Summary

You searched for: Spectrum0=0,1,1,2

Your search produced 482 matches
 1-30  31-60  61-90  91-120  121-150  151-180 
 181-210  211-240  241-270  271-300  301-330  331-360 
 361-390  391-420  421-450  451-480  481-482 

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1

New Number: 2.10 |  AESZ: 70  |  Superseeker: 27 18089  |  Hash: 3d2adae6eaf26a56c76b8b67d92cc5df  

Degree: 2

\(\theta^4-3 x(3\theta+1)(3\theta+2)(10\theta^2+10\theta+3)+3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1350, 156240, 22141350, ...
--> OEIS
Normalized instanton numbers (n0=1): 27, 432, 18089, 997785, 68438142, ... ; Common denominator:...

Discriminant

\((243z-1)(27z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 243}\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast c$.

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2

New Number: 2.11 |  AESZ: 69  |  Superseeker: 64 246848  |  Hash: 729adc350de26d9415643078ed8d3867  

Degree: 2

\(\theta^4-2^{2} x(4\theta+1)(4\theta+3)(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 6300, 1718640, 575675100, ...
--> OEIS
Normalized instanton numbers (n0=1): 64, 2616, 246848, 32024824, 5160268864, ... ; Common denominator:...

Discriminant

\((576z-1)(64z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 576}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast c$

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3

New Number: 2.12 |  AESZ: 64  |  Superseeker: 432 78259376  |  Hash: 43991f21e20c16ab91690259b788b4cd  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(10\theta^2+10\theta+3)+2^{4} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 180, 207900, 379819440, 855338063580, ...
--> OEIS
Normalized instanton numbers (n0=1): 432, 130842, 78259376, 68104755558, 73096116588720, ... ; Common denominator:...

Discriminant

\((3888z-1)(432z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3888}\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product $B\ast c$.

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4

New Number: 2.13 |  AESZ: 36  |  Superseeker: 16 1232  |  Hash: dea6fdf568a5907a24ba30fef2caf124  

Degree: 2

\(\theta^4-2^{4} x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{9} x^{2}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 720, 44800, 3312400, ...
--> OEIS
Normalized instanton numbers (n0=1): 16, 42, 1232, 32159, 990128, ... ; Common denominator:...

Discriminant

\((128z-1)(64z-1)\)

Local exponents

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

Note:

A*d

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5

New Number: 2.14 |  AESZ: 48  |  Superseeker: 24 5832  |  Hash: 8081a3989d09a7d612953dac3341d90c  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1800, 188160, 23423400, ...
--> OEIS
Normalized instanton numbers (n0=1): 24, 291/2, 5832, 247116, 12634944, ... ; Common denominator:...

Discriminant

\((216z-1)(108z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 216}\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(\frac{ 5}{ 3}\)

Note:

B*d

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6

New Number: 2.15 |  AESZ: 38  |  Superseeker: 48 73328  |  Hash: 9ce26bb7405c3b98d8aeae5b1102c611  

Degree: 2

\(\theta^4-2^{4} x(4\theta+1)(4\theta+3)(3\theta^2+3\theta+1)+2^{9} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 8400, 2069760, 609008400, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 998, 73328, 7388135, 857248528, ... ; Common denominator:...

Discriminant

\((512z-1)(256z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 512}\)\(\frac{ 1}{ 256}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast d$

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7

New Number: 2.16 |  AESZ: 65  |  Superseeker: 240 19105840  |  Hash: 13ba368bcbb10731ac8727b510731ff2  

Degree: 2

\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{9} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 277200, 457416960, 904864680720, ...
--> OEIS
Normalized instanton numbers (n0=1): 240, 57102, 19105840, 14810143935, 10017820614480, ... ; Common denominator:...

Discriminant

\((3456z-1)(1728z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3456}\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*d

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8

New Number: 2.1 |  AESZ: 45  |  Superseeker: 12 3204  |  Hash: cdf289f6febf84eb577a238542a57457  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 360, 22400, 1695400, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, 163, 3204, 107582, 4203360, ... ; Common denominator:...

