Summary

You searched for: Spectrum0=2/3,1,1,4/3

Your search produced 11 matches

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1

New Number: 2.50 |  AESZ:  |  Superseeker: -201888 -40177844666400  |  Hash: 5309f0b5a4362f22faafad07a0eb1bb8  

Degree: 2

\(\theta^4-2^{4} 3^{2} x\left(10368\theta^4+20736\theta^3+24048\theta^2+13680\theta+2927\right)+2^{20} 3^{10} x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 421488, 241251334416, 151434902650832640, 99396938275247309913360, ...
--> OEIS
Normalized instanton numbers (n0=1): -201888, -1567499400, -40177844666400, -988883543512335600, -35724019937142805037280, ... ; Common denominator:...

Discriminant

\((746496z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 746496}\)\(\infty\)
\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(-\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 4}{ 3}\)

Note:

Operator equivalent to $\hat{13}$ of AESZ

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2

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

Degree: 2

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

Maple   LaTex

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: 5.110 |  AESZ: 377  |  Superseeker: 32/3 6752/3  |  Hash: 4b8e1b4341fae957e1766a0071de5ba5  

Degree: 5

\(3^{2} \theta^4-2^{3} 3 x\left(61\theta^4+74\theta^3+58\theta^2+21\theta+3\right)+2^{4} x^{2}\left(3883\theta^4+5356\theta^3+3451\theta^2+1278\theta+228\right)-2^{7} x^{3}\left(8067\theta^4+13410\theta^3+12875\theta^2+6336\theta+1236\right)+2^{14} x^{4}\left(413\theta^4+1069\theta^3+1206\theta^2+658\theta+140\right)-2^{19} 3 x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 264, 13760, 873640, ...
--> OEIS
Normalized instanton numbers (n0=1): 32/3, 731/6, 6752/3, 355219/6, 5936896/3, ... ; Common denominator:...

Discriminant

\(-(4z-1)(108z-1)(8z-1)(-3+64z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 3}{ 64}\)\(\frac{ 1}{ 8}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.110" from ...

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4

New Number: 5.24 |  AESZ: 195  |  Superseeker: 285/29 40626/29  |  Hash: 49a600431b3e9aaa9d9d6947f8df7d2b  

Degree: 5

\(29^{2} \theta^4-29 x\left(3026\theta^4+5848\theta^3+4577\theta^2+1653\theta+232\right)+x^{2}\left(5568+57768\theta+239159\theta^2+424220\theta^3+258647\theta^4\right)-x^{3}\left(76560+336864\theta+581647\theta^2+532614\theta^3+272743\theta^4\right)+2^{2} 17 x^{4}\left(1922\theta^4+6193\theta^3+8121\theta^2+4894\theta+1112\right)-2^{2} 3 17^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 264, 13040, 778840, ...
--> OEIS
Normalized instanton numbers (n0=1): 285/29, 2362/29, 40626/29, 997476/29, 30096841/29, ... ; Common denominator:...

Discriminant

\(-(27z^3-67z^2+102z-1)(-29+34z)^2\)

Local exponents

\(0\) ≈\(0.009868\)\(\frac{ 29}{ 34}\) ≈\(1.235807-1.492036I\) ≈\(1.235807+1.492036I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.24" from ...

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5

New Number: 5.2 |  AESZ: 19  |  Superseeker: 80/23 4655/23  |  Hash: 4532f44d62f644bf66aa7b153d4f5c5a  

Degree: 5

\(23^{2} \theta^4-23 x\left(921\theta^4+2046\theta^3+1644\theta^2+621\theta+92\right)-x^{2}\left(380851\theta^4+1328584\theta^3+1772673\theta^2+1033528\theta+221168\right)-2 x^{3}\left(475861\theta^4+1310172\theta^3+1028791\theta^2+208932\theta-27232\right)-2^{2} 17 x^{4}\left(8873\theta^4+14020\theta^3+5139\theta^2-1664\theta-976\right)+2^{3} 3 17^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 84, 2200, 71140, ...
--> OEIS
Normalized instanton numbers (n0=1): 80/23, 1157/46, 4655/23, 71184/23, 1156690/23, ... ; Common denominator:...

Discriminant

\((54z-1)(z^2-11z-1)(23+34z)^2\)

Local exponents

\(-\frac{ 23}{ 34}\)\(\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\)\(0\)\(\frac{ 1}{ 54}\)\(\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(4\)\(2\)\(0\)\(2\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.2" from ...

