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You searched for: degz=16

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1

New Number: 16.10 |  AESZ:  |  Superseeker: 329 13943182/3  |  Hash: 7cb8fc81ff4291911b5851bbe0ce87d6  

Degree: 16

\(2^{4} \theta^4-2^{3} x\left(2080\theta^4+5492\theta^3+3852\theta^2+1106\theta+123\right)-2^{2} x^{2}\left(1038596\theta^4+1086968\theta^3-704594\theta^2-662048\theta-187335\right)-2^{3} x^{3}\left(27355744\theta^4-10845696\theta^3-21419382\theta^2-14835501\theta-3262365\right)+x^{4}\left(1168690425+4302182312\theta+5668764816\theta^2+2884561664\theta^3+1677501472\theta^4\right)-2^{2} x^{5}\left(849165344\theta^4+2919787280\theta^3+4022619556\theta^2+2039376070\theta+366467247\right)-3^{2} x^{6}\left(8324768\theta^4+297404352\theta^3+2276617440\theta^2+4641056376\theta+3089907999\right)+2^{3} 3 x^{7}\left(244118416\theta^4+1798723424\theta^3+5748847278\theta^2+8821060157\theta+5366375049\right)-3 x^{8}\left(1625452048\theta^4+14076026368\theta^3+49562511152\theta^2+83071853528\theta+55103713119\right)-2^{2} x^{9}\left(178897952\theta^4+2122081992\theta^3+10132715124\theta^2+21613786686\theta+17327468673\right)+x^{10}\left(343834041327+412402739864\theta+188061957144\theta^2+38888851616\theta^3+3117930160\theta^4\right)-2^{3} x^{11}\left(201536272\theta^4+2923803328\theta^3+15925294184\theta^2+38512357328\theta+34889020821\right)+2^{4} x^{12}\left(11465776\theta^4+256005312\theta^3+1831886232\theta^2+5368776336\theta+5619083607\right)+2^{7} x^{13}\left(664304\theta^4+6926800\theta^3+21920928\theta^2+15290236\theta-18835647\right)-2^{6} x^{14}\left(375632\theta^4+5919776\theta^3+32756008\theta^2+77419000\theta+66760065\right)-2^{9} 3 x^{15}\left(304\theta^4-3264\theta^3-49992\theta^2-180720\theta-205137\right)+2^{12} 3^{2} x^{16}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, 123/2, 171123/8, 202026919/16, 1175932456419/128, ...
--> OEIS
Normalized instanton numbers (n0=1): 329, 38309/2, 13943182/3, 2778535173/2, 533274129153, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.10" from ...

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2

New Number: 16.11 |  AESZ:  |  Superseeker: 38/3 117997/81  |  Hash: 438ab76047e8f77ecfe291026e2970a0  

Degree: 16

\(3^{2} \theta^4-3 x\left(19\theta^4+470\theta^3+414\theta^2+179\theta+34\right)+x^{2}\left(41308\theta^3-23477\theta^4+78614\theta+24216+112043\theta^2\right)+2^{4} x^{3}\left(41519\theta^4+148341\theta^3-124008\theta^2-154719\theta-69971\right)+2^{4} x^{4}\left(716611\theta^4-5967778\theta^3-839688\theta^2+788291\theta+833002\right)-2^{6} x^{5}\left(12596017\theta^4-6393470\theta^3+2392202\theta^2+4900019\theta+4099566\right)+2^{6} x^{6}\left(194870635\theta^4+297635664\theta^3+556055121\theta^2+599417856\theta+294269276\right)-2^{10} x^{7}\left(22362244\theta^4+47811167\theta^3+124981710\theta^2+251213093\theta+208323007\right)-2^{11} 3 x^{8}\left(203181506\theta^4+1085037788\theta^3+2654369977\theta^2+3167097718\theta+1487844351\right)+2^{14} 3 x^{9}\left(244118416\theta^4+1618934400\theta^3+4804954902\theta^2+7184093301\theta+4428796652\right)-2^{14} 3^{2} x^{10}\left(8324768\theta^4-180857600\theta^3-234257808\theta^2+1793353480\theta+3232798229\right)-2^{19} x^{11}\left(849165344\theta^4+8968527536\theta^3+35778505900\theta^2+64448634778\theta+44747735367\right)+2^{20} x^{12}\left(1677501472\theta^4+20600458944\theta^3+98677225536\theta^2+217063032696\theta+183607904627\right)-2^{26} x^{13}\left(27355744\theta^4+393826112\theta^3+2103107610\theta^2+4954989251\theta+4356355009\right)-2^{26} x^{14}\left(4154384\theta^4+53813504\theta^3+256876192\theta^2+535612120\theta+410996463\right)-2^{31} x^{15}\left(4160\theta^4+47256\theta^3+198132\theta^2+361494\theta+240199\right)+2^{32} x^{16}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, 34/3, 286/3, 8528/27, -797638/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 38/3, -2035/18, 117997/81, -12892349/486, 394521557/729, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.11" from ...

