1
New Number: 21.1 | AESZ: | Superseeker: -3 -836/9 | Hash: 0fe5589e355c32f4ff99894c93da5ebd
Degree: 21
\(\theta^4-3 x\left(594\theta^4+388\theta^3+449\theta^2+255\theta+57\right)+3^{2} x^{2}\left(167949\theta^4+219736\theta^3+296165\theta^2+206058\theta+60327\right)-3^{3} x^{3}\left(30062564\theta^4+59082628\theta^3+90938680\theta^2+73390824\theta+25169787\right)+3^{4} x^{4}\left(3821918586\theta^4+10028695224\theta^3+17362063000\theta^2+15752079416\theta+6042025251\right)-3^{6} x^{5}\left(122323515588\theta^4+401741477192\theta^3+772934505898\theta^2+772767973606\theta+323443209951\right)+3^{7} x^{6}\left(9208285046694\theta^4+36335830001264\theta^3+76933908262582\theta^2+83605114571476\theta+37610075824851\right)-3^{8} x^{7}\left(556804111648224\theta^4+2566374206107640\theta^3+5931468185457740\theta^2+6936766968119084\theta+3319720514504883\right)+3^{9} x^{8}\left(27485425030131487\theta^4+144945187887393360\theta^3+363188370704177600\theta^2+453656002398028056\theta+229261144684401603\right)-3^{11} x^{9}\left(373144117026480050\theta^4+2216159730666735988\theta^3+5985131626117997505\theta^2+7937745663167991583\theta+4212346965321976686\right)+3^{12} x^{10}\left(12620773799957764793\theta^4+83371681116879474616\theta^3+241456176625052857369\theta^2+338390948699279517242\theta+187738474353413402628\right)-2^{2} 3^{13} x^{11}\left(88897318990506843163\theta^4+646615088663747698317\theta^3+1999372114801235907923\theta^2+2949327067455333140727\theta+1704572854502964047766\right)+2^{3} 3^{15} x^{12}\left(347739693458697250535\theta^4+2761194118785869833761\theta^3+9082378345988744152060\theta^2+14055373737057643782774\theta+8437449682549590949014\right)-2^{4} 3^{16} x^{13}\left(3388892533211296225843\theta^4+29186241106744032096123\theta^3+101718484183047761368709\theta^2+164675983283376235096123\theta+102422453838975446750766\right)+2^{5} 3^{17} x^{14}\left(27249665649734532251102\theta^4+252958456234974974975776421\theta^3+931464075137305276054819\theta^2+1573701956965471162096164\theta+1011951623372019370481502\right)-2^{6} 3^{19} x^{15}\left(59624661642978107387279\theta^4+593534732512385311078207\theta^3+2302778787973910263222855\theta^2+4051392721321863680953049\theta+2688523708721489677735446\right)+2^{7} 3^{21} x^{16}\left(104798156862907596826923\theta^4+1113675430740135170361867\theta^3+454112769317336457207052\theta^2+8304013490920595240792750\theta+5677660112851097019157260\right)-2^{8} 3^{23} x^{17}\left(144414331908091729604\theta^4+1631880922420590560058519\theta^3+6977539346859077115802728\theta^2+13239245712821134606222476\theta+9313169920208225411283528\right)+2^{8} 3^{25} x^{18}(\theta+2)(300609744176461608186257\theta^3+2998248186426335727135492\theta^2+10108382642002404275847711\theta+11441919541626435036478660)-2^{11} 3^{29} 5 13 x^{19}(\theta+2)(\theta+3)(94966488350134307817\theta^2+726354035060929832235\theta+1411592559746293379510)+2^{17} 3^{34} 5^{2} 13^{2} 277 x^{20}(\theta+2)(\theta+3)(\theta+4)(2857062816013\theta+12353662367364)-2^{21} 3^{37} 5^{3} 13^{3} 197 277^{2} 7477 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 171, 21951, 2506887, 268618923, ... --> OEIS Normalized instanton numbers (n0=1): -3, -12, -836/9, -777, -7284, ... ; Common denominator:...