Discriminant

\(-(16z+1)(128z-1)\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $A \ast a$, where $A$ is (:case 2.1.1)

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9

New Number: 2.20 |  AESZ: 133  |  Superseeker: 12 -3284/3  |  Hash: 4c9628f7dd48f4e9e6ec75303e557389  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 324, 8400, 44100, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, -42, -3284/3, -20538, -103776, ... ; Common denominator:...

Discriminant

\(1-144z+6912z^2\)

Local exponents

\(0\)\(\frac{ 1}{ 96}-\frac{ 1}{ 288}\sqrt{ 3}I\)\(\frac{ 1}{ 96}+\frac{ 1}{ 288}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product A*f
Explicit solution not yet verified

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10

New Number: 2.21 |  AESZ: 134  |  Superseeker: 18 -5177  |  Hash: cc6d92c4b8a8dadb92b447c54e3a2a2f  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 810, 35280, 311850, ...
--> OEIS
Normalized instanton numbers (n0=1): 18, -207/2, -5177, -155979, -923301, ... ; Common denominator:...

Discriminant

\(1-243z+19683z^2\)

Local exponents

\(0\)\(\frac{ 1}{ 162}-\frac{ 1}{ 486}\sqrt{ 3}I\)\(\frac{ 1}{ 162}+\frac{ 1}{ 486}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast f$

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11

New Number: 2.22 |  AESZ: 135  |  Superseeker: 36 -206716/3  |  Hash: 85e55291bd94bb32087b43f104c60645  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 388080, 8108100, ...
--> OEIS
Normalized instanton numbers (n0=1): 36, -477, -206716/3, -4431924, -27005472, ... ; Common denominator:...

Discriminant

\(1-576z+110592z^2\)

Local exponents

\(0\)\(\frac{ 1}{ 384}-\frac{ 1}{ 1152}\sqrt{ 3}I\)\(\frac{ 1}{ 384}+\frac{ 1}{ 1152}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

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12

New Number: 2.23 |  AESZ: 136  |  Superseeker: 180 -21847076  |  Hash: ff626c2fb953cb886f45f717a6a98a20  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 180, 124740, 85765680, 12047014980, ...
--> OEIS
Normalized instanton numbers (n0=1): 180, -15615, -21847076, -7438074210, 255591208800, ... ; Common denominator:...

Discriminant

\(1-3888z+5038848z^2\)

Local exponents

\(0\)\(\frac{ 1}{ 2592}-\frac{ 1}{ 7776}\sqrt{ 3}I\)\(\frac{ 1}{ 2592}+\frac{ 1}{ 7776}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product $D \ast f$

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13

New Number: 2.24 |  AESZ: 137  |  Superseeker: 20 1684/3  |  Hash: 198d6c822d6c46225ac2553d60df6539  

Degree: 2

\(\theta^4-2^{2} x(2\theta+1)^2(17\theta^2+17\theta+6)+2^{7} 3^{2} x^{2}(2\theta+1)^2(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1512, 124800, 11730600, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 2, 1684/3, 7602, 173472, ... ; Common denominator:...

Discriminant

\((144z-1)(128z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 144}\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $A \ast g$.

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14

New Number: 2.25 |  AESZ: 138  |  Superseeker: 27 2618  |  Hash: c524254b716132352b27914640b03c8b  

Degree: 2

\(\theta^4-3 x(3\theta+1)(3\theta+2)(17\theta^2+17\theta+6)+2^{3} 3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 524160, 82952100, ...
--> OEIS
Normalized instanton numbers (n0=1): 27, 189/4, 2618, 43713, 2319057, ... ; Common denominator:...

Discriminant

\((243z-1)(216z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 243}\)\(\frac{ 1}{ 216}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast g$.

