Summary

You searched for: sol=-36

Your search produced 5 matches

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1

New Number: 3.4 |  AESZ:  |  Superseeker: -9 -748  |  Hash: 350ef7c6e038467a3f50bfbe164fa73a  

Degree: 3

\(\theta^4+3^{2} x\left(33\theta^4+66\theta^3+57\theta^2+24\theta+4\right)+2^{3} 3^{6} x^{2}(\theta+1)^2(5\theta^2+10\theta+4)+2^{2} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, -36, 2268, -168840, 13664700, ...
--> OEIS
Normalized instanton numbers (n0=1): -9, -279/4, -748, -9612, -155448, ... ; Common denominator:...

Discriminant

\((81z+1)(1+108z)^2\)

Local exponents

\(-\frac{ 1}{ 81}\)\(-\frac{ 1}{ 108}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(0\)\(2\)
\(2\)\(1\)\(0\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 165= $f \ast f$.

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2

New Number: 4.59 |  AESZ: 283  |  Superseeker: -188 -807540  |  Hash: 987222cb05e8a3d02c76c47abefbb9f4  

Degree: 4

\(\theta^4+2^{2} x\left(20\theta^4+400\theta^3+281\theta^2+81\theta+9\right)-2^{4} 3 x^{2}\left(5696\theta^4+13184\theta^3+3928\theta^2+628\theta+39\right)+2^{10} 3^{2} 5 x^{3}\left(1348\theta^4+1944\theta^3+1415\theta^2+486\theta+63\right)-2^{12} 3^{7} 5^{2} x^{4}\left((2\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -36, 7236, -2257200, 860876100, ...
--> OEIS
Normalized instanton numbers (n0=1): -188, 831, -807540, 39235244, -18812436256, ... ; Common denominator:...

Discriminant

\(-(62208z^2-560z-1)(-1+240z)^2\)

Local exponents

\(\frac{ 35}{ 7776}-\frac{ 13}{ 7776}\sqrt{ 13}\)\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 240}\)\(\frac{ 35}{ 7776}+\frac{ 13}{ 7776}\sqrt{ 13}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to AESZ 282/4.58

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3

New Number: 5.45 |  AESZ: 242  |  Superseeker: -18 1568/3  |  Hash: 562c18d54c0080ebb0bb01b14a8241ce  

Degree: 5

\(\theta^4+2 3 x\left(72\theta^4+108\theta^3+91\theta^2+37\theta+6\right)+2^{2} 3^{3} x^{2}\left(648\theta^4+1800\theta^3+2211\theta^2+1248\theta+260\right)+2^{4} 3^{5} x^{3}\left(1344\theta^4+4968\theta^3+7320\theta^2+4749\theta+1072\right)+2^{6} 3^{7} x^{4}(2\theta+1)(630\theta^3+2241\theta^2+2617\theta+971)+2^{8} 3^{10} x^{5}(2\theta+1)(6\theta+5)(6\theta+7)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, -36, 2484, -208080, 19221300, ...
--> OEIS
Normalized instanton numbers (n0=1): -18, 99/2, 1568/3, 22698, -165960, ... ; Common denominator:...

Discriminant

\((1+144z)(36z+1)^2(108z+1)^2\)

Local exponents

\(-\frac{ 1}{ 36}\)\(-\frac{ 1}{ 108}\)\(-\frac{ 1}{ 144}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 5}{ 6}\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 7}{ 6}\)
\(4\)\(1\)\(2\)\(0\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.45" from ...

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4

New Number: 24.17 |  AESZ:  |  Superseeker: -24 -9598768/30375  |  Hash: 1eb6cea72aa2a282481ca5e3b2422017  

Degree: 24

\(5^{2} \theta^4+2^{2} 5 x\left(47\theta^4-23\theta^3-20\theta-5\right)-2^{4} x^{2}\left(179\theta^4-5548\theta^3-7291\theta^2-4350\theta-905\right)-2^{7} x^{3}\left(2935\theta^4-7002\theta^3+8317\theta^2+33810\theta+15415\right)-2^{10} x^{4}\left(5449\theta^4+91862\theta^3+82862\theta^2-10173\theta-6981\right)+2^{12} x^{5}\left(16533\theta^4-102630\theta^3-137351\theta^2-442384\theta-214109\right)+2^{14} x^{6}\left(377045\theta^4+2384088\theta^3+768917\theta^2+3480360\theta+214109\right)-2^{17} x^{7}\left(238805\theta^4+58138\theta^3-4280001\theta^2-3095246\theta-1210167\right)-2^{20} x^{8}\left(2326731\theta^4+9363624\theta^3+12365844\theta^2+16867914\theta+8008789\right)+2^{23} x^{9}\left(27688\theta^4+2998464\theta^3+263994\theta^2+1516404\theta-885283\right)+2^{26} x^{10}\left(5764462\theta^4+2998464\theta^3+263994\theta^2+1516404\theta-885283\right)-2^{29} x^{11}\left(11329982\theta^4+30867704\theta^3+61886406\theta^2+61158272\theta+23162227\right)-2^{32} x^{12}\left(2120418\theta^4+36058992\theta^3+87838628\theta^2+106632978\theta+502460529\right)+2^{35} x^{13}\left(16849298\theta^4+91712872\theta^3+212023454\theta^2+244238244\theta+110360529\right)-2^{38} x^{14}\left(10049328\theta^4+37236768\theta^3+66644650\theta^2+63907082\theta+25441423\right)-2^{41} x^{15}\left(4736512\theta^4+53071212\theta^3+174736084\theta^2+241175316\theta+122040421\right)+2^{44} x^{16}\left(8122336\theta^4+67434512\theta^3+211414476\theta^2+291782162\theta+149636409\right)-2^{47} x^{17}\left(3596934\theta^4+30695376\theta^3+102692394\theta^2+149709348\theta+804776873\right)+2^{50} x^{18}\left(344350\theta^4+4792416\theta^3+22792344\theta^2+40780218\theta+25076261\right)+2^{53} x^{19}\left(255290\theta^4+1201696\theta^3+241498\theta^2-4145416\theta-4163853\right)-2^{56} x^{20}\left(91962\theta^4+642936\theta^3+1364188\theta^2+959498\theta+45723\right)+2^{59} x^{21}\left(6076\theta^4+85188\theta^3+269096\theta^2+322380\theta+129693\right)+2^{62} 3 x^{22}\left(777\theta^4+2264\theta^3+431\theta^2-3906\theta-3016\right)-2^{65} 3^{2} x^{23}\left(51\theta^4+314\theta^3+741\theta^2+794\theta+326\right)+2^{68} 3^{3} x^{24}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 4, -36, 8912/15, 688859/150, ...
--> OEIS
Normalized instanton numbers (n0=1): -24, 802/25, -9598768/30375, 31786366/5625, -5158982190959/52734375, ... ; Common denominator:...