\(1-1782z+1511541z^2-811689228z^3+309575405466z^4-89173842863652z^5+20138519397119778z^6-3653191776523997664z^7+540995620868078058621z^8-66101360898889861417350z^9+6707196649023354479356713z^10-566924161219607366848654596z^11+39917476173178841512659321960z^12-2334091382018078442915465772848z^13+112608840438470988852354214708032z^14-4435164589474967381812635371410752z^15+140316894183604724782276689879599232z^16-3480479814145334228077850084994048z^17+65204022304842271542325554911494361856z^18-867621039332733698991089432847107512320z^19+7309015082771056267093644376086154444800z^20-29309576848365568314888988820481245184000z^21\)
No data for singularities
2
New Number: 21.2 | AESZ: | Superseeker: 145 806426 | Hash: ddf19942f4f52eca019abc999883d2e7
Degree: 21
\(\theta^4+x\left(587\theta^4+1246\theta^3+1369\theta^2+746\theta+147\right)-3^{2} x^{2}\left(4538\theta^4-110564\theta^3-185120\theta^2-147112\theta-41397\right)-3^{4} x^{3}\left(1035076\theta^4-1297528\theta^3-8818306\theta^2-12503444\theta-4451169\right)-3^{7} x^{4}\left(5161406\theta^4+38827744\theta^3-45479050\theta^2-167480140\theta-75253687\right)+3^{9} x^{5}\left(159899054\theta^4-1101213860\theta^3-1078605448\theta^2+3804990452\theta+2248946345\right)+3^{11} x^{6}\left(5267876320\theta^4+1946686040\theta^3-46791251270\theta^2+55528150012\theta+43890742249\right)+3^{13} x^{7}\left(17563180564\theta^4+401225871896\theta^3-655901346714\theta^2+606985455256\theta+604845400313\right)-3^{15} x^{8}\left(1259994296701\theta^4-4866373217248\theta^3+7077412135434\theta^2-2790221590796\theta-5020648151389\right)-3^{17} x^{9}\left(21213265990559\theta^4-8676665828906\theta^3+94601175296907\theta^2+60465698226818\theta+1680107104942\right)-2 3^{18} x^{10}\left(133064543096719\theta^4+54611528872550\theta^3+827508655813091\theta^2+1146281402499166\theta+486206586252414\right)+2^{2} 3^{20} x^{11}\left(836923718327372\theta^4+2812362687153940\theta^3+5749183912231555\theta^2+4551769716928361\theta+1498713844152636\right)+2^{3} 3^{22} x^{12}\left(6319644778425140\theta^4+21326885735408572\theta^3+51147468714283207\theta^2+55973943665205875\theta+25369328578636674\right)+2^{5} 3^{25} x^{13}\left(2515491341994233\theta^4+6636150963865252\theta^3+14766167680355081\theta^2+16085059047306740\theta+7728573825488804\right)-2^{6} 3^{27} x^{14}\left(1595788631100577\theta^4+31396355573419520\theta^3+99907101725437\theta^2+139949892911938966\theta+73481106611183740\right)-2^{6} 3^{29} x^{15}\left(54083947078919144\theta^4+458699316857101780\theta^3+1422193189173287603\theta^2+201146712387012863\theta+1091964433392840746\right)-2^{7} 3^{31} x^{16}\left(165377087197890154\theta^4+1379147217221991764\theta^3+4462174444406121927\theta^2+6607618876639848145\theta+3750999772752974582\right)-2^{8} 3^{33} x^{17}\left(275947984666295227\theta^4+2447447182773658994\theta^3+8424466306726177521\theta^2+13208651399879365162\theta+7892383981185068576\right)-2^{9} 3^{35} x^{18}(\theta+2)(275184606695268577\theta^3+2132288326473162492\theta^2+5728810650212969151\theta+5299681055825250460)-2^{12} 3^{36} 5 13 x^{19}(\theta+2)(\theta+3)(1830325216082219\theta^2+10883451053945415\theta+16805179155093040)-2^{15} 3^{38} 5^{2} 13^{2} 113 x^{20}(\theta+2)(\theta+3)(\theta+4)(18882098189\theta+63995895157)+2^{18} 3^{40} 5^{3} 13^{3} 31 113^{2} 2543 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -147, 14337, -1302879, 104484303, ... --> OEIS Normalized instanton numbers (n0=1): 145, 8867/2, 806426, 294534843/2, 36788237721, ... ; Common denominator:...
