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You searched for: inst=19810

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1

New Number: 13.16 |  AESZ:  |  Superseeker: 5 581/3  |  Hash: 2ab5512d2cfda3cde6ee0ea98a12d6fb  

Degree: 13

\(\theta^4-x\left(106\theta^4+140\theta^3+125\theta^2+55\theta+10\right)+x^{2}\left(2472+4265\theta^4+12596\theta^3+15925\theta^2+9718\theta\right)-2^{3} x^{3}\left(9346\theta^4+58443\theta^3+105118\theta^2+80373\theta+24412\right)+2^{4} 3 x^{4}\left(1747\theta^4+173306\theta^3+488163\theta^2+460544\theta+161900\right)+2^{6} 3 x^{5}\left(108841\theta^4-198029\theta^3-1835967\theta^2-2248271\theta-919518\right)-2^{8} 3 x^{6}\left(510411\theta^4+1710438\theta^3-2652339\theta^2-5816622\theta-2956384\right)+2^{12} 3 x^{7}\left(213944\theta^4+2327365\theta^3+1622852\theta^2-837189\theta-1027734\right)+2^{10} 3 x^{8}\left(4640003\theta^4-76516006\theta^3-140342311\theta^2-92680566\theta-16297224\right)-2^{13} x^{9}\left(56543147\theta^4-21416544\theta^3-251991507\theta^2-314165376\theta-118113840\right)+2^{16} x^{10}\left(70691941\theta^4+213840362\theta^3+253613996\theta^2+121602823\theta+15102754\right)-2^{19} 73 x^{11}(\theta+1)(680053\theta^3+2794143\theta^2+4238129\theta+2311527)+2^{22} 73^{2} x^{12}(\theta+2)(\theta+1)(3707\theta^2+13713\theta+13693)-2^{25} 3^{2} 73^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 10, 118, 1864, 38566, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, -53/4, 581/3, -1231, 19810, ... ; Common denominator:...

Discriminant

\(-(9z-1)(8z-1)(4672z^3-840z^2+57z-1)(64z^2-8z+1)(1-12z-192z^2+2336z^3)^2\)

Local exponents

≈\(-0.071938\)\(0\) ≈\(0.026164\)\(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 3}I\)\(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 3}I\) ≈\(0.076815-0.047751I\) ≈\(0.076815+0.047751I\) ≈\(0.077065-0.003429I\) ≈\(0.077065+0.003429I\)\(\frac{ 1}{ 9}\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(3\)\(3\)\(1\)\(1\)\(2\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(2\)\(2\)\(4\)\(4\)\(2\)\(2\)\(3\)

Note:

This is operator "13.16" from ...

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2

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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