Summary

You searched for: dim_h=6

Your search produced 13 matches

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1

New Number: 2.8 |  AESZ: 63  |  Superseeker: 684 195638820  |  Hash: 06c1a4c0aa33f5051126908a9898430d  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(11\theta^2+11\theta+3)-2^{4} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

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Coefficients of the holomorphic solution: 1, 180, 263340, 600359760, 1674535082220, ...
--> OEIS
Normalized instanton numbers (n0=1): 684, 253314, 195638820, 225040578570, 319342448936304, ... ; Common denominator:...

Discriminant

\(1-4752z-186624z^2\)

No data for singularities

Note:

Hadamard product D*b

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2

New Number: 4.33 |  AESZ: 55  |  Superseeker: 76/3 144196/3  |  Hash: 7e88cd5b7dc1c51022b66ac6f009218f  

Degree: 4

\(3^{2} \theta^4-2^{2} 3 x\left(208\theta^4+224\theta^3+163\theta^2+51\theta+6\right)+2^{9} x^{2}\left(32\theta^4-928\theta^3-1606\theta^2-837\theta-141\right)+2^{16} x^{3}\left(144\theta^4+576\theta^3+467\theta^2+144\theta+15\right)-2^{24} x^{4}\left((2\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 8, 936, 108800, 16748200, ...
--> OEIS
Normalized instanton numbers (n0=1): 76/3, 3476/3, 144196/3, 3563196, 309069600, ... ; Common denominator:...

Discriminant

\(-(64z+1)(256z-1)(-3+128z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 3}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic operator. There is a second MUM-point
hiding at infinity, corresponding to Operator 4.56

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3

New Number: 4.44 |  AESZ: 232  |  Superseeker: 379/5 1364199/5  |  Hash: 8d5ff690c87757ed51a092dee764eede  

Degree: 4

\(5^{2} \theta^4-5 x\left(2617\theta^4+4658\theta^3+3379\theta^2+1050\theta+120\right)+2^{6} 3 x^{2}\left(673\theta^4-4871\theta^3-10282\theta^2-5410\theta-860\right)+2^{10} 3^{2} x^{3}\left(955\theta^4+4320\theta^3+3477\theta^2+1020\theta+100\right)-2^{17} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

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Coefficients of the holomorphic solution: 1, 24, 3960, 974400, 292030200, ...
--> OEIS
Normalized instanton numbers (n0=1): 379/5, 3346, 1364199/5, 177727432/5, 5658116533, ... ; Common denominator:...

Discriminant

\(-(27z+1)(512z-1)(-5+96z)^2\)

Local exponents

\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 512}\)\(\frac{ 5}{ 96}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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4

New Number: 5.101 |  AESZ: 348  |  Superseeker: -52 -44772  |  Hash: 8759f016475d17d0fc88f4b98a374d3f  

Degree: 5

\(\theta^4+2^{2} x\left(70\theta^4+194\theta^3+145\theta^2+48\theta+6\right)-2^{4} 3 x^{2}\left(141\theta^4-858\theta^3-2111\theta^2-1192\theta-206\right)-2^{8} 3^{2} x^{3}\left(18\theta^4-324\theta^3-2364\theta^2-1953\theta-403\right)-2^{10} 3^{4} x^{4}(3\theta+1)(3\theta+2)(42\theta^2+258\theta+223)+2^{14} 3^{6} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, 2160, -309120, 54608400, ...
--> OEIS
Normalized instanton numbers (n0=1): -52, 461/2, -44772, 3546761/2, -178670332, ... ; Common denominator:...

Discriminant

\((746496z^3+17280z^2+352z+1)(-1+36z)^2\)

Local exponents

≈\(-0.009925-0.017537I\) ≈\(-0.009925+0.017537I\) ≈\(-0.003299\)\(0\)\(\frac{ 1}{ 36}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(1\)\(0\)\(3\)\(\frac{ 4}{ 3}\)
\(2\)\(2\)\(2\)\(0\)\(4\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.101" from ...

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5

New Number: 5.14 |  AESZ: 116  |  Superseeker: 64 23360  |  Hash: 0b366ad8c78b6697205c5a7fff270f5b  

Degree: 5

\(\theta^4-2^{5} x\left(10\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(52\theta^4+472\theta^3+832\theta^2+492\theta+103\right)+2^{16} x^{3}\left(14\theta^4+12\theta^3-96\theta^2-105\theta-29\right)-2^{18} x^{4}(2\theta+1)(56\theta^3+468\theta^2+646\theta+249)-2^{24} x^{5}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 32, 2448, 273920, 38525200, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, 12, 23360, 654490, 53956288, ... ; Common denominator:...