\(1+587z-40842z^2-83841156z^3-11287994922z^4+3147293079882z^5+933188486459040z^6+28001382726338172z^7-18079540983893055807z^8-2739484627783145721117z^9-103103860710184898551182z^10+11672690263563194003696688z^11+1586537195995719323873362080z^12+68203109159174388131050951008z^13-778805873401050080066850399936z^14-237555308634149277903010689289728z^15-13075075470984609694044454343403264z^16-392706959354590699011966158179512576z^17-7049170462937511183873685713565152768z^18-73141984157202493941822430975661813760z^19-399036867705738488408133122130441830400z^20+881038976390638748871606297587515392000z^21\)
No data for singularities
3
New Number: 21.3 | AESZ: | Superseeker: 604 10582920 | Hash: 0fd57058f969bd31134f9f79e296c0f9
Degree: 21
\(\theta^4+x\left(1343\theta^4-1778\theta^3-764\theta^2+125\theta+66\right)-3^{2} x^{2}\left(45593\theta^4-39836\theta^3-300503\theta^2-49390\theta+8256\right)-3^{4} x^{3}\left(5315779\theta^4-22436590\theta^3+12417905\theta^2-4423046\theta-3436320\right)+2^{2} 3^{7} x^{4}\left(33165829\theta^4-83984944\theta^3+100931541\theta^2+65464310\theta+14379928\right)-2^{3} 3^{9} x^{5}\left(412867595\theta^4-807745220\theta^3+267839757\theta^2-775291748\theta-485511652\right)-2^{3} 3^{11} x^{6}\left(556633861\theta^4+23806734464\theta^3+32810072733\theta^2+3266735078\theta-4113971432\right)+2^{5} 3^{13} x^{7}\left(44865639929\theta^4+87314088364\theta^3+29372482841\theta^2-10389885822\theta-5801470580\right)-2^{5} 3^{15} x^{8}\left(248191185725\theta^4-1319906045564\theta^3-3008579460343\theta^2-3570359521002\theta-1619621855768\right)-2^{7} 3^{17} x^{9}\left(2027030169181\theta^4+8095416687338\theta^3+14847403664785\theta^2+12875521238580\theta+4137217359368\right)-2^{7} 3^{18} x^{10}\left(19769084125697\theta^4-23207015817320\theta^3-224931042213455\theta^2-414933989772154\theta-241223039844120\right)+2^{10} 3^{20} x^{11}\left(66470699961674\theta^4+356123349215404\theta^3+877696588249501\theta^2+986031897348491\theta+410402769146784\right)+2^{9} 3^{22} x^{12}\left(204476790719405\theta^4+1284198957269596\theta^3+4909805476904377\theta^2+8658668243389046\theta+5572245515714712\right)-2^{11} 3^{25} x^{13}\left(260642609069191\theta^4+2103631653651272\theta^3+6084644826452157\theta^2+7673591239771328\theta+3552810226513072\right)-2^{11} 3^{27} x^{14}\left(1672493659058951\theta^4+14558288605969720\theta^3+47922274214521863\theta^2+71039786187088354\theta+39928172322101096\right)-2^{13} 3^{29} x^{15}\left(1261266627490045\theta^4+11763130646927540\theta^3+41808812800607697\theta^2+67062525689554466\theta+40756862573452768\right)-2^{13} 3^{31} x^{16}\left(2353158847326895\theta^4+23388116071478852\theta^3+8848723658887083\theta^2+150434052273819498\theta+96333532960547480\right)-2^{16} 3^{33} x^{17}\left(729502329854189\theta^4+7715603649955858\theta^3+30907912005592067\theta^2+55250394473974194\theta+36919821250343152\right)-2^{16} 3^{35} x^{18}(\theta+2)(607445335050553\theta^3+5632812354059238\theta^2+17734223488403989\theta+18870922058442340)-2^{17} 3^{36} 5 13 x^{19}(\theta+2)(\theta+3)(7578367862189\theta^2+53502084304365\theta+96619101737140)-2^{18} 3^{38} 5^{2} 13^{2} 29 x^{20}(\theta+2)(\theta+3)(\theta+4)(640015067\theta+2536482721)-2^{21} 3^{40} 5^{3} 13^{3} 29^{2} 6053 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -66, 486, -1000344, -31772358, ... --> OEIS Normalized instanton numbers (n0=1): 604, -114415/2, 10582920, -5127425229/2, 729802869084, ... ; Common denominator:...
\(1+1343z-410337z^2-430578099z^3+290134672092z^4-65011782979080z^5-788848148596536z^6+2288970292752738144z^7-113960711750008082400z^8-33506688826105845312384z^9-980345374599637658346624z^10+237331455743914189872408576z^11+3285349559410005144582474240z^12-452279324262052460468163815424z^13-26119707525481762395689919768576z^14-709109388102656843246920415109120z^15-11906937792299181277244210008596480z^16-265771262614097226799419400902868992z^17-1991732669694524121606165442590867456z^18-9690900519638033397250239867320401920z^19-27769145151723697688948088004037836800z^20-35644033024133812048728597903704064000z^21\)