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3

New Number: 16.12 |  AESZ:  |  Superseeker: 644 33686276/3  |  Hash: 7404efbb9f6ea7f9f47767e4c0319a14  

Degree: 16

\(\theta^4+2^{2} x\left(244\theta^4-1096\theta^3-1017\theta^2-469\theta-102\right)-2^{7} x^{2}\left(6880\theta^4+23416\theta^3-23704\theta^2-32167\theta-15345\right)-2^{12} x^{3}\left(113153\theta^4-550050\theta^3-602160\theta^2-409347\theta-5121\right)+2^{16} x^{4}\left(5180356\theta^4+4909796\theta^3+3805572\theta^2-964483\theta-632775\right)-2^{20} x^{5}\left(57912116\theta^4+220612856\theta^3+369961747\theta^2+321640069\theta+133205688\right)+2^{26} 3^{2} x^{6}\left(3335230\theta^4+23883174\theta^3+55731471\theta^2+59241423\theta+26111727\right)+2^{30} 3 x^{7}\left(138627389\theta^4+1043758594\theta^3+3398672757\theta^2+5428677484\theta+3474324555\right)-2^{36} 3 x^{8}\left(178212361\theta^4+1781109910\theta^3+6943057886\theta^2+12445880096\theta+8609393916\right)-2^{41} x^{9}\left(306347392\theta^4+3494924784\theta^3+15467273775\theta^2+31401487755\theta+24645250080\right)+2^{46} x^{10}\left(1346555872\theta^4+18540298208\theta^3+95714831970\theta^2+219162899618\theta+187657830249\right)-2^{50} x^{11}\left(386398880\theta^4+5738560448\theta^3+31530165304\theta^2+76167521656\theta+68494914693\right)-2^{56} x^{12}\left(65461088\theta^4+737270976\theta^3+2844482520\theta^2+4211538840\theta+1624907583\right)+2^{63} x^{13}\left(2159168\theta^4+27966784\theta^3+131159148\theta^2+265135132\theta+194618469\right)+2^{69} x^{14}\left(95936\theta^4+748544\theta^3+1701484\theta^2+328684\theta-1876743\right)-2^{74} 3 x^{15}\left(3440\theta^4+40416\theta^3+177864\theta^2+347256\theta+253575\right)+2^{80} 3^{2} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 408, 126120, 35465344, 9778724520, ...
--> OEIS
Normalized instanton numbers (n0=1): 644, -56540, 33686276/3, -2690029452, 784608924960, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.12" from ...

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4

New Number: 16.13 |  AESZ:  |  Superseeker: 25/3 -3148/81  |  Hash: f92ca2d0c89454e356895526b06ab255  

Degree: 16

\(2^{4} 3^{2} \theta^4-2^{3} 3 x\left(430\theta^4+968\theta^3+792\theta^2+308\theta+49\right)+2^{2} x^{2}\left(47968\theta^4+297280\theta^3+446534\theta^2+262868\theta+59307\right)+2^{2} x^{3}\left(1079584\theta^4+1130784\theta^3-1896618\theta^2-2251548\theta-860323\right)+x^{4}\left(57806065+168292976\theta-179184256\theta^3-65461088\theta^4+85472760\theta^2\right)+x^{5}\left(328976128\theta^3+324401720\theta^2+81053072\theta-96316593-386398880\theta^4\right)+2 x^{6}\left(2693111744\theta^4+622968000\theta^3+27114756\theta^2+838594152\theta+493256185\right)-2 x^{7}\left(1225389568\theta^4+3175754816\theta^3+5148387420\theta^2+3878082344\theta+1362008317\right)-3 x^{8}\left(2851397776\theta^4+11421810304\theta^3+21440197832\theta^2+20210493200\theta+7666843437\right)+3 x^{9}\left(2218038224\theta^4+14352397632\theta^3+42053129784\theta^2+60456011184\theta+34549079653\right)+2^{3} 3^{2} x^{10}\left(26681840\theta^4+182480368\theta^3+400780392\theta^2+201313396\theta-176166937\right)-2^{5} x^{11}\left(115824232\theta^4+1180313536\theta^3+4620134570\theta^2+8184995192\theta+5542315107\right)+2^{6} x^{12}\left(20721424\theta^4+270460752\theta^3+1332035520\theta^2+2942398152\theta+2464923365\right)-2^{6} x^{13}\left(1810448\theta^4+34147072\theta^3+215841768\theta^2+573028864\theta+553832789\right)-2^{10} x^{14}\left(13760\theta^4+145808\theta^3+472216\theta^2+371242\theta-329331\right)+2^{11} x^{15}\left(488\theta^4+9024\theta^3+56850\theta^2+150948\theta+145375\right)+2^{12} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 49/6, 2729/24, 645229/432, 29683/10368, ...
--> OEIS
Normalized instanton numbers (n0=1): 25/3, -995/36, -3148/81, -799579/243, 7826116/729, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.13" from ...