Discriminant

\(-(-1+256z)(32z+1)^2(64z-1)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 4}\)
\(3\)\(0\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 5}{ 4}\)
\(4\)\(0\)\(2\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.14" from ...

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6

New Number: 5.32 |  AESZ: 215  |  Superseeker: 220/3 89212  |  Hash: ced61f5675491a3c4446c0e55e7bc36b  

Degree: 5

\(3^{2} \theta^4-2^{2} 3 x\left(268\theta^4+632\theta^3+463\theta^2+147\theta+18\right)-2^{7} x^{2}\left(448\theta^4-1616\theta^3-4280\theta^2-2418\theta-441\right)+2^{12} x^{3}\left(416\theta^4+2016\theta^3+756\theta^2-288\theta-135\right)+2^{19} x^{4}(8\theta^2-28\theta-33)(2\theta+1)^2-2^{24} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 2664, 470400, 102047400, ...
--> OEIS
Normalized instanton numbers (n0=1): 220/3, 3538/3, 89212, 7484350, 2459418080/3, ... ; Common denominator:...

Discriminant

\(-(16z-1)(4096z^2-384z+1)(3+64z)^2\)

Local exponents

\(-\frac{ 3}{ 64}\)\(0\)\(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\)\(\frac{ 1}{ 16}\)\(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.32" from ...

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7

New Number: 5.83 |  AESZ: 316  |  Superseeker: 852/11 1678156/11  |  Hash: b8201d587a016cc013e2477aadb5c1ff  

Degree: 5

\(11^{2} \theta^4-2^{2} 3 11 x\left(364\theta^4+824\theta^3+599\theta^2+187\theta+22\right)-2^{5} x^{2}\left(62164\theta^4+84496\theta^3+12499\theta^2-6402\theta-1584\right)-2^{4} 3 x^{3}\left(484016\theta^4+474144\theta^3+366952\theta^2+161832\theta+27027\right)-2^{11} 3^{2} x^{4}(964\theta^2+1360\theta+669)(2\theta+1)^2-2^{16} 3^{4} x^{5}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 3240, 675600, 171901800, ...
--> OEIS
Normalized instanton numbers (n0=1): 852/11, 21572/11, 1678156/11, 15912512, 22956446184/11, ... ; Common denominator:...

Discriminant

\(-(2304z^3+1664z^2+432z-1)(11+192z)^2\)

Local exponents

≈\(-0.362258-0.240689I\) ≈\(-0.362258+0.240689I\)\(-\frac{ 11}{ 192}\)\(0\) ≈\(0.002294\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.83" from ...

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8

New Number: 5.86 |  AESZ: 320  |  Superseeker: 741/11 138745  |  Hash: d19e7569ce62abdd5393977835e411a9  

Degree: 5

\(11^{2} \theta^4-11 x\left(4843\theta^4+8918\theta^3+6505\theta^2+2046\theta+242\right)+2^{2} x^{2}\left(312184\theta^4+343456\theta^3-23371\theta^2-73942\theta-14883\right)-2^{4} x^{3}\left(511972\theta^4+256344\theta^3+144969\theta^2+78639\theta+15642\right)+2^{11} x^{4}(2\theta+1)(1964\theta^3+3078\theta^2+1853\theta+419)-2^{18} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 22, 2850, 568300, 138119170, ...
--> OEIS
Normalized instanton numbers (n0=1): 741/11, 22232/11, 138745, 157326644/11, 19999995398/11, ... ; Common denominator:...

Discriminant

\(-(z-1)(64z^2-416z+1)(-11+128z)^2\)

Local exponents

\(0\)\(\frac{ 13}{ 4}-\frac{ 15}{ 8}\sqrt{ 3}\)\(\frac{ 11}{ 128}\)\(1\)\(\frac{ 13}{ 4}+\frac{ 15}{ 8}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.86" from ...

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9

New Number: 5.91 |  AESZ: 331  |  Superseeker: 112 186800  |  Hash: a30093d8c1ab2f66122cef8935b79efb  

Degree: 5

\(\theta^4+2^{4} x\left(18\theta^4-48\theta^3-33\theta^2-9\theta-1\right)-2^{9} x^{2}\left(86\theta^4+512\theta^3+125\theta^2+45\theta+10\right)-2^{14} x^{3}\left(1138\theta^4+2040\theta^3+1883\theta^2+879\theta+157\right)-2^{19} 7 x^{4}(2\theta+1)(186\theta^3+375\theta^2+317\theta+100)-2^{27} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1488, 183040, 27611920, ...
--> OEIS
Normalized instanton numbers (n0=1): 112, -2242, 186800, -11675813, 1250599376, ... ; Common denominator:...

Discriminant

\(-(32z+1)(256z-1)(64z+1)(1+224z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 224}\)\(0\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.91" from ...