No data for singularities
4
New Number: 21.4 | AESZ: | Superseeker: 12 -73270936/9 | Hash: ea0a19e2bbcb75ab0103e861337b3f2a
Degree: 21
\(\theta^4+3 x\left(573\theta^4+346\theta^3+412\theta^2+239\theta+54\right)+3^{2} x^{2}\left(156063\theta^4+190252\theta^3+259127\theta^2+180550\theta+52656\right)+3^{3} x^{3}\left(26873063\theta^4+49571770\theta^3+76212373\theta^2+6106354\theta+20777568\right)+2^{2} 3^{4} x^{4}\left(820581957\theta^4+2034754740\theta^3+3492838265\theta^2+3133962118\theta+1190460168\right)+2^{4} 3^{6} x^{5}\left(6300362534\theta^4+19676778467\theta^3+37370330484\theta^2+36883703215\theta+15276339186\right)+2^{3} 3^{7} x^{6}\left(909135259983\theta^4+3431279279032\theta^3+7154070873743\theta^2+7670002845554\theta+3413524335720\right)+2^{6} 3^{8} x^{7}\left(6578661109677\theta^4+29157693414323\theta^3+66290838226280\theta^2+76488360260036\theta+36219329073882\right)+2^{5} 3^{9} x^{8}\left(621118841654771\theta^4+3165334819559244\theta^3+7801391210481967\theta^2+9618732171727698\theta+4811767929521208\right)-2^{8} 3^{11} x^{9}\left(1006971762683339\theta^4+5805767585264362\theta^3+154317312352859336\theta^2+20216923376831949\theta+10626549650623836\right)+2^{7} 3^{12} x^{10}\left(65010659394650453\theta^4+418646275727401384\theta^3+1194551569101777997\theta^2+1655275652516026742\theta+910294388309482488\right)+2^{9} 3^{13} x^{11}\left(436618025486403133\theta^4+3107758129098031614\theta^3+9480179119729435361\theta^2+13841832366370196760\theta+7936511785428285000\right)+2^{9} 3^{15} x^{12}\left(3253974365419639343\theta^4+25378994322658850220\theta^3+82459599652886212555\theta^2+1264452814346649241666\theta+7537566452320106004\right)+2^{12} 3^{16} x^{13}\left(7545567178315476151\theta^4+64015361780620462923\theta^3+220793041913868320297\theta^2+354629201172868320135\theta+219217347256983574500\right)+2^{11} 3^{17} x^{14}\left(2307919988301912384493\theta^4+2116501102196476284048\theta^3+7725401378678907468469\theta^2+12964454588967176832582\theta+8293341868591288772952\right)+2^{14} 3^{19} x^{15}\left(119959654773054384185\theta^4+1182698869985222762683\theta^3+4555730636505118858198\theta^2+7970714706688080962144\theta+5266713350723171529432\right)+2^{13} 3^{21} x^{16}\left(800735133480737687025\theta^4+8446905845515949546700\theta^3+34248485289203789137933\theta^2+62351252711799696042686\theta+42485364821351640163944\right)+2^{17} 3^{23} x^{17}\left(130854593635281335447\theta^4+1470740687678042633052\theta^3+6261882273616975205334\theta^2+11841616915017568640538\theta+8308392497254055969184\right)+2^{15} 3^{25} 23 43 x^{18}(\theta+2)(1044375511951501991\theta^3+10371017408154621546\theta^2+34841428344375119043\theta+39324906832335439780)+2^{16} 3^{29} 5 13 23^{2} 43 x^{19}(\theta+2)(\theta+3)(54356917074933\theta^2+414255137487765\theta+802667272851940)+2^{17} 3^{34} 5^{2} 13^{2} 23^{3} 43^{2} x^{20}(\theta+2)(\theta+3)(\theta+4)(13874987\theta+59815761)+2^{20} 3^{37} 5^{3} 13^{3} 23^{4} 43^{2} 163 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -162, 19710, -2134872, -11551097421/16, ... --> OEIS Normalized instanton numbers (n0=1): 12, -219/2, -73270936/9, 864369416211/512, -257294880950199/1000, ... ; Common denominator:...
\(1+1719z+1404567z^2+725572701z^3+265868554068z^4+73487428596576z^5+15906230508662568z^6+2762406114597811008z^7+391215429129307442976z^8-45665798872080756181248z^9+4422314219437111218274944z^10+356408402046750055533547008z^11+23905779481492695503999027712z^12+1330429645257537748395011567616z^13+610396494807586935900456329951232z^14+2284330751383039846541552834887680z^15+68615965231184830490826918224486400z^16+1614684803424676318995060487706247168z^17+28677036868562929135397434363145650176z^18+361483616787491842925284831575581982720z^19+2882785335303214648482273607706807500800z^20+10936094830042478173776091777549860864000z^21\)