Discriminant

\(25+940z+10749840108954241204224z^22-16934111059665368383488z^23+7968993439842526298112z^24+6177505280z^6-31300648960z^7-2439754285056z^8+232263778304z^9+386846496391168z^10+142889646027257675776z^16-506223456939883364352z^17-2864z^2-375680z^3-5579776z^4+67719168z^5+387703632921257574400z^18-6082737769283584z^11-9107125963849728z^12+578937470964465664z^13-2762338246833733632z^14-10415700038201114624z^15+2299447897742827847680z^19-6626560462915928850432z^20+3502575530995601113088z^21\)

No data for singularities

Note:

This is operator "24.17" from ...

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5

New Number: 24.1 |  AESZ:  |  Superseeker: 3 1322/9  |  Hash: d77f5cce80101a4e8f097ff7dc1cac1f  

Degree: 24

\(\theta^4-3 x\theta(8\theta^2+5\theta+1)-3^{2} x^{2}\left(141\theta^4-76\theta^3-53\theta^2+74\theta+48\right)+3^{3} x^{3}\left(350\theta^4+268\theta^3-911\theta^2+193\theta+366\right)+2^{2} 3^{4} x^{4}\left(1536\theta^4-210\theta^3+5498\theta^2+3259\theta+432\right)-3^{6} x^{5}\left(9982\theta^4-4940\theta^3+26473\theta^2+14567\theta+72\right)-3^{7} x^{6}\left(13329\theta^4+128212\theta^3+141347\theta^2+176702\theta+93936\right)+3^{8} x^{7}\left(179988\theta^4+489272\theta^3+581261\theta^2+545387\theta+236754\right)-3^{9} x^{8}\left(473261\theta^4-322200\theta^3-1952576\theta^2-2540184\theta-1052928\right)+2 3^{11} x^{9}\left(89272\theta^4-647728\theta^3-1032101\theta^2-477573\theta+275604\right)+2 3^{12} x^{10}\left(380267\theta^4+3534580\theta^3+6813301\theta^2+7672754\theta+3370032\right)-2 3^{13} x^{11}\left(2824394\theta^4+21447564\theta^3+70086871\theta^2+111632667\theta+67101174\right)+2^{3} 3^{15} x^{12}\left(604658\theta^4+4211064\theta^3+13816867\theta^2+20606976\theta+11731242\right)-2 3^{16} x^{13}\left(2513086\theta^4-1029540\theta^3-71899267\theta^2-199754241\theta-151321716\right)-2 3^{17} x^{14}\left(4936477\theta^4+113054700\theta^3+624917375\theta^2+1236797682\theta+810302688\right)+2 3^{19} x^{15}\left(10447060\theta^4+141814160\theta^3+623159411\theta^2+1236797682\theta+658549626\right)-3^{21} x^{16}\left(15883703\theta^4+190281632\theta^3+7662783992\theta^2+1272288312\theta+742283280\right)+3^{24} x^{17}\left(2257088\theta^4+24107672\theta^3+94611213\theta^2+157783505\theta+93169704\right)-3^{25} x^{18}\left(1409659\theta^4+13667804\theta^3+60904285\theta^2+118238478\theta+79019856\right)-3^{27} x^{19}\left(372282\theta^4+2964756\theta^3+4412579\theta^2-3409349\theta-6851134\right)+2^{2} 3^{29} x^{20}\left(79892\theta^4+648390\theta^3+1698852\theta^2+1619127\theta+396380\right)-3^{31} x^{21}\left(42578\theta^4+351292\theta^3+908415\theta^2+928057\theta+321472\right)-3^{33} x^{22}\left(10861\theta^4+68980\theta^3+157607\theta^2+161390\theta+65296\right)+3^{35} 5 x^{23}\left(444\theta^4+2616\theta^3+5783\theta^2+5673\theta+2078\right)+3^{37} 5^{2} x^{24}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 0, 27, -36, 891, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, -24, 1322/9, -1824, 19551, ... ; Common denominator:...

Discriminant

\((9z-1)(81z^2-9z-1)(6561z^6+66339z^5-16767z^4+2106z^3-297z^2+27z-1)(9z+1)^2(32805z^5+12393z^4-324z^3+432z^2-9z-1)^2(3z-1)^3\)

No data for singularities

Note:

This is operator "24.1" from ...

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