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1

New Number: 14.10 |  AESZ:  |  Superseeker: 2 38  |  Hash: 364dddcd3359111a8e01be8efc1de60c  

Degree: 14

\(\theta^4+2 x\left(72\theta^4+48\theta^3+59\theta^2+35\theta+8\right)+2^{2} x^{2}\left(2277\theta^4+3252\theta^3+4573\theta^2+3266\theta+992\right)+2^{4} x^{3}\left(20907\theta^4+47634\theta^3+77375\theta^2+65724\theta+24022\right)+2^{7} x^{4}\left(62171\theta^4+199492\theta^3+375946\theta^2+371450\theta+156488\right)+2^{9} x^{5}\left(253302\theta^4+1066440\theta^3+2327568\theta^2+2630202\theta+1250623\right)+2^{10} x^{6}\left(1459436\theta^4+7698000\theta^3+19344508\theta^2+24706800\theta+13098093\right)+2^{12} x^{7}\left(3024300\theta^4+19348248\theta^3+55554208\theta^2+79484188\theta+46581901\right)+2^{15} x^{8}\left(2268548\theta^4+17191376\theta^3+55960360\theta^2+89050336\theta+57303573\right)+2^{18} x^{9}\left(1227744\theta^4+10826688\theta^3+39662704\theta^2+69775740\theta+49021017\right)+2^{20} x^{10}\left(945104\theta^4+9566080\theta^3+39177592\theta^2+75788768\theta+57836847\right)+2^{22} x^{11}\left(502368\theta^4+5772864\theta^3+26266668\theta^2+55590540\theta+45853745\right)+2^{25} x^{12}\left(87264\theta^4+1128192\theta^3+5668024\theta^2+13052400\theta+11573495\right)+2^{30} 5 x^{13}\left(444\theta^4+6408\theta^3+35315\theta^2+87905\theta+83203\right)+2^{35} 5^{2} x^{14}\left((\theta+4)^4\right)\)

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Coefficients of the holomorphic solution: 1, -16, 196, -2352, 29920, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...

Discriminant

\((4z+1)(2z+1)^2(64z^2+24z+1)^2(160z^2+32z+1)^2(8z+1)^3\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\)\(-\frac{ 1}{ 8}\)\(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(4\)
\(-2\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(4\)
\(3\)\(1\)\(2\)\(4\)\(0\)\(1\)\(4\)\(0\)\(4\)

Note:

This is operator "14.10" from ...

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2

New Number: 15.2 |  AESZ:  |  Superseeker: 2 38  |  Hash: 76d5c5e186c39f14d8f32dfa0f13e22a  

Degree: 15

\(\theta^4+2 x\left(73\theta^4+40\theta^3+47\theta^2+27\theta+6\right)+2^{2} x^{2}\left(2349\theta^4+2724\theta^3+3516\theta^2+2273\theta+614\right)+2^{3} x^{3}\left(44091\theta^4+80304\theta^3+115043\theta^2+84574\theta+26356\right)+2^{5} x^{4}\left(269591\theta^4+678346\theta^3+1084179\theta^2+893856\theta+309842\right)+2^{8} x^{5}\left(568775\theta^4+1835004\theta^3+3266314\theta^2+2971734\theta+1120498\right)+2^{11} x^{6}\left(856369\theta^4+3369012\theta^3+6631886\theta^2+6564309\theta+2651780\right)+2^{11} x^{7}\left(7508036\theta^4+34719008\theta^3+74840604\theta^2+79593816\theta+34039943\right)+2^{13} x^{8}\left(12098492\theta^4+63919352\theta^3+149239952\theta^2+168641212\theta+75569097\right)+2^{16} x^{9}\left(7179524\theta^4+42349744\theta^3+105902696\theta^2+125838704\theta+58525593\right)+2^{19} x^{10}\left(3117952\theta^4+20136896\theta^3+53326176\theta^2+65967996\theta+31556287\right)+2^{21} x^{11}\left(1949840\theta^4+13550976\theta^3+37571920\theta^2+47915544\theta+23371681\right)+2^{23} x^{12}\left(851424\theta^4+6266688\theta^3+17985676\theta^2+23424156\theta+11560933\right)+2^{26} x^{13}\left(122784\theta^4+942720\theta^3+2770088\theta^2+3654240\theta+1815239\right)+2^{31} 5 x^{14}\left(524\theta^4+4136\theta^3+12323\theta^2+16373\theta+8173\right)+2^{36} 5^{2} x^{15}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, -12, 136, -1632, 21296, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -29/4, 38, -2077/8, 2034, ... ; Common denominator:...

Discriminant

\((4z+1)(64z^2+24z+1)^2(160z^2+32z+1)^2(2z+1)^3(8z+1)^3\)

Local exponents

\(-\frac{ 1}{ 2}\)\(-\frac{ 3}{ 16}-\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 10}-\frac{ 1}{ 40}\sqrt{ 6}\)\(-\frac{ 1}{ 8}\)\(-\frac{ 3}{ 16}+\frac{ 1}{ 16}\sqrt{ 5}\)\(-\frac{ 1}{ 10}+\frac{ 1}{ 40}\sqrt{ 6}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(2\)
\(2\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(2\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(3\)\(0\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(2\)
\(5\)\(1\)\(2\)\(4\)\(0\)\(1\)\(4\)\(0\)\(2\)

Note:

This is operator "15.2" from ...

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3

New Number: 8.31 |  AESZ: 315  |  Superseeker: 38 26135  |  Hash: 44be55b95bb1c725c5aaa2c9a6635e89  

Degree: 8

\(5^{2} \theta^4-5^{2} x\left(239\theta^4+496\theta^3+368\theta^2+120\theta+15\right)-2 3 5 x^{2}\left(1727\theta^4+3206\theta^3+2341\theta^2+1090\theta+245\right)-3^{2} 5 x^{3}\left(1519\theta^4+7338\theta^3+14271\theta^2+8340\theta+1690\right)+3^{3} x^{4}\left(10358\theta^4-16622\theta^3-49763\theta^2-37900\theta-10210\right)+3^{4} 5 x^{5}\left(922\theta^4+3526\theta^3-1357\theta^2-3028\theta-1031\right)-3^{5} x^{6}\left(1219\theta^4-6030\theta^3-6441\theta^2-1740\theta+160\right)-2^{2} 3^{6} x^{7}\left(162\theta^4+234\theta^3+65\theta^2-52\theta-25\right)-2^{4} 3^{8} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 15, 1179, 140505, 20362059, ...
--> OEIS
Normalized instanton numbers (n0=1): 38, 3068/5, 26135, 7871998/5, 117518569, ... ; Common denominator:...

Discriminant

\(-(z+1)(81z^3+351z^2+246z-1)(-5-15z+36z^2)^2\)

Local exponents

≈\(-3.452681\)\(-1\) ≈\(-0.884694\)\(\frac{ 5}{ 24}-\frac{ 1}{ 24}\sqrt{ 105}\)\(0\) ≈\(0.004042\)\(\frac{ 5}{ 24}+\frac{ 1}{ 24}\sqrt{ 105}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(1\)\(3\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(2\)\(4\)\(0\)\(2\)\(4\)\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.32

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