No data for singularities
5
New Number: 21.5 | AESZ: | Superseeker: 68 1294532/3 | Hash: 4366cc0350a0cd6b6cada2d063210cca
Degree: 21
\(3^{42} \theta^4+2^{2} 3^{40} x\left(84\theta^4+2744\theta^3+2767\theta^2+1395\theta+266\right)-2^{7} 3^{38} x^{2}\left(28632\theta^4-64616\theta^3-401808\theta^2-457195\theta-145577\right)-2^{12} 3^{36} x^{3}\left(1796465\theta^4+4387486\theta^3-13907708\theta^2-38720521\theta-16882079\right)-2^{16} 3^{34} x^{4}\left(12888324\theta^4+883132620\theta^3-376920528\theta^2-4705538121\theta-2356225465\right)+2^{20} 3^{32} x^{5}\left(15110087508\theta^4-59416327992\theta^3-93935305179\theta^2+473636919819\theta+276322691378\right)+2^{26} 3^{30} x^{6}\left(368607593226\theta^4+2752098222\theta^3-4203192602301\theta^2+7661991124374\theta+5590781200123\right)+2^{30} 3^{28} x^{7}\left(8976035576583\theta^4+86869344212022\theta^3-352928067611241\theta^2+324848061028908\theta+304756694298380\right)-2^{36} 3^{26} x^{8}\left(287345565585063\theta^4-2058497615772744\theta^3+5114776744081692\theta^2-2723154486628800\theta-3338412865794115\right)-2^{42} 3^{24} x^{9}\left(8086348524095191\theta^4-26542274634468426\theta^3+57031331334711288\theta^2-10359594846687183\theta-28531041907407590\right)-2^{48} 3^{22} x^{10}\left(9138167063224382\theta^4-210786417171295732\theta^3+385718056174963201\theta^2+135920796138151506\theta-109222517440189964\right)-2^{56} 3^{20} x^{11}\left(69459893095336185\theta^4-302456301362585951\theta^3-20357692020292143\theta^2+272843233489824071\theta+56730080742496994\right)+2^{63} 3^{18} x^{12}\left(743025570226011919\theta^4+1722851886386622743\theta^3+4279395328918008662\theta^2+2387785701116330890\theta+460663159312368262\right)+2^{70} 3^{16} x^{13}\left(5328543651426881559\theta^4+12106074639731324439\theta^3+27206670237984316473\theta^2+23454463830806413755\theta+7973392735071986314\right)-2^{77} 3^{14} x^{14}\left(12814290043833983598\theta^4+29486286695176916655\theta^3+54559002172004010549\theta^2+47244767076328000884\theta+16349527240751334310\right)-2^{84} 3^{12} x^{15}\left(11241006670596368517\theta^4+140148225681755811675\theta^3+426004004156158265613\theta^2+568862491428556891473\theta+288735461646223842494\right)-2^{91} 3^{10} x^{16}\left(149313501026215021737\theta^4+1160889124895193502299\theta^3+3499844598801376071558\theta^2+4848134454175048557246\theta+2583172451610721942964\right)-2^{98} 3^{8} x^{17}\left(399191805902016390924\theta^4+3365435815479226427853\theta^3+11022203202943884018777\theta^2+16468321771715730056394\theta+9401073993084275038112\right)-2^{104} 3^{6} x^{18}(\theta+2)(1049708323072676363423\theta^3+7841867367394433134508\theta^2+20281913557507730486849\theta+18053683715529608744540)-2^{113} 3^{4} 5 13 x^{19}(\theta+2)(\theta+3)(2756169614187243177\theta^2+15979386173427193195\theta+24003427310340038070)-2^{125} 3^{2} 5^{2} 13^{2} 277 x^{20}(\theta+2)(\theta+3)(\theta+4)(1612801380441\theta+5372303849908)-2^{135} 5^{3} 13^{3} 197 277^{2} 7477 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -1064/9, 255160/27, -518636416/729, 324919050152/6561, ... --> OEIS Normalized instanton numbers (n0=1): 68, 3884, 1294532/3, 70075068, 14264173344, ... ; Common denominator:...