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15

New Number: 2.26 |  AESZ: 139  |  Superseeker: 44 22500  |  Hash: f5d9215987323abcff6ed8709927af5d  

Degree: 2

\(\theta^4-2^{2} x(4\theta+1)(4\theta+3)(17\theta^2+17\theta+6)+2^{7} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 72, 17640, 5765760, 2156754600, ...
--> OEIS
Normalized instanton numbers (n0=1): 44, 607, 22500, 1444678, 128626784, ... ; Common denominator:...

Discriminant

\((576z-1)(512z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 576}\)\(\frac{ 1}{ 512}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 4}\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C \ast g$

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16

New Number: 2.27 |  AESZ: 140  |  Superseeker: 108 -4945756  |  Hash: 74692097f8183c067c2c4b1a5c93387b  

Degree: 2

\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(17\theta^2+17\theta+6)+2^{7} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 360, 582120, 1274232960, 3204505984680, ...
--> OEIS
Normalized instanton numbers (n0=1): 108, 54135, -4945756, 7925523138, -2434666062240, ... ; Common denominator:...

Discriminant

\((3888z-1)(3456z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 3888}\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(2\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product $D \ast g$

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17

New Number: 2.2 |  AESZ: 15  |  Superseeker: 21 15894  |  Hash: c8053e0e9c05ef468263fafd5e3fc764  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ...
--> OEIS
Normalized instanton numbers (n0=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...

Discriminant

\(-(27z+1)(216z-1)\)

Local exponents

\(-\frac{ 1}{ 27}\)\(0\)\(\frac{ 1}{ 216}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(2\)\(0\)\(2\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast a$.

A-Incarnation: diagonal of (3,3)-intersection in $P^2 \times P^2$

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18

New Number: 2.3 |  AESZ: 68  |  Superseeker: 52 220220  |  Hash: 13a48045ff0a42a9fcfbdb710baf1997  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 4200, 1034880, 311711400, ...
--> OEIS
Normalized instanton numbers (n0=1): 52, 2814, 220220, 29135058, 4512922272, ... ; Common denominator:...

Discriminant

\(-(64z+1)(512z-1)\)

Local exponents

\(-\frac{ 1}{ 64}\)\(0\)\(\frac{ 1}{ 512}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(0\)\(2\)\(\frac{ 7}{ 4}\)

Note:

C*a

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19

New Number: 2.4 |  AESZ: 62  |  Superseeker: 372 71562236  |  Hash: 07a3fd7577f878056e765831c6820f3d  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 120, 138600, 228708480, 463140798120, ...
--> OEIS
Normalized instanton numbers (n0=1): 372, 136182, 71562236, 63364481358, 65860679690400, ... ; Common denominator:...

Discriminant

\(-(432z+1)(3456z-1)\)

Local exponents

\(-\frac{ 1}{ 432}\)\(0\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 6}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 6}\)
\(1\)\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(2\)\(0\)\(2\)\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*a

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20

New Number: 2.52 |  AESZ: 16  |  Superseeker: 4 644/3  |  Hash: 05af0662662bfbec63e3186c4f363313  

Degree: 2

\(\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{8} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 168, 5120, 190120, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 20, 644/3, 3072, 52512, ... ; Common denominator:...

Discriminant

\((64z-1)(16z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \alpha$
A-Incarnation: diagonal subfamily of 1,1,1,1-intersection in $P^1 \times P^1 \times P^1 \times \P^1$
B-Incarnations:
Fibre products: 62211- x 632--1, S62211

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21

New Number: 2.53 |  AESZ: 29  |  Superseeker: 14 10424/3  |  Hash: 92e8a038051b3fb8e0cc6ad6a52b8bfb  

Degree: 2

\(\theta^4-2 x(2\theta+1)^2(17\theta^2+17\theta+5)+2^{2} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 10, 438, 28900, 2310070, ...
--> OEIS
Normalized instanton numbers (n0=1): 14, 303/2, 10424/3, 113664, 4579068, ... ; Common denominator:...

