Summary

You searched for: inst=3

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1

New Number: 3.29 |  AESZ: 411  |  Superseeker: 3 237  |  Hash: 767c4e8d5a7bc53fbbd0d49797e65358  

Degree: 3

\(\theta^4-x\left(16+98\theta+235\theta^2+274\theta^3+145\theta^4\right)+2^{3} x^{2}(2\theta+1)(4\theta+5)(97\theta^2+190\theta+120)-2^{4} 3^{4} x^{3}(4\theta+5)(2\theta+3)(2\theta+1)(4\theta+9)\)

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Coefficients of the holomorphic solution: 1, 16, 468, 17520, 774060, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 36, 237, 4638, 72330, ... ; Common denominator:...

Discriminant

\(-(81z-1)(-1+32z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 4}\)\(\frac{ 5}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(2\)\(\frac{ 5}{ 4}\)\(\frac{ 9}{ 4}\)

Note:

This is operator "3.29" from ...

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2

New Number: 5.3 |  AESZ: 20  |  Superseeker: 3 245/3  |  Hash: a9a698dc5c79ffda497a7897390408b0  

Degree: 5

\(\theta^4-3 x\left(48\theta^4+60\theta^3+53\theta^2+23\theta+4\right)+3^{2} x^{2}\left(873\theta^4+1980\theta^3+2319\theta^2+1344\theta+304\right)-2 3^{4} x^{3}\left(1269\theta^4+3888\theta^3+5259\theta^2+3348\theta+800\right)+2^{2} 3^{6} x^{4}\left(891\theta^4+3240\theta^3+4653\theta^2+2952\theta+688\right)-2^{3} 3^{11} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

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Coefficients of the holomorphic solution: 1, 12, 252, 6600, 198540, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 33/2, 245/3, 879, 11829, ... ; Common denominator:...

Discriminant

\(-(54z-1)(27z-1)^2(18z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 54}\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 18}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(\frac{ 1}{ 3}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 2}{ 3}\)\(3\)\(1\)
\(0\)\(2\)\(1\)\(4\)\(\frac{ 4}{ 3}\)

Note:

A-Incarnation: (3,0),(0,3),(1,1) intersection in $P^3 \times \P^3$.

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3

New Number: 6.18 |  AESZ:  |  Superseeker: 3 64  |  Hash: b127e33287ed87a366c178fc4678cdc4  

Degree: 6

\(\theta^4-x\left(18+94\theta+199\theta^2+210\theta^3+105\theta^4\right)+2 x^{2}\left(2095\theta^4+8380\theta^3+13298\theta^2+9836\theta+2850\right)-2^{2} 3^{2} x^{3}\left(2310\theta^4+13860\theta^3+30739\theta^2+29847\theta+10763\right)+2^{3} 3^{3} x^{4}\left(4044\theta^4+32352\theta^3+91997\theta^2+109172\theta+45693\right)-2^{4} 3^{3} 5^{2} 7 x^{5}(\theta+4)(\theta+1)(61\theta^2+305\theta+345)+2^{5} 3^{5} 5^{2} 7^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, 18, 348, 7320, 168840, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...

Discriminant

\((6z-1)(15z-1)(14z-1)(42z-1)(18z-1)(10z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 42}\)\(\frac{ 1}{ 18}\)\(\frac{ 1}{ 15}\)\(\frac{ 1}{ 14}\)\(\frac{ 1}{ 10}\)\(\frac{ 1}{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(4\)
\(0\)\(2\)\(2\)\(2\)\(2\)\(2\)\(2\)\(5\)

Note:

This is operator "6.18" from ...

