theta+342\right)+3^{8} 5 x^{4}\left(473\theta^4+1000\theta^3+858\theta^2+358\theta+62\right)-3^{12} 5^{2} x^{5}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -21, 891, -48027, 2920779, ...
--> OEIS
Normalized instanton numbers (n0=1): -26, -475/2, -14942/3, -244479/2, -3574404, ... ; Common denominator:...

Discriminant

\(-(81z+1)(81z^2-92z-1)(-1+45z)^2\)

Local exponents

\(-\frac{ 1}{ 81}\)\(\frac{ 46}{ 81}-\frac{ 13}{ 81}\sqrt{ 13}\)\(0\)\(\frac{ 1}{ 45}\)\(\frac{ 46}{ 81}+\frac{ 13}{ 81}\sqrt{ 13}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding
to Operator AESZ 318/5.84
B-Incarnation:
Fibre product 53211- x 632--1(0)

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230

New Number: 5.86 |  AESZ: 320  |  Superseeker: 741/11 138745  |  Hash: d19e7569ce62abdd5393977835e411a9  

Degree: 5

\(11^{2} \theta^4-11 x\left(4843\theta^4+8918\theta^3+6505\theta^2+2046\theta+242\right)+2^{2} x^{2}\left(312184\theta^4+343456\theta^3-23371\theta^2-73942\theta-14883\right)-2^{4} x^{3}\left(511972\theta^4+256344\theta^3+144969\theta^2+78639\theta+15642\right)+2^{11} x^{4}(2\theta+1)(1964\theta^3+3078\theta^2+1853\theta+419)-2^{18} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 22, 2850, 568300, 138119170, ...
--> OEIS
Normalized instanton numbers (n0=1): 741/11, 22232/11, 138745, 157326644/11, 19999995398/11, ... ; Common denominator:...

Discriminant

\(-(z-1)(64z^2-416z+1)(-11+128z)^2\)

Local exponents

\(0\)\(\frac{ 13}{ 4}-\frac{ 15}{ 8}\sqrt{ 3}\)\(\frac{ 11}{ 128}\)\(1\)\(\frac{ 13}{ 4}+\frac{ 15}{ 8}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.86" from ...

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231

New Number: 5.87 |  AESZ: 321  |  Superseeker: 35/9 3002/9  |  Hash: b786027c217dd5d5c5abac7b1ecc570b  

Degree: 5

\(3^{4} \theta^4-3^{2} x\left(191\theta^4+862\theta^3+683\theta^2+252\theta+36\right)-2^{5} x^{2}\left(7225\theta^4+24835\theta^3+30634\theta^2+16173\theta+3069\right)-2^{8} x^{3}\left(13251\theta^4+35856\theta^3+27641\theta^2+6966\theta+180\right)-2^{12} 5 x^{4}(2\theta+1)(314\theta^3+363\theta^2+68\theta-31)+2^{16} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 132, 4000, 179620, ...
--> OEIS
Normalized instanton numbers (n0=1): 35/9, 261/4, 3002/9, 126800/9, 1727129/9, ... ; Common denominator:...

Discriminant

\((32z+1)(32z^2-71z+1)(9+80z)^2\)

Local exponents

\(-\frac{ 9}{ 80}\)\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\)\(\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.87" from ...

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232

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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233

New Number: 5.89 |  AESZ: 329  |  Superseeker: 48 25200  |  Hash: 8c526b3b825d5ad6a3d0fb83ee4e6059  

Degree: 5

\(\theta^4-2^{4} x\left(8\theta^4+34\theta^3+25\theta^2+8\theta+1\right)-2^{8} x^{2}\left(87\theta^4+150\theta^3+32\theta^2-2\theta-1\right)-2^{12} x^{3}\left(202\theta^4+240\theta^3+211\theta^2+102\theta+19\right)-2^{16} 3 x^{4}(2\theta+1)(22\theta^3+45\theta^2+38\theta+12)-2^{20} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1200, 136960, 19010320, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 270, 25200, 968066, 80892688, ... ; Common denominator:...

Discriminant

\(-(16384z^3+3072z^2+224z-1)(1+48z)^2\)

Local exponents

≈\(-0.095858-0.072741I\) ≈\(-0.095858+0.072741I\)\(-\frac{ 1}{ 48}\)\(0\) ≈\(0.004215\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.89" from ...

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234

New Number: 5.8 |  AESZ:  |  Superseeker: 84 1522388/3  |  Hash: f4b2a154823e983e64682b48f6254a15  

Degree: 5

\(\theta^4-2^{2} 3 x\left(192\theta^4+240\theta^3+191\theta^2+71\theta+10\right)+2^{7} 3^{2} x^{2}\left(1746\theta^4+3960\theta^3+4323\theta^2+2247\theta+395\right)-2^{12} 3^{4} x^{3}\left(2538\theta^4+7776\theta^3+9915\theta^2+5643\theta+1030\right)+2^{17} 3^{6} x^{4}\left(1782\theta^4+6480\theta^3+8793\theta^2+4905\theta+875\right)-2^{23} 3^{11} x^{5}(\theta+1)^2(3\theta+1)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 120, 34920, 13157760, 5790070440, ...
--> OEIS
Normalized instanton numbers (n0=1): 84, 9210, 1522388/3, 120348978, 19186016160, ... ; Common denominator:...

Discriminant

\(-(-1+864z)(432z-1)^2(288z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 864}\)\(\frac{ 1}{ 432}\)\(\frac{ 1}{ 288}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 6}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 5}{ 6}\)\(3\)\(1\)
\(0\)\(2\)\(1\)\(4\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.8" from ...