Discriminant

\(1-136z+16z^2\)

Local exponents

\(0\)\(\frac{ 17}{ 4}-3\sqrt{ 2}\)\(\frac{ 17}{ 4}+3\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \gamma$

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22

New Number: 2.54 |  AESZ: 41  |  Superseeker: 2 -104  |  Hash: a9ddeed4299f59fb9ac9f6f248383b8f  

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 6, 54, 60, -19530, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -7, -104, -588, 3300, ... ; Common denominator:...

Discriminant

\(1-56z+1296z^2\)

Local exponents

\(0\)\(\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I\)\(\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \delta$

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23

New Number: 2.55 |  AESZ: 42  |  Superseeker: 8 1000  |  Hash: c389d3bc0e31801bc4b7b3e186702bc9  

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 8, 240, 10880, 597520, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 63, 1000, 44369/2, 606168, ... ; Common denominator:...

Discriminant

\(1-96z+256z^2\)

Local exponents

\(0\)\(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\)\(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \epsilon$

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24

New Number: 2.56 |  AESZ: 185  |  Superseeker: 6 608  |  Hash: 80506439e4d4fdc41f5b16e246a69fbf  

Degree: 2

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

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Coefficients of the holomorphic solution: 1, 6, 162, 6180, 284130, ...
--> OEIS
Normalized instanton numbers (n0=1): 6, 93/2, 608, 11754, 275352, ... ; Common denominator:...

Discriminant

\(1-72z-432z^2\)

Local exponents

\(-\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}\)\(0\)\(-\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \zeta$

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25

New Number: 2.57 |  AESZ: 184  |  Superseeker: 2 -8  |  Hash: ee8bb517b329e58eeb4352dc3cdc3f81  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 210, 5500, 159250, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, 4, -8, -194, -2820, ... ; Common denominator:...

Discriminant

\(1-88z+2000z^2\)

Local exponents

\(0\)\(\frac{ 11}{ 500}-\frac{ 1}{ 250}I\)\(\frac{ 11}{ 500}+\frac{ 1}{ 250}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \eta$

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26

New Number: 2.5 |  AESZ: 25  |  Superseeker: 20 8220  |  Hash: 93279abcbeeade30c29508de7784e582  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 12, 684, 58800, 6129900, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 277, 8220, 352994, 18651536, ... ; Common denominator:...

Discriminant

\(1-176z-256z^2\)

Local exponents

\(-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}\)\(0\)\(-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $A\ast b$

A-incarnation: X(1,2,2) in G(2,5)

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27

New Number: 2.60 |  AESZ: 18  |  Superseeker: 4 364  |  Hash: bb479f8a4185bf4a943dba2d433e13e5  

Degree: 2

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

Maple   LaTex

Coefficients of the holomorphic solution: 1, 4, 108, 3280, 126700, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 39, 364, 6800, 662416/5, ... ; Common denominator:...

Discriminant

\(-(16z+1)(64z-1)\)

Local exponents

\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 5}{ 4}\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

A-Incarnation: (1,1) and (2,2) intersection in $P^3 \times P^3$

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28

New Number: 2.61 |  AESZ: 26  |  Superseeker: 10 1724  |  Hash: f3fc09474973b19b8bdb783e3322eb65  

Degree: 2

\(\theta^4-2 x(2\theta+1)^2(13\theta^2+13\theta+4)-2^{2} 3 x^{2}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 288, 15200, 968800, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 191/2, 1724, 45680, 1478214, ... ; Common denominator:...

Discriminant

\(-(4z+1)(108z-1)\)

Local exponents

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

Note:

A-incarnation: $X(1,1,1,1,2) \subset Grass(2,6)$

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29

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

Degree: 2

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

Maple   LaTex

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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30

New Number: 2.64 |  AESZ: 182  |  Superseeker: 1 7  |  Hash: 89ba4729efa82413b33fe6928ff8d2c9  

Degree: 2

\(\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...

Discriminant

\((27z-1)(16z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 6}\)

Note:

This is operator "2.64" from ...

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