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6

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

Degree: 5

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

Maple   LaTex

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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7

New Number: 5.76 |  AESZ: 306  |  Superseeker: 73/3 11119  |  Hash: d14307aa38b16c728ee31e5936937c44  

Degree: 5

\(3^{2} \theta^4-3 x\left(592\theta^4+1100\theta^3+829\theta^2+279\theta+36\right)+x^{2}\left(13801\theta^4+6652\theta^3-18041\theta^2-14904\theta-3312\right)-2 x^{3}\theta(8461\theta^3-29160\theta^2-28365\theta-7236)-2^{2} 3 7 x^{4}\left(513\theta^4+864\theta^3+487\theta^2+64\theta-16\right)-2^{3} 3 7^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 732, 67080, 7456140, ...
--> OEIS
Normalized instanton numbers (n0=1): 73/3, 2131/6, 11119, 518671, 29749701, ... ; Common denominator:...

Discriminant

\(-(z+1)(54z^2+189z-1)(-3+14z)^2\)

Local exponents

\(-\frac{ 7}{ 4}-\frac{ 11}{ 36}\sqrt{ 33}\)\(-1\)\(0\)\(-\frac{ 7}{ 4}+\frac{ 11}{ 36}\sqrt{ 33}\)\(\frac{ 3}{ 14}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.76" from ...

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8

New Number: 7.14 |  AESZ:  |  Superseeker: -48 -38929520  |  Hash: d8c602210ad81a2daef74d36a78ea933  

Degree: 7

\(\theta^4+2^{4} 3 x\left(99\theta^4+162\theta^3+151\theta^2+70\theta+13\right)+2^{9} 3^{4} x^{2}\left(135\theta^4+738\theta^3+945\theta^2+506\theta+113\right)-2^{14} 3^{7} x^{3}\left(117\theta^4-738\theta^3-1965\theta^2-1490\theta-409\right)-2^{19} 3^{10} x^{4}\left(333\theta^4+774\theta^3-919\theta^2-1242\theta-439\right)-2^{25} 3^{13} x^{5}\left(27\theta^4+612\theta^3+576\theta^2+154\theta-17\right)+2^{31} 3^{16} x^{6}\left(45\theta^4+18\theta^3-84\theta^2-89\theta-25\right)+2^{37} 3^{19} x^{7}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -624, 633744, -768218880, 1020122073360, ...
--> OEIS
Normalized instanton numbers (n0=1): -48, -160806, -38929520, -13792511646, -7174458915600, ... ; Common denominator:...

Discriminant

\((432z+1)(864z+1)(864z-1)^2(1728z+1)^3\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 1}{ 864}\)\(-\frac{ 1}{ 1728}\)\(0\)\(\frac{ 1}{ 864}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(2\)\(0\)\(3\)\(1\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(\frac{ 4}{ 3}\)

Note:

This is operator "7.14" from ...

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9

New Number: 8.47 |  AESZ:  |  Superseeker: 31/3 43174/9  |  Hash: b79bf25fcecf028aa40c1a6a8233efe7  

Degree: 8

\(3^{4} \theta^4-3^{3} x\left(367\theta^4+398\theta^3+295\theta^2+96\theta+12\right)-2^{4} 3^{3} x^{2}\left(200\theta^4+2081\theta^3+3614\theta^2+2009\theta+392\right)+2^{6} 3 x^{3}\left(72449\theta^4+102684\theta^3-48579\theta^2-77922\theta-22536\right)+2^{10} x^{4}\left(109873\theta^4+619970\theta^3+56260\theta^2-219027\theta-78216\right)-2^{14} 7 x^{5}\left(40669\theta^4-18266\theta^3-36570\theta^2-16190\theta-1955\right)-2^{17} 7 x^{6}\left(80805\theta^4+76590\theta^3+51265\theta^2+23076\theta+4780\right)-2^{24} 7^{2} x^{7}\left(437\theta^4+1117\theta^3+1236\theta^2+664\theta+140\right)-2^{29} 3 7^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 228, 12640, 901540, ...
--> OEIS
Normalized instanton numbers (n0=1): 31/3, 1964/9, 43174/9, 1469755/9, 19813517/3, ... ; Common denominator:...