\(109418989131512359209+4084975594243128077136z-4950731056692878015007744z^2-1104444452859181162116157440z^3-14086368208628838120839970816z^4+29359391068800421521682310627328z^5+5093095342081091319195606592782336z^6+220485263163106300057279729565171712z^7-50192284838132100451263027094405251072z^8-10044362703958757259932921898715614019584z^9-80717274527134170593908162833297627414528z^10-17451749161604119395832822379227954450268160z^11+2655070586111688069582739058208370586894204928z^12+270799775431202616087302711154595543168409665536z^13-9261936133799538427872587248902083856235877105664z^14-115552646865652918948418180372226694538155159191552z^15-21829371470305145024674994388194566220201357815578624z^16-830025110000015829298726502169762402902552084496777216z^17-15520857732060386886664917231765204268675241738734927872z^18-150693259232882498736033526949465598164668992007710965760z^19-722569018226175667213867459118067348751195156761909657600z^20-1351893965595951422473559533993541733676791231112282112000z^21\)
No data for singularities
6
New Number: 21.6 | AESZ: | Superseeker: -212 -9541288/3 | Hash: 8c1981dec801ba472f74dbd4aeb1e449
Degree: 21
\(3^{42} \theta^4+3^{40} x\left(11193\theta^4+17122\theta^3+11972\theta^2+3411\theta+358\right)+3^{38} x^{2}\left(17172543\theta^4+13944124\theta^3-7448961\theta^2-6698818\theta-1352912\right)+3^{36} x^{3}\left(7623986411\theta^4-1406689790\theta^3-4679143919\theta^2-2135598238\theta-309764480\right)+2^{2} 3^{34} x^{4}\left(107300539503\theta^4-250019955888\theta^3-258789849609\theta^2-85308330798\theta-6426153128\right)+2^{3} 3^{32} x^{5}\left(615466867905\theta^4-5615254012620\theta^3+477267402663\theta^2+5125873486044\theta+2004799055444\right)-2^{3} 3^{30} x^{6}\left(15179183204277\theta^4+44327693386848\theta^3-101837397904755\theta^2-6726284681610\theta+27866254625560\right)-2^{5} 3^{28} x^{7}\left(64186722819243\theta^4-215754980857932\theta^3-92042840400945\theta^2-18216499975542\theta-32264096279540\right)+2^{5} 3^{26} x^{8}\left(386629194544875\theta^4+2319591699806988\theta^3+894830654246679\theta^2+1892551732716642\theta+1120700575307192\right)+2^{7} 3^{24} x^{9}\left(1616015182940627\theta^4+1217853262464366\theta^3+2967631110001839\theta^2+3597366366918852\theta+1388109125074832\right)-2^{7} 3^{22} x^{10}\theta(1592969834664357\theta^3+19162710148196200\theta^2+22132017876039581\theta+182212539198009351879059498022480)-2^{10} 3^{20} x^{11}\left(6626709287214126\theta^4+26341224632123156\theta^3+71345263693353519\theta^2+90785623377229237\theta+42741564797848648\right)-2^{9} 3^{18} x^{12}\left(3871549560900\theta^4+326347669405541116\theta^3+1223711819698189381\theta^2+1839544688669958974\theta+966922025175624248\right)-2^{11} 3^{16} x^{13}\left(511314534419823\theta^4+193078136631892056\theta^3+912641397626713341\theta^2+1538845851584694384\theta+801897116393286272\right)+2^{11} 3^{14} x^{14}\left(162587482061140953\theta^4+1273206406385294760\theta^3+39650017967829652441\theta^2+5933358408898247118\theta+3857065877910470776\right)+2^{13} 3^{12} x^{15}\left(178957592048590095\theta^4+1855851103326597780\theta^3+6561834904460773839\theta^2+9926113364829701826\theta+5612697385389169816\right)-2^{13} 3^{10} x^{16}\left(227688589006017975\theta^4+2324715144518515764\theta^3+11081138940427797627\theta^2+23708402425378557378\theta+18162481390963839512\right)-2^{15} 3^{8} x^{17}\left(3860746249068313034881961590591083591572437149\theta^4+32548498012709213796585886344618269624195842578\theta^3+106600208328623406852081322203232349063701235267\theta^2+159271835164391048103635375699061089168021192514\theta+90921608658777455089535106580461128011022197752\right)+2^{15} 3^{6} 23 43 x^{18}(\theta+2)(352841632605151\theta^3+4603243815261546\theta^2+17376223714542763\theta+20363935534606180)+2^{16} 3^{4} 5 13 23^{2} 43 x^{19}(\theta+2)(\theta+3)(445250285823\theta^2+1903543123055\theta+1680093208380)-2^{17} 3^{2} 5^{2} 13^{3} 23^{2} 43^{2} x^{20}(\theta+2)(\theta+3)(\theta+4)(5162559\theta+15500717)+2^{20} 5^{3} 13^{3} 23^{4} 43^{2} 163 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -358/9, 356770/27, -4831185272/729, 26637349891226/6561, ... --> OEIS Normalized instanton numbers (n0=1): -212, 35981/2, -9541288/3, 1723495053/2, -290947666260, ... ; Common denominator:...