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4

New Number: 7.3 |  AESZ:  |  Superseeker: 3 64  |  Hash: 8413250555ca536f1bdccfeed506ea4e  

Degree: 7

\(\theta^4+x\theta(39\theta^3-30\theta^2-19\theta-4)+2 x^{2}\left(16\theta^4-1070\theta^3-1057\theta^2-676\theta-192\right)-2^{2} 3^{2} x^{3}(3\theta+2)(171\theta^3+566\theta^2+600\theta+316)-2^{5} 3^{3} x^{4}\left(384\theta^4+1542\theta^3+2635\theta^2+2173\theta+702\right)-2^{6} 3^{3} x^{5}(\theta+1)(1393\theta^3+5571\theta^2+8378\theta+4584)-2^{10} 3^{5} x^{6}(\theta+1)(\theta+2)(31\theta^2+105\theta+98)-2^{12} 3^{7} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 0, 24, 192, 3384, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, -4, 64, -253, 4292, ... ; Common denominator:...

Discriminant

\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(1+18z)^2\)

Local exponents

\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 12}\)\(-\frac{ 1}{ 18}\)\(0\)\(\frac{ 1}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(2\)
\(1\)\(1\)\(1\)\(1\)\(3\)\(0\)\(1\)\(2\)
\(2\)\(2\)\(2\)\(2\)\(4\)\(0\)\(2\)\(3\)

Note:

This is operator "7.3" from ...

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5

New Number: 8.18 |  AESZ: 197  |  Superseeker: 3 1621/13  |  Hash: 4cc8bdba73e5fa6cb4089fa5296429de  

Degree: 8

\(13^{2} \theta^4-13^{2} x\left(41\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-2^{3} 13 x^{2}\left(471\theta^4+1788\theta^3+2555\theta^2+1534\theta+338\right)+2^{6} 13 x^{3}\left(251\theta^4+1014\theta^3+1798\theta^2+1413\theta+405\right)+2^{9} x^{4}\left(749\theta^4+436\theta^3-4908\theta^2-6266\theta-2145\right)-2^{12} x^{5}\left(379\theta^4+1270\theta^3+967\theta^2-42\theta-178\right)-2^{15} x^{6}\left(9\theta^4-156\theta^3-273\theta^2-156\theta-28\right)+2^{18} x^{7}\left(13\theta^4+26\theta^3+20\theta^2+7\theta+1\right)-2^{21} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 4, 68, 1552, 43156, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 226/13, 1621/13, 20666/13, 289056/13, ... ; Common denominator:...

Discriminant

\(-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2\)

Local exponents

\(-\frac{ 1}{ 8}\sqrt{ 13}\)\(-\frac{ 1}{ 8}\)\(0\)\(\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}\)\(\frac{ 1}{ 8}\sqrt{ 13}\)\(\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(4\)\(2\)\(2\)\(1\)

Note:

The operator has a second MUM-point at infinity, corresponding to operator 8.19.

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6

New Number: 8.24 |  AESZ: 286  |  Superseeker: 3 437/3  |  Hash: 94afcd38a40c3a3e54fc3c57b4b85459  

Degree: 8

\(3^{2} \theta^4-3^{2} x\left(38\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-3 x^{2}\left(2045\theta^4+5702\theta^3+7535\theta^2+4170\theta+852\right)+2^{3} 3 x^{3}\left(2208\theta^4+5925\theta^3+7925\theta^2+5607\theta+1512\right)+2^{3} x^{4}\left(60287\theta^4+56374\theta^3-215983\theta^2-268986\theta-85452\right)-2^{4} x^{5}\left(205651\theta^4+605608\theta^3+603579\theta^2+204622\theta+8104\right)-2^{7} x^{6}\left(51414\theta^4-273267\theta^3-502700\theta^2-305649\theta-63398\right)+2^{8} 37 x^{7}\left(7909\theta^4+18122\theta^3+17595\theta^2+8462\theta+1672\right)-2^{13} 37^{2} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)\)

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Coefficients of the holomorphic solution: 1, 4, 72, 1696, 49960, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 539/24, 437/3, 18531/8, 90274/3, ... ; Common denominator:...