Discriminant

\(-(27z+1)(2048z^3+768z^2+112z-1)(-9+168z+3584z^2)^2\)

Local exponents

≈\(-0.191715-0.145483I\) ≈\(-0.191715+0.145483I\)\(-\frac{ 3}{ 128}-\frac{ 3}{ 896}\sqrt{ 273}\)\(-\frac{ 1}{ 27}\)\(0\) ≈\(0.00843\)\(-\frac{ 3}{ 128}+\frac{ 3}{ 896}\sqrt{ 273}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(4\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 4}{ 3}\)

Note:

This is operator "8.47" from ...

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10

New Number: 8.76 |  AESZ:  |  Superseeker: -204 66054580/3  |  Hash: a1b606169a188129e64002b152d24330  

Degree: 8

\(\theta^4+2^{2} 3 x\left(444\theta^4+744\theta^3+697\theta^2+325\theta+62\right)+2^{7} 3^{2} x^{2}\left(10116\theta^4+27720\theta^3+38031\theta^2+24393\theta+5891\right)+2^{12} 3^{4} x^{3}\left(45468\theta^4+131544\theta^3+190749\theta^2+142371\theta+37390\right)+2^{17} 3^{6} x^{4}\left(148068\theta^4+401112\theta^3+412641\theta^2+216243\theta+39599\right)+2^{23} 3^{9} x^{5}\left(58320\theta^4+161352\theta^3+168390\theta^2+50175\theta-1409\right)+2^{29} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53397\theta^2+29754\theta+6131\right)+2^{35} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1038\theta^2+558\theta+119\right)+2^{43} 3^{20} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -744, 843624, -1099121280, 1536242069160, ...
--> OEIS
Normalized instanton numbers (n0=1): -204, 6654, 66054580/3, 6573546582, 118182295200, ... ; Common denominator:...

Discriminant

\((432z+1)(864z+1)(1728z+1)^2(497664z^2+288z+1)^2\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 1}{ 864}\)\(-\frac{ 1}{ 1728}\)\(-\frac{ 1}{ 3456}-\frac{ 1}{ 3456}\sqrt{ 23}I\)\(-\frac{ 1}{ 3456}+\frac{ 1}{ 3456}\sqrt{ 23}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(-\frac{ 1}{ 6}\)\(1\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)
\(2\)\(2\)\(\frac{ 7}{ 6}\)\(4\)\(4\)\(0\)\(\frac{ 4}{ 3}\)

Note:

This is operator "8.76" from ...

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11

New Number: 8.77 |  AESZ:  |  Superseeker: 91/5 25991/5  |  Hash: fa37d863a8d0cc4b7a34e7d9b5e3a1a5  

Degree: 8

\(5^{2} \theta^4-5 x\left(693\theta^4+1242\theta^3+931\theta^2+310\theta+40\right)-2^{4} x^{2}\left(659\theta^4+9977\theta^3+17174\theta^2+10200\theta+2160\right)-2^{5} x^{3}\left(7235\theta^4-19374\theta^3-34715\theta^2-7290\theta+1560\right)-2^{8} x^{4}\left(14861\theta^4+40168\theta^3-70511\theta^2-88342\theta-26424\right)-2^{10} x^{5}\left(6973\theta^4+29386\theta^3+99859\theta^2+58446\theta+9864\right)-2^{14} x^{6}\left(6951\theta^4-25713\theta^3-34544\theta^2-14472\theta-1680\right)-2^{15} 11 x^{7}\left(2029\theta^4+5030\theta^3+5139\theta^2+2570\theta+520\right)+2^{18} 3 11^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 408, 28160, 2360440, ...
--> OEIS
Normalized instanton numbers (n0=1): 91/5, 1158/5, 25991/5, 192163, 42855113/5, ... ; Common denominator:...

Discriminant

\((z-1)(8z+1)(864z^2+136z-1)(5-24z+352z^2)^2\)

Local exponents

\(-\frac{ 17}{ 216}-\frac{ 7}{ 216}\sqrt{ 7}\)\(-\frac{ 1}{ 8}\)\(0\)\(-\frac{ 17}{ 216}+\frac{ 7}{ 216}\sqrt{ 7}\)\(\frac{ 3}{ 88}-\frac{ 1}{ 88}\sqrt{ 101}I\)\(\frac{ 3}{ 88}+\frac{ 1}{ 88}\sqrt{ 101}I\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(4\)\(2\)\(\frac{ 4}{ 3}\)

Note:

This is operator "8.77" from ...

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