Summary

You searched for: inst=5

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1

New Number: 2.62 |  AESZ: 28  |  Superseeker: 5 312  |  Hash: 06dd455cafc5097e4f671d385984c1a2  

Degree: 2

\(\theta^4-x\left(65\theta^4+130\theta^3+105\theta^2+40\theta+6\right)+2^{2} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)\)

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Coefficients of the holomorphic solution: 1, 6, 126, 3948, 149310, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 28, 312, 4808, 91048, ... ; Common denominator:...

Discriminant

\((64z-1)(z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 64}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 5}{ 4}\)

Note:

A-incarnation: $X(1, 1, 1, 1, 1, 1) \subset Grass(3, 6)$

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2

New Number: 2.69 |  AESZ: 205  |  Superseeker: 1 5  |  Hash: 4fb2e7002e630237d0458c3985cd6a18  

Degree: 2

\(\theta^4-x\left(59\theta^4+118\theta^3+105\theta^2+46\theta+8\right)+2^{5} 3 x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)\)

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Coefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...

Discriminant

\((32z-1)(27z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "2.69" from ...

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3

New Number: 3.8 |  AESZ: ~100  |  Superseeker: 5 454  |  Hash: 82a1ac6ac6fb9ab2e4d6b5d5790d1d9b  

Degree: 3

\(\theta^4+x\left(15\theta^4+30\theta^3+35\theta^2+20\theta+4\right)-2^{5} x^{2}(\theta+1)^2(66\theta^2+132\theta+53)-2^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, -4, 132, -1120, 72100, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 42, 454, 7498, 154351, ... ; Common denominator:...

Discriminant

\(-(49z-1)(1+32z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 1}{ 49}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(2\)
\(1\)\(0\)\(2\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 100= $ a \ast a$

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4

New Number: 4.30 |  AESZ: 281  |  Superseeker: 5 -420  |  Hash: d24d5f19c8a8bf23ea9abd62ea9242b2  

Degree: 4

\(\theta^4+x\left(164\theta^4+328\theta^3+402\theta^2+238\theta+109/2\right)+x^{2}\left(12974\theta^4+51896\theta^3+200863/2\theta^2+97071\theta+151081/4\right)+5 x^{3}\left(102500\theta^4+615000\theta^3+1476125\theta^2+1660875\theta+728918\right)+x^{4}15625/16(10\theta+17)(10\theta+19)(10\theta+21)(10\theta+23)\)

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Coefficients of the holomorphic solution: 1, -109/2, 13447/8, 58747/16, -556301557/128, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 95/4, -420, 2555, 19930, ... ; Common denominator:...

Discriminant

\((1+82z+3125z^2)^2\)

Local exponents

\(-\frac{ 41}{ 3125}-\frac{ 38}{ 3125}I\)\(-\frac{ 41}{ 3125}+\frac{ 38}{ 3125}I\)\(0\)\(s_1\)\(s_2\)\(\infty\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 17}{ 10}\)
\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(\frac{ 19}{ 10}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 21}{ 10}\)
\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 23}{ 10}\)

Note:

Sporadic YY-Operator

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5

New Number: 10.7 |  AESZ:  |  Superseeker: 4 -628/9  |  Hash: d5910f048831bb407eb8998c7c57e09f  

Degree: 10

\(\theta^4-2^{2} x\left(48\theta^4+48\theta^3+45\theta^2+21\theta+4\right)+2^{6} x^{2}\left(261\theta^4+489\theta^3+590\theta^2+364\theta+93\right)-2^{6} x^{3}\left(13530\theta^4+35628\theta^3+50795\theta^2+36813\theta+10853\right)+2^{8} 3 x^{4}\left(38616\theta^4+128020\theta^3+206502\theta^2+165712\theta+53013\right)-2^{10} x^{5}\left(685404\theta^4+2714928\theta^3+4854121\theta^2+4193537\theta+1415126\right)+2^{13} x^{6}\left(1419108\theta^4+6542898\theta^3+12841310\theta^2+11823966\theta+4167463\right)-2^{14} x^{7}\left(8117226\theta^4+43045764\theta^3+92299521\theta^2+90336771\theta+33184985\right)+2^{16} x^{8}\left(15319683\theta^4+93106380\theta^3+218052374\theta^2+226725820\theta+86734943\right)-2^{19} 5^{2} x^{9}(2\theta+3)(171838\theta^3+939735\theta^2+1668155\theta+905358)+2^{22} 3 5^{4} 17^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 16, 292, 5728, 115012, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...

Discriminant

\((12z-1)(18496z^3-2352z^2+84z-1)(16z-1)^2(400z^2-32z+1)^2\)

Local exponents

\(0\) ≈\(0.024764-0.009119I\) ≈\(0.024764+0.009119I\)\(\frac{ 1}{ 25}-\frac{ 3}{ 100}I\)\(\frac{ 1}{ 25}+\frac{ 3}{ 100}I\)\(\frac{ 1}{ 16}\) ≈\(0.077634\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(3\)

Note:

This is operator "10.7" from ...