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10

New Number: 8.30 |  AESZ: 314  |  Superseeker: 229/4 297111/4  |  Hash: 893692ba7eb3effcbc0c3b48d405456a  

Degree: 8

\(2^{4} \theta^4-2^{2} x\left(1282\theta^4+2618\theta^3+1909\theta^2+600\theta+72\right)-3^{2} x^{2}\left(9503\theta^4+26810\theta^3+31755\theta^2+15944\theta+2936\right)+3^{4} x^{3}\left(15627\theta^4-18288\theta^3-91412\theta^2-53256\theta-9688\right)+2 3^{6} x^{4}\left(15106\theta^4+20300\theta^3-20421\theta^2-23443\theta-5907\right)-2^{2} 3^{8} x^{5}\left(2072\theta^4-18256\theta^3-2563\theta^2+4626\theta+1495\right)-2^{2} 3^{10} x^{6}\left(6204\theta^4+360\theta^3-281\theta^2+1017\theta+434\right)-2^{5} 3^{12} x^{7}(2\theta+1)(100\theta^3+162\theta^2+95\theta+21)+2^{8} 3^{14} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1926, 310860, 61060230, ...
--> OEIS
Normalized instanton numbers (n0=1): 229/4, 1293, 297111/4, 6150238, 2540085295/4, ... ; Common denominator:...

Discriminant

\((z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2\)

Local exponents

≈\(-0.168156-0.022431I\) ≈\(-0.168156+0.022431I\)\(\frac{ 1}{ 144}-\frac{ 1}{ 144}\sqrt{ 129}\)\(0\)\(\frac{ 1}{ 18}2^(\frac{ 1}{ 3})+\frac{ 1}{ 36}2^(\frac{ 2}{ 3})-\frac{ 1}{ 9}\)\(\frac{ 1}{ 144}+\frac{ 1}{ 144}\sqrt{ 129}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "8.30" from ...

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11

New Number: 8.32 |  AESZ: 317  |  Superseeker: 69/4 14365/12  |  Hash: cda8cce31025f51636125bea67a820d1  

Degree: 8

\(2^{4} \theta^4-2^{2} 3 x\left(162\theta^4+414\theta^3+335\theta^2+128\theta+20\right)+3^{3} x^{2}\left(1219\theta^4+10906\theta^3+18963\theta^2+11824\theta+2708\right)+3^{5} 5 x^{3}\left(922\theta^4+162\theta^3-6403\theta^2-6576\theta-1964\right)-3^{7} x^{4}\left(10358\theta^4+58054\theta^3+62251\theta^2+29672\theta+4907\right)-3^{9} 5 x^{5}\left(1519\theta^4-1262\theta^3+1371\theta^2+4264\theta+1802\right)+2 3^{11} 5 x^{6}\left(1727\theta^4+3702\theta^3+3085\theta^2+882\theta+17\right)-3^{13} 5^{2} x^{7}\left(239\theta^4+460\theta^3+314\theta^2+84\theta+6\right)-3^{16} 5^{2} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 15, 459, 19545, 1019259, ...
--> OEIS
Normalized instanton numbers (n0=1): 69/4, -30, 14365/12, 3015/2, 1376205/4, ... ; Common denominator:...

Discriminant

\(-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2\)

Local exponents

≈\(-9.163702\)\(\frac{ 1}{ 18}-\frac{ 1}{ 90}\sqrt{ 105}\)\(0\) ≈\(0.010727\)\(\frac{ 1}{ 27}\) ≈\(0.041864\)\(\frac{ 1}{ 18}+\frac{ 1}{ 90}\sqrt{ 105}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This operator has a second MUM-point at infininty corresponding to operator 8.31

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12

New Number: 1.4 |  AESZ: 4  |  Superseeker: 117 713814  |  Hash: 1f2a9672b7cdc68eae658b2304b40dbd  

Degree: 1

\(\theta^4-3^{2} x(3\theta+1)^2(3\theta+2)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 8100, 2822400, 1200622500, ...
--> OEIS
Normalized instanton numbers (n0=1): 117, 5868, 713814, 126605376, 27754210287, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

A-incarnation: X(3,3) in P^5.

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13

New Number: 1.6 |  AESZ: 6  |  Superseeker: 160 1956896  |  Hash: 483b4ca5270ed3bfca9243827b62064e  

Degree: 1

\(\theta^4-2^{4} x(4\theta+1)(2\theta+1)^2(4\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 15120, 7392000, 4414410000, ...
--> OEIS
Normalized instanton numbers (n0=1): 160, 11536, 1956896, 485487816, 148865410272, ... ; Common denominator:...

Discriminant

\(\)

No data for singularities

Note:

A-incarnation of $X(2,4)$ in $P^5$.

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