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You searched for: degz=18

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1

New Number: 18.1 |  AESZ:  |  Superseeker: 32 74144  |  Hash: f898da39070d0f65b96891f225273ac8  

Degree: 18

\(3^{36} \theta^4-2^{4} 3^{34} x\left(333\theta^4-14\theta^3-52\theta^2-45\theta-11\right)+2^{9} 3^{32} x^{2}\left(19692\theta^4-14974\theta^3-24933\theta^2-14648\theta-2899\right)-2^{13} 3^{30} x^{3}\left(978450\theta^4-2297356\theta^3-2203108\theta^2-351038\theta+150293\right)+2^{16} 3^{28} x^{4}\left(29162034\theta^4-228074816\theta^3-41034760\theta^2+129318642\theta+56632337\right)+2^{20} 3^{26} x^{5}\left(587116062\theta^4+2884581236\theta^3-5110414872\theta^2-4354953074\theta-719634683\right)-2^{25} 3^{24} x^{6}\left(7788212430\theta^4-25994187260\theta^3-36307798646\theta^2+22596130679\theta+17870398220\right)-2^{30} 3^{22} x^{7}\left(24952379517\theta^4+215382922768\theta^3-193917927994\theta^2+68687254791\theta+118177203129\right)+2^{32} 3^{20} x^{8}\left(2465059314285\theta^4-6257533070480\theta^3-160224268608\theta^2-2321915485018\theta-2939103970827\right)+2^{36} 3^{18} x^{9}\left(19196808612383\theta^4+40471527323966\theta^3+47011511994668\theta^2+29979826610437\theta-3798547377438\right)-2^{41} 3^{16} x^{10}\left(31815915596118\theta^4-91985871789250\theta^3-243694332457379\theta^2-412337070880227\theta-225096344703166\right)-2^{47} 3^{14} x^{11}\left(152409250801971\theta^4+392522456009119\theta^3+483307141123011\theta^2-23876260594498\theta-261430636861709\right)-2^{52} 3^{12} x^{12}\left(341239631092419\theta^4+2089976311699567\theta^3+6237679550918137\theta^2+8770476560885579\theta+4635246761447824\right)+2^{56} 3^{10} x^{13}\left(529561889839080\theta^4+2701783513427734\theta^3+2623668209036513\theta^2-4470872132749815\theta-6908279580524476\right)+2^{61} 3^{8} x^{14}\left(5372561842952418\theta^4+44975097147122878\theta^3+143025130667911083\theta^2+203932774055033813\theta+109645866522838268\right)+2^{67} 3^{6} x^{15}(\theta+2)(4847763038128923\theta^3+36798926507269013\theta^2+95492964503573704\theta+84453090506711840)+2^{72} 3^{4} 5 13 x^{16}(\theta+2)(\theta+3)(58496948477298\theta^2+345543721824865\theta+525022379845215)+2^{76} 3^{2} 5^{2} 13^{2} 233 x^{17}(\theta+2)(\theta+3)(\theta+4)(2800175409\theta+9490253627)+2^{83} 5^{3} 13^{3} 233^{2} 6343 x^{18}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)

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Coefficients of the holomorphic solution: 1, -176/9, 18544/27, 27113216/729, 43446571280/6561, ...
--> OEIS
Normalized instanton numbers (n0=1): 32, 1048, 74144, 7046865, 788076384, ... ; Common denominator:...

Discriminant

\((128z-9)(1662779392z^4-15777792z^3+6283008z^2-1632960z+6561)(-81+10080z+59648z^2)^2(416z-9)^3(160z+9)^3(16z+9)^3\)

No data for singularities

Note:

This is operator "18.1" from ...

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2

New Number: 18.2 |  AESZ:  |  Superseeker: 6 626/3  |  Hash: 55d34e33f80959a1cc22d89896602d12  