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5

New Number: 16.14 |  AESZ:  |  Superseeker: 256 1223936  |  Hash: d10cd1b312c30ab12f758790dc9274ac  

Degree: 16

\(\theta^4+2^{4} x\left(56\theta^4-104\theta^3-134\theta^2-82\theta-21\right)+2^{11} x^{2}\left(35\theta^4-436\theta^3-347\theta^2-119\theta+42\right)-2^{15} x^{3}\left(1966\theta^4+60\theta^3+16732\theta^2+19722\theta+9459\right)-2^{20} x^{4}\left(3584\theta^4+27304\theta^3+185836\theta^2+233924\theta+91509\right)-2^{27} x^{5}\left(12022\theta^4+11932\theta^3+55862\theta^2+66188\theta+7683\right)+2^{31} x^{6}\left(226300\theta^4+1586208\theta^3+4219376\theta^2+5722536\theta+3385737\right)+2^{36} x^{7}\left(438788\theta^4+2589688\theta^3+6773816\theta^2+9975396\theta+6761583\right)-2^{43} x^{8}\left(422486\theta^4+4780100\theta^3+19717558\theta^2+36354718\theta+25567071\right)-2^{49} x^{9}\left(303952\theta^4+3230064\theta^3+12848329\theta^2+23301081\theta+16479450\right)+2^{53} x^{10}\left(557664\theta^4+10324416\theta^3+63062300\theta^2+159895724\theta+146177745\right)+2^{58} x^{11}\left(989920\theta^4+15846592\theta^3+90575768\theta^2+223282616\theta+202862541\right)+2^{64} x^{12}\left(483232\theta^4+6857664\theta^3+35423928\theta^2+80004312\theta+67210461\right)+2^{71} x^{13}\left(63968\theta^4+880384\theta^3+4440756\theta^2+9817108\theta+8063427\right)+2^{79} x^{14}\left(2924\theta^4+38096\theta^3+187141\theta^2+410905\theta+340155\right)+2^{82} 3 x^{15}\left(880\theta^4+11424\theta^3+55992\theta^2+122760\theta+101547\right)+2^{88} 3^{2} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 336, 90384, 22565120, 5339450640, ...
--> OEIS
Normalized instanton numbers (n0=1): 256, -9340, 1223936, -91401864, 19822164736, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.14" from ...

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6

New Number: 16.15 |  AESZ:  |  Superseeker: 8/3 -6968/81  |  Hash: 8e0ac6cd32cd842a1e97a35376c0380d  

Degree: 16

\(3^{2} \theta^4-2 3 x\left(110\theta^4+112\theta^3+90\theta^2+34\theta+5\right)+2^{2} x^{2}\left(5848\theta^4+5680\theta^3+4094\theta^2+1040\theta-237\right)-2^{5} x^{3}\left(15992\theta^4+3792\theta^3-25407\theta^2-28854\theta-11114\right)+2^{4} x^{4}\left(483232\theta^4-92416\theta^3-1063992\theta^2-1181680\theta-368855\right)-2^{6} x^{5}\left(989920\theta^4-1987712\theta^3-3054328\theta^2-1843216\theta+53781\right)+2^{11} x^{6}\left(139416\theta^4-629280\theta^3-1088941\theta^2-560634\theta+20251\right)+2^{11} x^{7}\left(1215808\theta^4+4101056\theta^3+5092516\theta^2+240552\theta-2238001\right)-2^{12} x^{8}\left(3379888\theta^4+9077632\theta^3+4633832\theta^2-12353104\theta-13454709\right)-2^{14} x^{9}\left(1755152\theta^4+14213376\theta^3+47332040\theta^2+70089696\theta+38558777\right)+2^{17} x^{10}\left(905200\theta^4+6327968\theta^3+16788968\theta^2+17321608\theta+3978771\right)+2^{20} x^{11}\left(96176\theta^4+1251008\theta^3+6513544\theta^2+15584944\theta+14022411\right)-2^{24} x^{12}\left(3584\theta^4+22872\theta^3+162568\theta^2+678162\theta+916431\right)+2^{24} x^{13}\left(15728\theta^4+219712\theta^3+1284824\theta^2+3458928\theta+3502795\right)+2^{27} x^{14}\left(560\theta^4+14816\theta^3+108856\theta^2+315448\theta+322455\right)-2^{32} x^{15}\left(56\theta^4+888\theta^3+5074\theta^2+12570\theta+11487\right)+2^{32} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10/3, 166/3, 16700/27, 489746/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 8/3, 281/18, -6968/81, -460241/486, 774080/729, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.15" from ...

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7

New Number: 16.16 |  AESZ:  |  Superseeker: 368 2223792  |  Hash: cb63667ce6ab5ee8bbd15f2f42131e1b  