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6

New Number: 12.6 |  AESZ:  |  Superseeker: 5 953/3  |  Hash: 4ea78627bfc56ef9555d9b6b3c949e7a  

Degree: 12

\(\theta^4-x\theta(5\theta^3+46\theta^2+29\theta+6)-2 3 x^{2}\left(258\theta^4+1038\theta^3+1387\theta^2+818\theta+192\right)-2^{2} 3^{3} x^{3}\left(381\theta^4+1664\theta^3+2804\theta^2+2126\theta+624\right)-2^{4} 3^{3} x^{4}\left(1231\theta^4+5927\theta^3+11019\theta^2+9266\theta+3000\right)-2^{4} 3^{4} x^{5}\left(2621\theta^4+16730\theta^3+39069\theta^2+35141\theta+11748\right)-2^{5} 3^{5} x^{6}\left(150\theta^4+11268\theta^3+45560\theta^2+50253\theta+18756\right)+2^{6} 3^{7} x^{7}\left(1024\theta^4+800\theta^3-8483\theta^2-13641\theta-6108\right)+2^{8} 3^{7} x^{8}\left(1724\theta^4+6608\theta^3+1047\theta^2-7027\theta-4488\right)+2^{11} 3^{8} x^{9}\left(74\theta^4+1416\theta^3+1889\theta^2+687\theta-81\right)-2^{13} 3^{10} x^{10}\left(26\theta^4-16\theta^3-125\theta^2-128\theta-39\right)-2^{14} 3^{11} x^{11}(\theta+1)(16\theta^3+40\theta^2+31\theta+6)-2^{16} 3^{11} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 0, 72, 1344, 48600, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 83/2, 953/3, 5319, 97812, ... ; Common denominator:...

Discriminant

\(-(4z+1)(12z+1)(3z+1)(1728z^3+864z^2+36z-1)(-1-6z-36z^2+432z^3)^2\)

Local exponents

≈\(-0.450956\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 12}\) ≈\(-0.067934\) ≈\(-0.061146-0.08671I\) ≈\(-0.061146+0.08671I\)\(0\) ≈\(0.01889\) ≈\(0.205625\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(2\)\(2\)\(2\)\(4\)\(4\)\(0\)\(2\)\(4\)\(2\)

Note:

This is operator "12.6" from ...

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7

New Number: 13.10 |  AESZ:  |  Superseeker: 4 -628/9  |  Hash: 2a9fda379889eb2fd218bd01f2520f7a  

Degree: 13

\(\theta^4-2^{2} x\left(35\theta^4+38\theta^3+35\theta^2+16\theta+3\right)+2^{4} x^{2}\left(546\theta^4+1068\theta^3+1287\theta^2+790\theta+201\right)-2^{6} x^{3}\left(4928\theta^4+12888\theta^3+17829\theta^2+12673\theta+3693\right)+2^{8} x^{4}\left(28123\theta^4+88408\theta^3+131977\theta^2+98226\theta+29511\right)-2^{10} 3^{2} x^{5}\left(11315\theta^4+41094\theta^3+65088\theta^2+47691\theta+13532\right)+2^{13} 3^{2} x^{6}\left(11674\theta^4+48674\theta^3+79399\theta^2+52683\theta+11716\right)-2^{15} 3^{3} x^{7}\left(2063\theta^4+11102\theta^3+11184\theta^2-9217\theta-10762\right)-2^{17} 3^{4} x^{8}\left(3277\theta^4+16284\theta^3+42329\theta^2+57018\theta+27266\right)+2^{20} 3^{5} x^{9}\left(1124\theta^4+7114\theta^3+18121\theta^2+22265\theta+10018\right)+2^{24} 3^{6} x^{10}(\theta+1)(\theta^3-105\theta^2-277\theta-267)-2^{25} 3^{7} x^{11}(\theta+1)(\theta+2)(93\theta^2+441\theta+607)+2^{27} 3^{10} x^{12}(\theta+3)(\theta+2)(\theta+1)(\theta+6)+2^{30} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 180, 2928, 47556, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...

Discriminant

\((8z-1)(10368z^3-1728z^2+72z-1)(12z-1)^2(288z^2-24z+1)^2(4z+1)^3\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\) ≈\(0.027033-0.011216I\) ≈\(0.027033+0.011216I\)\(\frac{ 1}{ 24}-\frac{ 1}{ 24}I\)\(\frac{ 1}{ 24}+\frac{ 1}{ 24}I\)\(\frac{ 1}{ 12}\) ≈\(0.112601\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(2\)
\(\frac{ 3}{ 2}\)\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(4\)

Note:

This is operator "13.10" from ...

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8

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

Degree: 13

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

Maple   LaTex

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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9

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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