Degree: 18

\(5^{36} \theta^4-2 5^{34} x\left(1062\theta^4+2334\theta^3+2431\theta^2+1264\theta+270\right)+2^{2} 5^{32} x^{2}\left(320093\theta^4+1596302\theta^3+3123745\theta^2+2942536\theta+1113630\right)-2^{4} 3 5^{30} x^{3}\left(6019044\theta^4+66147274\theta^3+199338689\theta^2+265716324\theta+140408820\right)-2^{6} 3 5^{29} x^{4}\left(21064589\theta^4-712686408\theta^3-3721395346\theta^2-6814704050\theta-4678647990\right)+2^{8} 3^{2} 5^{26} x^{5}\left(11975992794\theta^4+4988365790\theta^3-283865124355\theta^2-820252227200\theta-742428845375\right)-2^{10} 3^{2} 5^{24} x^{6}\left(751496765979\theta^4+5038722749418\theta^3+527774451452\theta^2-28210592089487\theta-40377165728685\right)+2^{12} 3^{4} 5^{22} x^{7}\left(2053839509132\theta^4+38726412983468\theta^3+100208705321045\theta^2+47075279827199\theta-94563567299555\right)+2^{15} 3^{3} 5^{20} x^{8}\left(74215848255703\theta^4-1839607623231932\theta^3-9356900275220062\theta^2-15606787340081617\theta-6586759478866260\right)-2^{16} 3^{4} 5^{19} x^{9}\left(1339553061158952\theta^4-346103919288724\theta^3-32183930062302533\theta^2-95644350146690865\theta-81488332660776420\right)+2^{18} 3^{4} 5^{16} x^{10}\left(324968843289985253\theta^4+1744047067693857210\theta^3+1715197129786435655\theta^2-6334532044956661400\theta-11513434792675853625\right)-2^{20} 3^{5} 5^{14} x^{11}\left(3460747049021132226\theta^4+31298336392269716602\theta^3+104978931469185513088\theta^2+140017817259283451897\theta+43613982781047056885\right)+2^{22} 3^{5} 5^{12} x^{12}\left(80350576998319299087\theta^4+976180200725417657808\theta^3+4579453875869380552810\theta^2+9705595934827681526144\theta+7732240714165421579820\right)-2^{24} 3^{6} 5^{10} x^{13}\left(458458033401826426866\theta^4+6886135463408824297206\theta^3+39806281802402968612276\theta^2+104618897609209760830741\theta+105167289421805219654955\right)+2^{26} 3^{7} 5^{9} x^{14}\left(367293230407611531891\theta^4+6543982621478903177718\theta^3+44412685133916057233996\theta^2+135976752518751744187635\theta+158331213388111123371340\right)-2^{29} 3^{9} 5^{6} x^{15}(\theta+5)(694133174853729835197\theta^3+11024532762694581883575\theta^2+58689640052713706224130\theta+104903464776686639708350)-2^{32} 3^{11} 5^{4} 7 x^{16}(\theta+5)(\theta+6)(5759026685592741133\theta^2+12188432611308644783\theta-75995642240452623249)+2^{35} 3^{13} 5^{2} 7^{2} 31 163 277 x^{17}(\theta+5)(\theta+6)(\theta+7)(3303544726261\theta+19442784399486)-2^{40} 3^{15} 7^{3} 17 31^{2} 163^{2} 277^{2} 2273 x^{18}(\theta+5)(\theta+6)(\theta+7)(\theta+8)\)

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Coefficients of the holomorphic solution: 1, 108/5, 43692/125, 20111184/3125, 12183126444/78125, ...
--> OEIS
Normalized instanton numbers (n0=1): 6, 41/4, 626/3, 12349/8, 33062, ... ; Common denominator:...

Discriminant

\(-(32z+25)(68z-25)(11783232z^3-2926800z^2+877500z-15625)(7824z^2-900z+625)^2(7419168z^3-913200z^2-33750z+15625)^2(168z-25)^3\)

No data for singularities

Note:

This is operator "18.2" from ...

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3

New Number: 18.3 |  AESZ:  |  Superseeker: 5 581/3  |  Hash: c372ce2dd494d34fc57b5df64936f51c  

Degree: 18

\(5^{36} \theta^4-5^{34} x\left(2\theta^4-836\theta^3-2699\theta^2-2281\theta-630\right)-5^{32} x^{2}\left(698887\theta^4+1310668\theta^3+3112955\theta^2+2997674\theta+746520\right)-2^{3} 5^{30} x^{3}\left(11282513\theta^4+199109973\theta^3+523177303\theta^2+578740323\theta+324038340\right)+2^{4} 3 5^{29} x^{4}\left(401317179\theta^4-227554138\theta^3-5373356281\theta^2-15895489200\theta-11599171620\right)+2^{6} 3 5^{26} x^{5}\left(11263243979\theta^4+791366221015\theta^3-160326658805\theta^2-4059898325575\theta-6755896203750\right)-2^{8} 3^{2} 5^{24} x^{6}\left(1934872049749\theta^4-1341096414492\theta^3-68511464240363\theta^2-102864986512622\theta-49357274747760\right)+2^{11} 3^{3} 5^{22} x^{7}\left(13607429754249\theta^4+16249747070826\theta^3+401876825987315\theta^2+1907807179296418\theta+1692428384442540\right)-2^{10} 3^{3} 5^{20} x^{8}\left(5160905706602149\theta^4+56441436274688694\theta^3+403661385606953279\theta^2+1047643523187770214\theta+804115159386277320\right)+2^{14} 3^{3} 5^{19} x^{9}\left(1151529820336588\theta^4-1181163155304381\theta^3+256764872757165398\theta^2+1536085185463393515\theta+2500640236867231260\right)+2^{16} 3^{5} 5^{16} x^{10}\left(594101245255781471\theta^4+8961670542502273220\theta^3+46437396299074878210\theta^2+99662030142446455325\theta+69216104374293171750\right)-2^{19} 3^{4} 5^{14} x^{11}\left(74291722029541059287\theta^4+1183574257365465059374\theta^3+6916514969712951297931\theta^2+17379353991370872028439\theta+15703785992015099051145\right)+2^{22} 3^{5} 5^{12} x^{12}\left(502416470536394155727\theta^4+8188709537490429503068\theta^3+52120056197714921204260\theta^2+158115009556434238002824\theta+194698477555407992900670\right)-2^{25} 3^{7} 5^{10} x^{13}\left(626005255350815781413\theta^4+13253881452262727928658\theta^3+117818372049993889931293\theta^2+483180100764903933673163\theta+741048860476069680967965\right)+2^{28} 3^{7} 5^{9} x^{14}\left(874420567310412314036\theta^4+25864434705237018552178\theta^3+245139839684154313479541\theta^2+921313118467583765994485\theta+1172999354237578100725020\right)+2^{31} 3^{8} 5^{6} x^{15}(\theta+5)(46373998524485412599597\theta^3+1168043097949189558948575\theta^2+9727205507156459014349380\theta+26051899533079859738783100)-2^{36} 3^{10} 5^{4} x^{16}(\theta+6)(\theta+5)(55660208813949982213753\theta^2+901081058326717633680903\theta+3551264663537211482323991)+2^{39} 3^{10} 5^{2} 7 29 163 2053 x^{17}(\theta+5)(\theta+6)(\theta+7)(9756026997943757\theta+78186644916385582)-2^{45} 3^{11} 7^{2} 17 29^{2} 89 163^{2} 14723 2053^{2} x^{18}(\theta+5)(\theta+6)(\theta+7)(\theta+8)\)