\(109418989131512359209+136080749483224204069593z+23197559208363316587012327z^2+1144319459868322247582944731z^3+7157882375055125475651900828z^4+9123780254378993426904504840z^5-25002073713605386261324910184z^6-46988362761597801888691664736z^7+31448305211135448961176444000z^8+58420533640215001875649739136z^9-6398602411128455875156020864z^10-23660448330362924322456090624z^11-767957823524665999411200z^12-45077328089937955943184384z^13+1592629015524338243234727936z^14+779103450528929945001123840z^15-110139666368236383484108800z^16-830025110000015829298726502264605882591043916090212352z^17+8335920762627502018756608z^18+3494673773019600451338240z^19-327175001077900728729600z^20+24287110169755516928000z^21\)
No data for singularities
7
New Number: 21.7 | AESZ: | Superseeker: 256 92084530550528/1594323 | Hash: 867d38cda894ef7022e4a26a9ab51f9f
Degree: 21
\(3^{42} \theta^4+2^{4} 3^{40} x\left(516\theta^4+56\theta^3+262\theta^2+234\theta+53\right)+2^{10} 3^{38} x^{2}\left(5106\theta^4+77152\theta^3+115008\theta^2+53996\theta+10861\right)-2^{16} 3^{40} x^{3}\left(936845\theta^4-4862594\theta^3-5824256\theta^2-8099077\theta-2757908\right)-2^{22} 3^{34} x^{4}\left(11529576\theta^4+128964300\theta^3-338189406\theta^2-493244082\theta-182618887\right)-2^{26} 3^{32} x^{5}\left(500514588\theta^4+18229970928\theta^3+12869733114\theta^2-52250982762\theta-29243697797\right)+2^{32} 3^{30} x^{6}\left(86560500054\theta^4-79326171672\theta^3-986791026876\theta^2+439137932532\theta+488195215531\right)+2^{38} 3^{28} x^{7}\left(1126031723163\theta^4+9599969470422\theta^3-4059316985772\theta^2+4912598573685\theta+5496269008325\right)-2^{44} 3^{26} x^{8}\left(26677160172243\theta^4-72478573381464\theta^3-50709683505690\theta^2-116036907294126\theta-81695413665157\right)-2^{50} 3^{24} x^{9}\left(431886524515891\theta^4+1240446363892854\theta^3+2665632295542705\theta^2+2481050505590616\theta+793903531758358\right)+2^{56} 3^{22} x^{10}\left(700712967968889\theta^4-2709756882427628\theta^3-14639173981543549\theta^2-26780589781572636\theta-15474398827136332\right)+2^{64} 3^{20} x^{11}\left(9898193420281905\theta^4+42920851850724761\theta^3+100622451838922220\theta^2+106744748333244562\theta+42463347175147072\right)+2^{71} 3^{18} x^{12}\left(24722907630742609\theta^4+116310833106402953\theta^3+330693823126018751\theta^2+466707603794972107\theta+257649103796643160\right)-2^{78} 3^{16} x^{13}\left(19649143340698131\theta^4+263671869154614351\theta^3+783324331440747042\theta^2+957472432148435814\theta+405300703763246138\right)-2^{85} 3^{14} x^{14}\left(244173068128534842\theta^4+2109126155081437095\theta^3+6637545711572260536\theta^2+94473006524713146265\theta+5150239951425584630\right)-2^{92} 3^{12} x^{15}\left(662899060891147947\theta^4+5734208452224329925\theta^3+18889404120939619698\theta^2+28390701290585380086\theta+16344452904891135644\right)-2^{99} 3^{10} x^{16}\left(1034136762175706067\theta^4+9302313907380436869\theta^3+32246016992803951179\theta^2+50845900556017658043\theta+3056089659265081906\right)-2^{106} 3^{8} x^{17}\left(1048654195870794174\theta^4+9991274965314101103\theta^3+36648985530772085517\theta^2+60817854421932015714\theta+38203485567226156952\right)-2^{112} 3^{6} x^{18}(\theta+2)(1401903453377697173\theta^3+11608617239437549508\theta^2+33186295023097225499\theta+32514799580697886340)-2^{121} 3^{4} 5 13 x^{19}(\theta+2)(\theta+3)(2277036191931927\theta^2+14321540957911945\theta+23373087372373470)-2^{132} 3^{2} 5^{2} 13^{2} 71 x^{20}(\theta+2)(\theta+3)(\theta+4)(7392016434\theta+26196344467)-2^{141} 5^{3} 13^{3} 47 71^{2} 877 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -848/9, 85168/27, -14454504603904/59049, 70939732324154384/531441, ... --> OEIS Normalized instanton numbers (n0=1): 256, -9340, 92084530550528/1594323, 697835016403112/177147, -1369272606998167491328/553584375, ... ; Common denominator:...