Degree: 16

\(\theta^4-2^{3} x\left(8\theta^4+340\theta^3+268\theta^2+98\theta+17\right)-2^{6} x^{2}\left(8168\theta^4+12440\theta^3-15934\theta^2-17544\theta-6943\right)-2^{11} x^{3}\left(45916\theta^4-111756\theta^3-171918\theta^2-131805\theta-24415\right)+2^{12} x^{4}\left(3809536\theta^4+5399840\theta^3+9867864\theta^2+7180376\theta+2158825\right)-2^{20} x^{5}\left(551864\theta^4+2050994\theta^3+3153877\theta^2+2299060\theta+833317\right)+2^{22} x^{6}\left(365384\theta^4+2086728\theta^3+60954\theta^2-7175844\theta-6824113\right)+2^{25} x^{7}\left(7491184\theta^4+56611952\theta^3+184122960\theta^2+289483532\theta+180904967\right)-2^{28} x^{8}\left(15242656\theta^4+143150176\theta^3+536869976\theta^2+940895864\theta+642764281\right)-2^{35} x^{9}\left(344968\theta^4+4155516\theta^3+19641672\theta^2+42019650\theta+34190687\right)+2^{38} x^{10}\left(2533416\theta^4+33180600\theta^3+165711314\theta^2+371280128\theta+313733969\right)-2^{42} x^{11}\left(789320\theta^4+11533112\theta^3+62901156\theta^2+151695242\theta+136669133\right)-2^{44} x^{12}\left(121856\theta^4-421728\theta^3-13434024\theta^2-56826792\theta-71106279\right)+2^{52} x^{13}\left(8320\theta^4+101786\theta^3+440511\theta^2+790310\theta+476913\right)-2^{54} x^{14}\left(1928\theta^4+38504\theta^3+239914\theta^2+609892\theta+553167\right)-2^{57} 3 x^{15}\left(208\theta^4+2064\theta^3+7104\theta^2+9252\theta+2691\right)+2^{60} 3^{2} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 136, 21936, 6207872, 2654088976, ...
--> OEIS
Normalized instanton numbers (n0=1): 368, -6434, 2223792, 7045475, 63017278672, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.16" from ...

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8

New Number: 16.17 |  AESZ:  |  Superseeker: 28/3 36092/81  |  Hash: 5149f445650e5115373b6acb592ca441  

Degree: 16

\(3^{2} \theta^4-2 3 x\left(52\theta^4+212\theta^3+180\theta^2+74\theta+13\right)-2^{2} x^{2}\left(1928\theta^4-11512\theta^3-22670\theta^2-14864\theta-4047\right)+2^{5} x^{3}\left(16640\theta^4+29388\theta^3-33444\theta^2-40977\theta-16934\right)-2^{4} x^{4}\left(121856\theta^4+2127712\theta^3-49464\theta^2-814568\theta-411697\right)-2^{7} x^{5}\left(1578640\theta^4-965264\theta^3-363000\theta^2+278728\theta+480205\right)+2^{10} x^{6}\left(2533416\theta^4+2287224\theta^3+3521090\theta^2+3792864\theta+1769631\right)-2^{13} x^{7}\left(344968\theta^4+674036\theta^3+1363902\theta^2+1918853\theta+1331406\right)-2^{12} x^{8}\left(15242656\theta^4+70247008\theta^3+154128344\theta^2+170540504\theta+76073233\right)+2^{16} x^{9}\left(3745592\theta^4+24132312\theta^3+70149744\theta^2+101813004\theta+60063611\right)+2^{18} x^{10}\left(365384\theta^4+3028648\theta^3+5006034\theta^2-6421376\theta-15599999\right)-2^{21} x^{11}\left(1103728\theta^4+11350204\theta^3+44360888\theta^2+78097451\theta+52598648\right)+2^{20} x^{12}\left(3809536\theta^4+47933664\theta^3+233170440\theta^2+516785976\theta+438059199\right)-2^{23} x^{13}\left(183664\theta^4+3018320\theta^3+17505384\theta^2+43640024\theta+40050861\right)-2^{26} x^{14}\left(8168\theta^4+101912\theta^3+453794\theta^2+849648\theta+551615\right)-2^{29} x^{15}\left(8\theta^4-228\theta^3-2714\theta^2-9345\theta-10420\right)+2^{28} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 26/3, 238/3, 14476/27, -527902/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 28/3, -497/9, 36092/81, -6997057/972, 74043424/729, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.17" from ...

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9

New Number: 16.1 |  AESZ:  |  Superseeker: 0 0  |  Hash: ce5c5b062cf22bc8935e236748d3c341  

Degree: 16

\(\theta^4-2 3^{3} x\left(20\theta^4+2\theta^3-2\theta^2-3\theta-1\right)+2^{2} x^{2}\left(151949\theta^4-14254\theta^3-70179\theta^2-42595\theta-6216\right)-2^{3} 3^{3} x^{3}\left(1072962\theta^4-437056\theta^3-954370\theta^2-299161\theta+63015\right)+2^{4} x^{4}\left(4076695248\theta^4-3035262048\theta^3-4506216565\theta^2-507642115\theta+724750374\right)-2^{6} 3^{3} x^{5}\left(8140262160\theta^4-8793595488\theta^3-8101604275\theta^2+976456152\theta+1899621139\right)+2^{8} x^{6}\left(9218034049688\theta^4-12854277745104\theta^3-5970652217281\theta^2+3294754727367\theta+1790401729671\right)-2^{10} 3^{3} x^{7}\left(11107333819640\theta^4-18438103960576\theta^3-2693186543039\theta^2+5732786101958\theta+1009111312972\right)+2^{12} x^{8}\left(7427475217648672\theta^4-13903863079521824\theta^3+549990096918185\theta^2+4264594906566611\theta-196065070315692\right)-2^{14} 3^{3} x^{9}\left(5006788889131248\theta^4-10423307017692208\theta^3+1148559437524935\theta^2+2739247379862508\theta-601863144518181\right)+2^{16} 3^{4} x^{10}\left(20921192499862036\theta^4-51546334623445432\theta^3+3958462764104225\theta^2+10021243264975981\theta-3621545193405921\right)-2^{18} 3^{7} x^{11}\left(5701586950847588\theta^4-21188224783674368\theta^3-757538843568497\theta^2+2746993547213600\theta-1268918638558608\right)+2^{23} 3^{10} x^{12}\left(39160297802908\theta^4-814299201549560\theta^3-95884988762411\theta^2+91861472904467\theta-44237005356800\right)+2^{28} 3^{13} x^{13}\left(5094274414759\theta^4+20214234618156\theta^3-2519812312315\theta^2-4449859616032\theta+1201444818880\right)-2^{35} 3^{16} 5 31 x^{14}\theta(269358010\theta^3+131761607\theta^2-826543489\theta-380205376)-2^{40} 3^{19} 5^{2} 31^{2} x^{15}\theta(\theta+1)(1997\theta^2+119865\theta+91208)+2^{47} 3^{22} 5^{3} 31^{3} x^{16}\theta(\theta+2)(\theta+1)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -54, -1362, -73548, -4170906, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, 12293/4, 0, -8127101, 0, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.1" from ...