Discriminant

\(-(-1+40z+504z^2-3088z^3+8192z^4)(-3-3z+148z^2)^2\)

Local exponents

\(\frac{ 3}{ 296}-\frac{ 1}{ 296}\sqrt{ 1785}\) ≈\(-0.070843\)\(0\) ≈\(0.020383\)\(\frac{ 3}{ 296}+\frac{ 1}{ 296}\sqrt{ 1785}\) ≈\(0.213707\) ≈\(0.213707\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 5}{ 4}\)

Note:

This is operator "8.24" from ...

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7

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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8

New Number: 24.1 |  AESZ:  |  Superseeker: 3 1322/9  |  Hash: d77f5cce80101a4e8f097ff7dc1cac1f  

Degree: 24

\(\theta^4-3 x\theta(8\theta^2+5\theta+1)-3^{2} x^{2}\left(141\theta^4-76\theta^3-53\theta^2+74\theta+48\right)+3^{3} x^{3}\left(350\theta^4+268\theta^3-911\theta^2+193\theta+366\right)+2^{2} 3^{4} x^{4}\left(1536\theta^4-210\theta^3+5498\theta^2+3259\theta+432\right)-3^{6} x^{5}\left(9982\theta^4-4940\theta^3+26473\theta^2+14567\theta+72\right)-3^{7} x^{6}\left(13329\theta^4+128212\theta^3+141347\theta^2+176702\theta+93936\right)+3^{8} x^{7}\left(179988\theta^4+489272\theta^3+581261\theta^2+545387\theta+236754\right)-3^{9} x^{8}\left(473261\theta^4-322200\theta^3-1952576\theta^2-2540184\theta-1052928\right)+2 3^{11} x^{9}\left(89272\theta^4-647728\theta^3-1032101\theta^2-477573\theta+275604\right)+2 3^{12} x^{10}\left(380267\theta^4+3534580\theta^3+6813301\theta^2+7672754\theta+3370032\right)-2 3^{13} x^{11}\left(2824394\theta^4+21447564\theta^3+70086871\theta^2+111632667\theta+67101174\right)+2^{3} 3^{15} x^{12}\left(604658\theta^4+4211064\theta^3+13816867\theta^2+20606976\theta+11731242\right)-2 3^{16} x^{13}\left(2513086\theta^4-1029540\theta^3-71899267\theta^2-199754241\theta-151321716\right)-2 3^{17} x^{14}\left(4936477\theta^4+113054700\theta^3+624917375\theta^2+1236797682\theta+810302688\right)+2 3^{19} x^{15}\left(10447060\theta^4+141814160\theta^3+623159411\theta^2+1236797682\theta+658549626\right)-3^{21} x^{16}\left(15883703\theta^4+190281632\theta^3+7662783992\theta^2+1272288312\theta+742283280\right)+3^{24} x^{17}\left(2257088\theta^4+24107672\theta^3+94611213\theta^2+157783505\theta+93169704\right)-3^{25} x^{18}\left(1409659\theta^4+13667804\theta^3+60904285\theta^2+118238478\theta+79019856\right)-3^{27} x^{19}\left(372282\theta^4+2964756\theta^3+4412579\theta^2-3409349\theta-6851134\right)+2^{2} 3^{29} x^{20}\left(79892\theta^4+648390\theta^3+1698852\theta^2+1619127\theta+396380\right)-3^{31} x^{21}\left(42578\theta^4+351292\theta^3+908415\theta^2+928057\theta+321472\right)-3^{33} x^{22}\left(10861\theta^4+68980\theta^3+157607\theta^2+161390\theta+65296\right)+3^{35} 5 x^{23}\left(444\theta^4+2616\theta^3+5783\theta^2+5673\theta+2078\right)+3^{37} 5^{2} x^{24}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 0, 27, -36, 891, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, -24, 1322/9, -1824, 19551, ... ; Common denominator:...

Discriminant

\((9z-1)(81z^2-9z-1)(6561z^6+66339z^5-16767z^4+2106z^3-297z^2+27z-1)(9z+1)^2(32805z^5+12393z^4-324z^3+432z^2-9z-1)^2(3z-1)^3\)

No data for singularities

Note:

This is operator "24.1" from ...

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