\(109418989131512359209+100373686029974004181056z+7062987643328816748988416z^2-746445084884348991083173969920z^3-806484270633146937800367538176z^4-62241031038694461573972898086912z^5+76545076159698125965612647098351616z^6+7080853241444582705320959087835348992z^7-1192921945893666868689298334584198397952z^8-137334468194573202747289452444424605794304z^9+1584482751944740171190741737051117464846336z^10+636650014024597676983282152085695920320020480z^11+22615793151499527393361507911408803437502005248z^12-255636791542251327762520748396465746061341753344z^13-45179868010266816932930894687697602012787335233536z^14-1744464200926051551190999129642204860103559366049792z^15-38704378215196897440953113468678900380771626677960704z^16-558189775343935223698486750397954445984347656915255296z^17-5306463095870822405952683199628214450686875958857695232z^18-31871153671791561476249434669565357463801575225488834560z^19-108655051712081260364593415600946897254348546192808345600z^20-159068288132124951306641350126931982587192100018716672000z^21\)
No data for singularities
8
New Number: 21.8 | AESZ: | Superseeker: 368 2223792 | Hash: 0384d7d9b55b9bb00bc5b7da443b2b67
Degree: 21
\(3^{42} \theta^4-2^{4} 3^{40} x\left(33\theta^4+1282\theta^3+839\theta^2+198\theta+16\right)-2^{8} 3^{38} x^{2}\left(165867\theta^4+256436\theta^3-66903\theta^2+12394\theta+16781\right)-2^{12} 3^{36} x^{3}\left(16894271\theta^4-177350\theta^3+50437558\theta^2+29161169\theta+5410228\right)+2^{18} 3^{34} x^{4}\left(406954548\theta^4-692255868\theta^3-581398986\theta^2-613195209\theta-217105625\right)-2^{21} 3^{32} x^{5}\left(13270775040\theta^4-76099518120\theta^3-2159096391\theta^2+65325040851\theta+28609334834\right)-2^{25} 3^{30} x^{6}\left(201841036653\theta^4+789469404672\theta^3-911224910913\theta^2+338527864212\theta+513077007046\right)+2^{30} 3^{28} x^{7}\left(2452509522369\theta^4-3673794538626\theta^3+1414207510998\theta^2-2041380320589\theta-2618785893082\right)+2^{35} 3^{26} x^{8}\left(3428263912050\theta^4+31018531109052\theta^3+55743885033885\theta^2+68072262812187\theta+28762665057794\right)-2^{39} 3^{24} x^{9}\left(134770503023432\theta^4+44220786514246\theta^3+854897543075037\theta^2+735106407627921\theta+239794954141160\right)+2^{43} 3^{22} x^{10}\left(285561396899733\theta^4-425722186789840\theta^3-3778537247395403\theta^2-6783090182323578\theta-3851365537124480\right)+2^{49} 3^{20} x^{11}\left(1988751429822117\theta^4+12663345850205017\theta^3+33813066815088828\theta^2+40424098952384816\theta+17898103572371030\right)-2^{54} 3^{18} x^{12}\left(2375893329099175\theta^4+12141859980769613\theta^3+20882006811668477\theta^2+746336887550535\theta+7797657410473724\right)-2^{59} 3^{16} x^{13}\left(13698727730250867\theta^4+105232724265125469\theta^3+307085244169131249\theta^2+401472251506540701\theta+201379032870113398\right)-2^{64} 3^{14} x^{14}\left(9392821253669106\theta^4+112683603426739545\theta^3+458013328942563855\theta^2+776829395241861720\theta+478305324329040970\right)+2^{69} 3^{12} x^{15}\left(486469944983265\theta^4+436375240170765\theta^3-11687299408814358\theta^2-35566272536551548\theta-29472768107383732\right)+2^{74} 3^{10} 13 x^{16}\left(600119354060505\theta^4+4924983621391941\theta^3+11173426471596111\theta^2+6029141449355253\theta-3475484736360946\right)+2^{79} 3^{8} 13^{2} x^{17}\left(6735475996983\theta^4+159804937427151\theta^3+687186728894484\theta^2+1071141829643598\theta+553233267862004\right)-2^{83} 3^{6} 13^{3} x^{18}(\theta+2)(910795566793\theta^3-858565445972\theta^2-1700009105341\theta-24193158545360)-2^{90} 3^{4} 5 13^{4} x^{19}(\theta+2)(\theta+3)(1924297932\theta^2+4015747745\theta-3880807755)-2^{95} 3^{2} 5^{2} 7 13^{5} x^{20}(\theta+2)(\theta+3)(\theta+4)(1470387\theta+3085381)+2^{102} 5^{3} 7^{2} 13^{6} 151 x^{21}(\theta+2)(\theta+3)(\theta+4)(\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 256/9, 291568/27, 3099047936/729, 13359907507472/6561, ... --> OEIS Normalized instanton numbers (n0=1): 368, -6434, 2223792, 7045475, 63017278672, ... ; Common denominator:...
\(109418989131512359209-6419247362382058406928z-57359800794948141779497728z^2-10386388764072626736888999936z^3+1779133301522872490552409980928z^4-51571094340671578415245327073280z^5-1394430910417966287996514209890304z^6+60242877029170935272131685636898816z^7+299417181579863302735177813957017600z^8-20925449387456831041266346069428535296z^9+78823717835155979893098714129368088576z^10+3903690581286269245634770173195246895104z^11-16581708989186520720128949742516096204800z^12-339930437804806825769634688310498574729216z^13-828730545260757004638032051759263801933824z^14+152609219552727848206463256168646972538880z^15+8701882439614489248472354860957845988311040z^16+4514344443886463107924979750295490302836736z^17-14108087138219983140836691252839143515881472z^18-27554996191247608648332067821897578383933440z^19-34062660196370463082935944573128239847833600z^20+22636157752673954488208327407288564318208000z^21\)
No data for singularities