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10

New Number: 16.2 |  AESZ:  |  Superseeker: 3 836/9  |  Hash: d055011e8b1a8de56a2637ad79926ae1  

Degree: 16

\(2^{4} \theta^4+2^{3} 3 x\left(50\theta^4-8\theta^3-8\theta^2-4\theta-1\right)+2^{2} 3^{2} x^{2}\left(928\theta^4-320\theta^3-506\theta^2-588\theta-245\right)+2^{2} 3^{3} x^{3}\left(3552\theta^4-6048\theta^3-14110\theta^2-14484\theta-5345\right)-3^{5} x^{4}\left(544\theta^4+96128\theta^3+203672\theta^2+185008\theta+53869\right)-3^{6} x^{5}\left(73120\theta^4+525568\theta^3+925064\theta^2+513776\theta-120503\right)-2 3^{7} x^{6}\left(132032\theta^4+530880\theta^3+30548\theta^2-1880952\theta-2071291\right)-2 3^{8} x^{7}\left(140288\theta^4-933824\theta^3-7980068\theta^2-16638040\theta-11395107\right)+3^{10} x^{8}\left(268112\theta^4+5084288\theta^3+21085352\theta^2+30037968\theta+11306601\right)+3^{12} x^{9}\left(423792\theta^4+4236736\theta^3+11088168\theta^2+2418320\theta-14704689\right)+2^{3} 3^{12} x^{10}\left(284560\theta^4+1792688\theta^3-564136\theta^2-20310620\theta-30974175\right)+2^{6} 3^{14} x^{11}\left(7876\theta^4-25232\theta^3-678697\theta^2-2637328\theta-3045324\right)-2^{6} 3^{15} x^{12}\left(9392\theta^4+211056\theta^3+1469488\theta^2+4274496\theta+4423455\right)-2^{6} 3^{16} x^{13}\left(28048\theta^4+326912\theta^3+1697000\theta^2+4309792\theta+4244109\right)-2^{11} 3^{18} x^{14}\left(200\theta^4+1064\theta^3+1960\theta^2+2683\theta+3648\right)+2^{11} 3^{20} x^{15}\left(8\theta^4+384\theta^3+2754\theta^2+7092\theta+6193\right)+2^{12} 3^{22} x^{16}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, 3/2, 243/8, 1359/16, 52515/128, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, -51/4, 836/9, -777, 7284, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.2" from ...

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11

New Number: 16.3 |  AESZ:  |  Superseeker: 68 1294532/3  |  Hash: ed2a3fd88f95da59e82dcb7b2feb1eb1  

Degree: 16

\(\theta^4+2^{2} x\left(4\theta^4-136\theta^3-345\theta^2-277\theta-78\right)-2^{7} x^{2}\left(200\theta^4+1736\theta^3+5488\theta^2+6235\theta+2661\right)-2^{12} x^{3}\left(1753\theta^4+4110\theta^3+20372\theta^2+22839\theta+8793\right)-2^{16} 3 x^{4}\left(2348\theta^4-19892\theta^3-14072\theta^2-33415\theta-43923\right)+2^{20} 3^{2} x^{5}\left(7876\theta^4+135496\theta^3+165125\theta^2+164459\theta+135000\right)+2^{26} 3^{2} x^{6}\left(35570\theta^4+273894\theta^3+190975\theta^2-89697\theta-119673\right)+2^{30} 3^{4} x^{7}\left(26487\theta^4+106022\theta^3-140553\theta^2-488804\theta-337095\right)+2^{36} 3^{4} x^{8}\left(16757\theta^4-83170\theta^3-787090\theta^2-1456680\theta-830376\right)-2^{41} 3^{4} x^{9}\left(35072\theta^4+724464\theta^3+3034063\theta^2+4788747\theta+2542968\right)-2^{46} 3^{5} x^{10}\left(66016\theta^4+658784\theta^3+2080330\theta^2+2614218\theta+968913\right)-2^{50} 3^{6} x^{11}\left(73120\theta^4+498112\theta^3+780920\theta^2-812872\theta-2147843\right)-2^{56} 3^{7} x^{12}\left(544\theta^4-88512\theta^3-765688\theta^2-2198712\theta-2138531\right)+2^{63} 3^{7} x^{13}\left(7104\theta^4+111552\theta^3+620932\theta^2+1494292\theta+1329663\right)+2^{69} 3^{8} x^{14}\left(1856\theta^4+26624\theta^3+142124\theta^2+335916\theta+297185\right)+2^{74} 3^{9} x^{15}\left(400\theta^4+5664\theta^3+30008\theta^2+70536\theta+62089\right)+2^{80} 3^{10} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 312, 86184, 21412224, 5052550824, ...
--> OEIS
Normalized instanton numbers (n0=1): 68, 3884, 1294532/3, 70075068, 14264173344, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.3" from ...