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235

New Number: 5.90 |  AESZ: 330  |  Superseeker: 352 3284448  |  Hash: ba5b66d5fe92237e6416a117563571e9  

Degree: 5

\(\theta^4+2^{4} x\left(112\theta^4-64\theta^3-32\theta^2+1\right)+2^{14} x^{2}\left(56\theta^4-64\theta^3+3\theta^2-10\theta-4\right)+2^{20} x^{3}\left(32\theta^4-384\theta^3-436\theta^2-264\theta-55\right)-2^{29} 3 x^{4}(2\theta+1)(10\theta+7)(2\theta^2+4\theta+3)-2^{38} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -16, 4368, -344320, 107445520, ...
--> OEIS
Normalized instanton numbers (n0=1): 352, -23368, 3284448, -578330224, 120252731680, ... ; Common denominator:...

Discriminant

\(-(-1+256z)(256z+1)^2(768z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(-\frac{ 1}{ 768}\)\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)
\(1\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

B-Incarnation as double octic D.O.20

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236

New Number: 5.91 |  AESZ: 331  |  Superseeker: 112 186800  |  Hash: a30093d8c1ab2f66122cef8935b79efb  

Degree: 5

\(\theta^4+2^{4} x\left(18\theta^4-48\theta^3-33\theta^2-9\theta-1\right)-2^{9} x^{2}\left(86\theta^4+512\theta^3+125\theta^2+45\theta+10\right)-2^{14} x^{3}\left(1138\theta^4+2040\theta^3+1883\theta^2+879\theta+157\right)-2^{19} 7 x^{4}(2\theta+1)(186\theta^3+375\theta^2+317\theta+100)-2^{27} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1488, 183040, 27611920, ...
--> OEIS
Normalized instanton numbers (n0=1): 112, -2242, 186800, -11675813, 1250599376, ... ; Common denominator:...

Discriminant

\(-(32z+1)(256z-1)(64z+1)(1+224z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 224}\)\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.91" from ...

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237

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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238

New Number: 5.93 |  AESZ: 333  |  Superseeker: 1 2668/3  |  Hash: dc274781605ee4262d8745e3fa3a8057  

Degree: 5

\(\theta^4+x\theta^2(71\theta^2-2\theta-1)+2^{3} 3 x^{2}\left(154\theta^4+334\theta^3+461\theta^2+248\theta+48\right)+2^{6} 3^{2} x^{3}(5\theta+3)(31\theta^3+39\theta^2-25\theta-21)+2^{9} 3^{4} x^{4}(2\theta+1)(2\theta^3-33\theta^2-56\theta-24)-2^{12} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, -72, 1440, 22680, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, -66, 2668/3, -2774, -167786, ... ; Common denominator:...

Discriminant

\(-(9z-1)(2304z^2+32z+1)(1+24z)^2\)

Local exponents

\(-\frac{ 1}{ 24}\)\(-\frac{ 1}{ 144}-\frac{ 1}{ 72}\sqrt{ 2}I\)\(-\frac{ 1}{ 144}+\frac{ 1}{ 72}\sqrt{ 2}I\)\(0\)\(\frac{ 1}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(3\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(4\)\(2\)\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.93" from ...

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239

New Number: 5.94 |  AESZ: 334  |  Superseeker: 7/3 -4843/81  |  Hash: 1ab1dce2847b14dd89a8f8f48ddc7214  

Degree: 5

\(3^{2} \theta^4-3 x\left(166\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+x^{2}\left(11155\theta^4+42652\theta^3+60463\theta^2+36876\theta+8172\right)-3^{2} x^{3}\left(4705\theta^4+23418\theta^3+42217\theta^2+31152\theta+7932\right)+2^{2} 3 x^{4}\left(3514\theta^4+16403\theta^3+25581\theta^2+16442\theta+3744\right)-2^{2} 5 x^{5}(5\theta+3)(5\theta+4)(5\theta+6)(5\theta+7)\)

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Coefficients of the holomorphic solution: 1, 6, 54, 240, -9450, ...
--> OEIS
Normalized instanton numbers (n0=1): 7/3, -79/12, -4843/81, -1058/3, 3620/3, ... ; Common denominator:...

Discriminant

\(-(3125z^3-1167z^2+54z-1)(2z-3)^2\)

Local exponents

\(0\) ≈\(0.025215-0.018839I\) ≈\(0.025215+0.018839I\) ≈\(0.32301\)\(\frac{ 3}{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 5}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 4}{ 5}\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 6}{ 5}\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(\frac{ 7}{ 5}\)

Note:

This is operator "5.94" from ...

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240

New Number: 5.95 |  AESZ: 338  |  Superseeker: -140/3 -66092  |  Hash: eb4f6d6e59fafa4e794fb664dbdeab3f  

Degree: 5

\(3^{2} \theta^4+2^{2} 3 x\left(278\theta^4+424\theta^3+311\theta^2+99\theta+12\right)+2^{5} x^{2}\left(5210\theta^4+3944\theta^3-2635\theta^2-2433\theta-492\right)+2^{8} x^{3}\left(8190\theta^4-3528\theta^3-3991\theta^2-585\theta+114\right)-2^{11} 11 x^{4}(2\theta+1)(86\theta^3+57\theta^2-39\theta-32)+2^{15} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, -16, 1608, -243520, 44810920, ...
--> OEIS
Normalized instanton numbers (n0=1): -140/3, 1293, -66092, 5236719, -1553321056/3, ... ; Common denominator:...

Discriminant

\((2048z^3-640z^2+312z+1)(3+88z)^2\)

Local exponents

\(-\frac{ 3}{ 88}\) ≈\(-0.003184\)\(0\) ≈\(0.157842-0.358378I\) ≈\(0.157842+0.358378I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.95" from ...

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