///////////////////////////////////////////////////////////////////////////
// "Complete classification of the torsion structures of 
//   rational elliptic curves over quintic number fields"
// Enrique González-Jiménez
///////////////////////////////////////////////////////////////////////////

// 9/6/2016 - Magma 2.21

// Magma output that determine for any subgroup in Zywina's notation (in Equations.txt) the corresponding Sutherland's label.


Magma V2.21-7     Tue Mar 29 2016 11:24:35 on luna     [Seed = 4116310685]
Type ? for help.  Type <Ctrl>-D to quit.
> load "subgroups.m";
Loading file "subgroups.m"
> load "Equations.txt";
Loading "Equations.txt"
> for G in G2 do GL2SubgroupLabel(G); end for;
2Cs
2B
2Cn
> for G in G3 do GL2SubgroupLabel(G); end for;
3Cs
3Ns
3B
3Nn
> GL2SubgroupLabel(H3[1][1]);
3Cs.1.1
> GL2SubgroupLabel(H3[3][1]);
3B.1.1
> GL2SubgroupLabel(H3[3][2]);
3B.1.2
> for G in G5 do GL2SubgroupLabel(G); end for;
5Cs.4.1
5Cs
5Ns.2.1
5Ns
5B.4.2
5B.4.1
5Nn
5B
5S4
> GL2SubgroupLabel(H5[1][1]);
5Cs.1.1
> GL2SubgroupLabel(H5[1][2]);
5Cs.1.3
> GL2SubgroupLabel(H5[5][1]);
5B.1.2
> GL2SubgroupLabel(H5[5][2]);
5B.1.3
> GL2SubgroupLabel(H5[6][1]);
5B.1.1
> GL2SubgroupLabel(H5[6][2]);
5B.1.4
> for G in G7 do GL2SubgroupLabel(G); end for;
7Ns.3.1
7Ns
7B.6.1
7B.6.3
7B.6.2
7Nn
7B
> GL2SubgroupLabel(H7[1][1]);
7Ns.2.1
> GL2SubgroupLabel(H7[3][1]);
7B.1.1
> GL2SubgroupLabel(H7[3][2]);
7B.1.6
> GL2SubgroupLabel(H7[4][1]);
7B.1.3
> GL2SubgroupLabel(H7[4][2]);
7B.1.4
> GL2SubgroupLabel(H7[5][1]);
7B.1.5
> GL2SubgroupLabel(H7[5][2]);
7B.1.2
> GL2SubgroupLabel(H7[7][1]);
7B.2.3
> GL2SubgroupLabel(H7[7][2]);
7B.2.1
> for G in G11 do GL2SubgroupLabel(G); end for;
11B.10.4
11B.10.5
11Nn
> GL2SubgroupLabel(H11[1][1]);                 
11B.1.4
> GL2SubgroupLabel(H11[1][2]);
11B.1.7
> GL2SubgroupLabel(H11[2][1]);
11B.1.5
> GL2SubgroupLabel(H11[2][2]);
11B.1.6
> for G in G13 do GL2SubgroupLabel(G); end for;
13B.5.2
13B.5.1
13B.5.4
13B.4.2
13B.4.1
13B
13S4
> GL2SubgroupLabel(H13[4][1]);
13B.3.2
> GL2SubgroupLabel(H13[4][2]);
13B.3.7
> GL2SubgroupLabel(H13[5][1]);
13B.3.1
> GL2SubgroupLabel(H13[5][2]);
13B.3.4
> for G in G17 do GL2SubgroupLabel(G); end for;
17B.4.2
17B.4.6
> for G in G37 do GL2SubgroupLabel(G); end for;
37B.8.1
37B.8.2