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12

New Number: 16.4 |  AESZ:  |  Superseeker: 145 806426  |  Hash: e830ad7dc816bd020e0829b4201ed6ef  

Degree: 16

\(2^{4} \theta^4+2^{3} x\left(1120\theta^4-1972\theta^3-3868\theta^2-2882\theta-795\right)-2^{2} 3^{3} x^{2}\left(2828\theta^4+107624\theta^3+261482\theta^2+236736\theta+81531\right)-2^{3} 3^{6} x^{3}\left(166976\theta^4+510336\theta^3+1934650\theta^2+2127915\theta+835767\right)-3^{10} x^{4}\left(2426592\theta^4-1426176\theta^3+21304688\theta^2+28115480\theta+8918063\right)+2^{2} 3^{13} x^{5}\left(3093152\theta^4+35896400\theta^3+52847444\theta^2+60960414\theta+43992675\right)+3^{18} x^{6}\left(17651552\theta^4+115861568\theta^3+222158496\theta^2+266977288\theta+172865617\right)+2^{3} 3^{20} x^{7}\left(17249008\theta^4+47477792\theta^3-93884230\theta^2-319423097\theta-217950375\right)-3^{24} x^{8}\left(102317104\theta^4+1926767104\theta^3+8931639056\theta^2+16543419656\theta+11251205757\right)-2^{2} 3^{28} x^{9}\left(67685152\theta^4+752204232\theta^3+2843775988\theta^2+4682925630\theta+2900858497\right)-3^{32} x^{10}\left(169863760\theta^4+1219175264\theta^3+1858150248\theta^2-2723936152\theta-6458797919\right)+2^{3} 3^{36} x^{11}\left(3071888\theta^4+138114752\theta^3+1052933928\theta^2+2939453264\theta+2845108445\right)+2^{4} 3^{40} x^{12}\left(6607696\theta^4+109695552\theta^3+627419112\theta^2+1530482544\theta+1371274737\right)+2^{7} 3^{44} x^{13}\left(595184\theta^4+8689360\theta^3+46323360\theta^2+108260284\theta+94203393\right)+2^{6} 3^{48} x^{14}\left(453808\theta^4+6314464\theta^3+32788184\theta^2+75507848\theta+65158911\right)+2^{9} 3^{53} x^{15}\left(4016\theta^4+55104\theta^3+284280\theta^2+653328\theta+564183\right)+2^{12} 3^{58} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 795/2, 1109619/8, 698413767/16, 1667994030819/128, ...
--> OEIS
Normalized instanton numbers (n0=1): 145, 8867/2, 806426, 294534843/2, 36788237721, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.4" from ...

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13

New Number: 16.5 |  AESZ:  |  Superseeker: 2/3 -3557/81  |  Hash: b0d936e56acdf03e3e72e1814442ab50  

Degree: 16

\(3^{2} \theta^4+3 x\left(251\theta^4+70\theta^3+54\theta^2+19\theta+2\right)-x^{2}\left(9925\theta^2+13690\theta-2428\theta^3-28363\theta^4+6024\right)+2^{4} x^{3}\left(37199\theta^4-22299\theta^3-73056\theta^2-78543\theta-30497\right)+2^{4} x^{4}\left(412981\theta^4-1074238\theta^3-2419908\theta^2-2290027\theta-697466\right)+2^{6} x^{5}\left(191993\theta^4-5944270\theta^3-10717950\theta^2-7362757\theta-327010\right)-2^{6} x^{6}\left(10616485\theta^4+72432336\theta^3+96362271\theta^2+3620736\theta-59039988\right)-2^{10} x^{7}\left(8460644\theta^4+24423487\theta^3-9938722\theta^2-101499459\theta-93359835\right)-2^{11} x^{8}\left(12789638\theta^4-61790956\theta^3-472388549\theta^2-910406750\theta-561795471\right)+2^{14} x^{9}\left(17249008\theta^4+194008320\theta^3+675401042\theta^2+875629503\theta+302767578\right)+2^{14} 3^{2} x^{10}\left(17651552\theta^4+131260160\theta^3+303001104\theta^2+57460728\theta-358842021\right)+2^{19} 3 x^{11}\left(3093152\theta^4+7407728\theta^3-96718084\theta^2-479745438\theta-596879613\right)-2^{20} 3^{2} x^{12}\left(2426592\theta^4+35398464\theta^3+214634048\theta^2+589589832\theta+596784069\right)-2^{26} 3^{2} x^{13}\left(166976\theta^4+1827328\theta^3+8848858\theta^2+21296171\theta+20263707\right)-2^{26} 3^{3} x^{14}\left(11312\theta^4-272128\theta^3-2642848\theta^2-7506168\theta-6935571\right)+2^{31} 3^{4} x^{15}\left(2240\theta^4+35304\theta^3+198316\theta^2+480714\theta+429057\right)+2^{32} 3^{8} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -2/3, 142/3, -7312/27, 314042/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 2/3, 76/9, -3557/81, -5159/486, 1429691/729, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.5" from ...