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Coefficients of the holomorphic solution: 1, -126/5, 60078/125, -24187032/3125, 10439413614/78125, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, -53/4, 581/3, -1231, 19810, ... ; Common denominator:...

Discriminant

\(-(136z+25)(89z-25)(64z-25)(25441344z^3-4822200z^2+635625z-15625)(336z+25)^2(31296z^2+1800z+625)^2(17146656z^3-3652800z^2+67500z+15625)^2\)

No data for singularities

Note:

This is operator "18.3" from ...

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4

New Number: 18.4 |  AESZ:  |  Superseeker: 247/36 4444/9  |  Hash: 32fa46e290b3c9bee37ffb7a8fd9f4a9  

Degree: 18

\(2^{4} 3^{4} \theta^4-2^{2} 3^{2} x\left(3682\theta^4+5390\theta^3+4351\theta^2+1656\theta+252\right)+x^{2}\left(649332+6404206\theta^3+6069697\theta^2+3305113\theta^4+3016440\theta\right)-x^{3}\left(38636254\theta^4+15489180+108265181\theta^2+63679392\theta+93415794\theta^3\right)+x^{4}\left(764158344\theta^3+1036668572\theta^2+689221538\theta+184349683+256670733\theta^4\right)-x^{5}\left(3757797824\theta^3+5722058716\theta^2+4199976622\theta+1217504498+1069676441\theta^4\right)+x^{6}\left(14417904540\theta+4453297047+18342984749\theta^2+11509059738\theta^3+3046889312\theta^4\right)-x^{7}\left(6642155473\theta^4+24242800968\theta+7538554014+23131598018\theta^3+32019404863\theta^2\right)+2 x^{8}\left(6215749063\theta^4+17569348834\theta^3+11741029033\theta^2+1346877246\theta-1108958294\right)-2 x^{9}\left(10076009995\theta^4+24440563356\theta^3-1322218878\theta^2-28555856598\theta-15696067310\right)-x^{10}\left(49102102354-26413304169\theta^4-56670410178\theta^3+1614281629\theta^2+82337880208\theta\right)+x^{11}\left(47360089904\theta-39036891766\theta^3-6364831971\theta^2+31465171724-28479483424\theta^4\right)-x^{12}\left(43718118390\theta+18381816153+26430580224\theta^2-14524633248\theta^3-26803569313\theta^4\right)-x^{13}\left(18753392101\theta^4-62656633898\theta-24930556682+10542306176\theta^3-41804612332\theta^2\right)-x^{14}\left(20759304217+48901375684\theta+32921264817\theta^2-554448182\theta^3-6038807150\theta^4\right)+x^{15}\left(54976569672\theta+20722418334+2052372607\theta^4+51517404847\theta^2+19282089834\theta^3\right)-2 13 x^{16}\left(90710726\theta^4+669539662\theta^3+1753919819\theta^2+1925558652\theta+749345011\right)+2^{2} 7 13^{2} x^{17}(\theta+1)(100405\theta^3+577503\theta^2+1023193\theta+571997)-2^{4} 7^{2} 13^{3} x^{18}(\theta+1)(\theta+2)(4\theta+5)(4\theta+7)\)

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Coefficients of the holomorphic solution: 1, 7, 155, 5389, 228523, ...
--> OEIS
Normalized instanton numbers (n0=1): 247/36, 1427/36, 4444/9, 306173/36, 2193041/12, ... ; Common denominator:...

Discriminant

\(-(z-1)(832z^7-355z^6-2395z^5+4723z^4-3034z^3+823z^2-83z+1)(-36+329z-457z^2+269z^3-1439z^4+182z^5)^2\)

No data for singularities

Note:

This is operator "18.4" from ...

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