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14

New Number: 16.6 |  AESZ:  |  Superseeker: 604 10582920  |  Hash: ae9e6afa6a64c66b14ecc57c090a2276  

Degree: 16

\(2^{4} \theta^4+2^{3} x\left(2632\theta^4-8020\theta^3-8134\theta^2-4124\theta-957\right)-2^{2} 3^{3} x^{2}\left(59584\theta^4+447880\theta^3-266330\theta^2-470004\theta-257157\right)-2^{2} 3^{6} x^{3}\left(2084848\theta^4-10624248\theta^3-6613144\theta^2-2338506\theta+2575629\right)+3^{10} x^{4}\left(76860224\theta^4+37515040\theta^3-123523576\theta^2-230682216\theta-89646143\right)-2^{4} 3^{13} x^{5}\left(47627428\theta^4+177706198\theta^3+314770123\theta^2+293923803\theta+123197247\right)+2 3^{18} x^{6}\left(109348352\theta^4+791269264\theta^3+2037777532\theta^2+2503390304\theta+1301617959\right)+2^{2} 3^{20} x^{7}\left(1118115152\theta^4+8230409176\theta^3+26430670096\theta^2+42292381622\theta+27424948395\right)-3^{24} x^{8}\left(6553002016\theta^4+67555786336\theta^3+267811589048\theta^2+484625497784\theta+337209119577\right)-2^{3} 3^{28} x^{9}\left(304315688\theta^4+3377868156\theta^3+14426600138\theta^2+28319769288\theta+21624447113\right)+2^{3} 3^{32} x^{10}\left(477772768\theta^4+6828823100\theta^3+36140835237\theta^2+84133602806\theta+72831614902\right)+2^{2} 3^{36} x^{11}\left(79307440\theta^4+1193232808\theta^3+6600824472\theta^2+15994957990\theta+14398159609\right)+3^{40} x^{12}\left(76769344\theta^4+964818528\theta^3+4370936856\theta^2+8483539176\theta+5938160775\right)+2^{4} 3^{44} x^{13}\left(268060\theta^4+3542666\theta^3+17044857\theta^2+35620691\theta+27340212\right)+2 3^{48} x^{14}\left(184064\theta^4+2048432\theta^3+8660500\theta^2+16541392\theta+12080907\right)+2^{2} 3^{53} x^{15}\left(976\theta^4+11928\theta^3+54912\theta^2+112878\theta+87435\right)+3^{58} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 957/2, 1357479/8, 851677269/16, 2013405923979/128, ...
--> OEIS
Normalized instanton numbers (n0=1): 604, -114415/2, 10582920, -5127425229/2, 729802869084, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.6" from ...

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15

New Number: 16.7 |  AESZ:  |  Superseeker: 20/3 -21368/81  |  Hash: ed36d7830ecca61b6e5c113a96a492a0  

Degree: 16

\(2^{4} 3^{2} \theta^4-2^{3} 3 x\left(488\theta^4+868\theta^3+702\theta^2+268\theta+41\right)+2^{2} x^{2}\left(92032\theta^4+264232\theta^3+340334\theta^2+184604\theta+35871\right)-2^{2} x^{3}\left(1072240\theta^4+840696\theta^3-1802904\theta^2-2109510\theta-795037\right)-x^{4}\left(117110904\theta^2+178119592\theta-76769344\theta^4-109952288\theta^3+56644559\right)-2^{3} x^{5}\left(39653720\theta^4-41464324\theta^3-49511586\theta^2-19633210\theta+8561249\right)+2 x^{6}\left(1911091072\theta^4-560017392\theta^3-1782035460\theta^2-675901440\theta-3110721\right)+2^{2} x^{7}\left(608631376\theta^4+1765102952\theta^3+2652375136\theta^2+1439834874\theta+142764075\right)-x^{8}\left(24186241888\theta^3+31220323448\theta+40121480696\theta^2+8617369041+6553002016\theta^4\right)-2^{3} x^{9}\left(559057576\theta^4+3711601476\theta^3+11096418710\theta^2+16005760200\theta+9042841485\right)+2^{3} 3^{2} x^{10}\left(27337088\theta^4+184901916\theta^3+441638533\theta^2+358787334\theta-3513990\right)+2^{2} 3 x^{11}\left(190509712\theta^4+1956311176\theta^3+7797884008\theta^2+14187472734\theta+9913342473\right)+3^{2} x^{12}\left(76860224\theta^4+1038528096\theta^3+5131794968\theta^2+11168867880\theta+9129957831\right)+2^{3} 3^{2} x^{13}\left(1042424\theta^4+19906060\theta^3+129088894\theta^2+352019522\theta+349060761\right)-2 3^{3} x^{14}\left(119168\theta^4+772592\theta^3-1179292\theta^2-15270480\theta-24272433\right)-2^{2} 3^{4} x^{15}\left(5264\theta^4+89736\theta^3+539056\theta^2+1386618\theta+1305315\right)+3^{8} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 41/6, 2549/24, 666089/432, 84731131/10368, ...
--> OEIS
Normalized instanton numbers (n0=1): 20/3, -55/18, -21368/81, -562673/486, -6431620/729, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.7" from ...

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16

New Number: 16.8 |  AESZ:  |  Superseeker: 12 13064/9  |  Hash: 6df7a0657df14d871f878801092f412c  

Degree: 16

\(2^{4} \theta^4+2^{3} 3 x\left(8\theta^4-92\theta^3-82\theta^2-36\theta-7\right)-2^{2} 3^{2} x^{2}\left(1088\theta^4-1192\theta^3-4206\theta^2-3004\theta-959\right)+2^{2} 3^{3} x^{3}\left(4560\theta^4+33768\theta^3-25736\theta^2-31794\theta-14623\right)+3^{5} x^{4}\left(100032\theta^4-536736\theta^3-96744\theta^2+29064\theta+61715\right)-2^{3} 3^{6} x^{5}\left(169160\theta^4-91804\theta^3+41266\theta^2+53386\theta+40577\right)+2 3^{7} x^{6}\left(3414784\theta^4+6784176\theta^3+13515220\theta^2+15009792\theta+7398205\right)-2^{2} 3^{8} x^{7}\left(1392976\theta^4+4030952\theta^3+11019392\theta^2+21953818\theta+17966595\right)-3^{10} x^{8}\left(33964576\theta^4+198076768\theta^3+508864632\theta^2+625406200\theta+298971681\right)+2^{3} 3^{12} x^{9}\left(5514696\theta^4+37470916\theta^3+113533894\theta^2+174129464\theta+110762081\right)-2^{3} 3^{12} x^{10}\left(2307232\theta^4-10413916\theta^3-29280133\theta^2+104107498\theta+229795002\right)-2^{2} 3^{14} x^{11}\left(55805104\theta^4+602312152\theta^3+2446466552\theta^2+4496900138\theta+3199953147\right)+3^{15} x^{12}\left(354369472\theta^4+4305262368\theta^3+20428056776\theta^2+44627766264\theta+37585137717\right)-2^{3} 3^{16} x^{13}\left(20975576\theta^4+285973420\theta^3+1472576206\theta^2+3384942194\theta+2924420331\right)+2 3^{18} x^{14}\left(1698304\theta^4+22123696\theta^3+107456180\theta^2+230344688\theta+183698835\right)-2^{2} 3^{20} x^{15}\left(4976\theta^4+61944\theta^3+290160\theta^2+606438\theta+477397\right)+3^{22} x^{16}\left((2\theta+7)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 21/2, 567/8, 2205/16, -261333/128, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, -219/2, 13064/9, -51069/2, 518412, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.8" from ...

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17

New Number: 16.9 |  AESZ:  |  Superseeker: 212 9541288/3  |  Hash: 240105a4e36aa5b2249227693cab5eda  

Degree: 16

\(2^{4} \theta^4-2^{3} x\left(2488\theta^4+3860\theta^3+2742\theta^2+812\theta+93\right)+2^{2} x^{2}\left(849152\theta^4+826280\theta^3-8642\theta^2+30940\theta+64455\right)-2^{2} x^{3}\left(41951152\theta^4+15369288\theta^3+23120264\theta^2+21758694\theta+5436333\right)+3 x^{4}\left(354369472\theta^4+655910240\theta^3+1268958104\theta^2+924603592\theta+221096163\right)-2^{4} 3^{2} x^{5}\left(13951276\theta^4+44739826\theta^3+55966025\theta^2+15992369\theta-4965543\right)-2 3^{2} x^{6}\left(9228928\theta^4+170860656\theta^3+998590148\theta^2+1877333088\theta+1197851121\right)+2^{2} 3^{4} x^{7}\left(11029392\theta^4+79469656\theta^3+250838864\theta^2+378643990\theta+226165407\right)-3^{4} x^{8}\left(33964576\theta^4+277427296\theta^3+925454904\theta^2+1482249784\theta+947909481\right)-2^{3} 3^{4} x^{9}\left(696488\theta^4+7735356\theta^3+35539066\theta^2+72969912\theta+56161089\right)+2^{3} 3^{5} x^{10}\left(853696\theta^4+10255700\theta^3+48316999\theta^2+103978434\theta+85496214\right)-2^{2} 3^{6} x^{11}\left(338320\theta^4+4920088\theta^3+26876936\theta^2+65240426\theta+59359807\right)+3^{7} x^{12}\left(100032\theta^4+1937184\theta^3+12891336\theta^2+36174264\theta+36798485\right)+2^{4} 3^{7} x^{13}\left(1140\theta^4+7518\theta^3-11285\theta^2-151823\theta-245532\right)-2 3^{8} x^{14}\left(2176\theta^4+32848\theta^3+176556\theta^2+407920\theta+344813\right)+2^{2} 3^{9} x^{15}\left(16\theta^4+408\theta^3+2944\theta^2+8430\theta+8519\right)+3^{10} x^{16}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, 93/2, 108135/8, 107524917/16, 525715348491/128, ...
--> OEIS
Normalized instanton numbers (n0=1): 212, 35875/2, 9541288/3, 1723495053/2, 290947666260, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

This is operator "16.9" from ...

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