// Magma code for the lmfdb family of higher genus curves 10.72-41.0.4-4-4.1
// The results are stored in a list of records called 'data'

RecFormat:=recformat<group,gp_id, signature,gen_vectors,conj_classes,genus,dimension,r,g0, passport_label,gen_vect_label, is_hyperelliptic, hyp_involution, is_cyclic_trigonal,cyc_auto,full_auto, full_sign,topological_class,braid_class>;

data:=[];

// Create group as a permutation group, and generate data which is the same for all entries.
gp_id:=[72,41];
H:=SmallGroup(gp_id[1],gp_id[2]); n:=#H; LP:=[]; LG:=[g : g in H]; for i in [1..n] do x:=LG[i]; Tx:=[LG[j]*x : j in [1..n]]; permL:=[]; for j in [1..n] do for k in [1..n] do if Tx[j] eq LG[k] then permL[j]:=k;  break; end if; end for; end for; Append(~LP,permL); end for; G:=PermutationGroup<n|LP>; 
signature:=[0,4,4,4];
genus:=10;
r:=#signature-1;
g0:=signature[1];
dim:=3*g0-3+r;
S:=Sym(gp_id[1]);

// Here we add an action to data.
gen_vectors:=[[19, 25, 22, 20, 26, 23, 21, 27, 24, 28, 34, 31, 29, 35, 32, 30, 36, 33, 10, 16, 13, 11, 17, 14, 12, 18, 15, 1, 7, 4, 2, 8, 5, 3, 9, 6, 55, 61, 58, 56, 62, 59, 57, 63, 60, 64, 70, 67, 65, 71, 68, 66, 72, 69, 46, 52, 49, 47, 53, 50, 48, 54, 51, 37, 43, 40, 38, 44, 41, 39, 45, 42], [42, 38, 43, 44, 40, 39, 37, 45, 41, 51, 47, 52, 53, 49, 48, 46, 54, 50, 69, 65, 70, 71, 67, 66, 64, 72, 68, 60, 56, 61, 62, 58, 57, 55, 63, 59, 15, 11, 16, 17, 13, 12, 10, 18, 14, 6, 2, 7, 8, 4, 3, 1, 9, 5, 24, 20, 25, 26, 22, 21, 19, 27, 23, 33, 29, 34, 35, 31, 30, 28, 36, 32], [56, 58, 63, 60, 62, 55, 61, 57, 59, 65, 67, 72, 69, 71, 64, 70, 66, 68, 38, 40, 45, 42, 44, 37, 43, 39, 41, 47, 49, 54, 51, 53, 46, 52, 48, 50, 29, 31, 36, 33, 35, 28, 34, 30, 32, 20, 22, 27, 24, 26, 19, 25, 21, 23, 11, 13, 18, 15, 17, 10, 16, 12, 14, 2, 4, 9, 6, 8, 1, 7, 3, 5]];
cc:=[4,5,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[432,734];
full_sign:=[0,2,3,8];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[19, 25, 22, 20, 26, 23, 21, 27, 24, 28, 34, 31, 29, 35, 32, 30, 36, 33, 10, 16, 13, 11, 17, 14, 12, 18, 15, 1, 7, 4, 2, 8, 5, 3, 9, 6, 55, 61, 58, 56, 62, 59, 57, 63, 60, 64, 70, 67, 65, 71, 68, 66, 72, 69, 46, 52, 49, 47, 53, 50, 48, 54, 51, 37, 43, 40, 38, 44, 41, 39, 45, 42], [38, 43, 42, 40, 39, 44, 45, 41, 37, 47, 52, 51, 49, 48, 53, 54, 50, 46, 65, 70, 69, 67, 66, 71, 72, 68, 64, 56, 61, 60, 58, 57, 62, 63, 59, 55, 11, 16, 15, 13, 12, 17, 18, 14, 10, 2, 7, 6, 4, 3, 8, 9, 5, 1, 20, 25, 24, 22, 21, 26, 27, 23, 19, 29, 34, 33, 31, 30, 35, 36, 32, 28], [62, 55, 60, 57, 59, 61, 58, 63, 56, 71, 64, 69, 66, 68, 70, 67, 72, 65, 44, 37, 42, 39, 41, 43, 40, 45, 38, 53, 46, 51, 48, 50, 52, 49, 54, 47, 35, 28, 33, 30, 32, 34, 31, 36, 29, 26, 19, 24, 21, 23, 25, 22, 27, 20, 17, 10, 15, 12, 14, 16, 13, 18, 11, 8, 1, 6, 3, 5, 7, 4, 9, 2]];
cc:=[4,5,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=2;
full_auto:=[432,734];
full_sign:=[0,2,3,8];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[19, 25, 22, 20, 26, 23, 21, 27, 24, 28, 34, 31, 29, 35, 32, 30, 36, 33, 10, 16, 13, 11, 17, 14, 12, 18, 15, 1, 7, 4, 2, 8, 5, 3, 9, 6, 55, 61, 58, 56, 62, 59, 57, 63, 60, 64, 70, 67, 65, 71, 68, 66, 72, 69, 46, 52, 49, 47, 53, 50, 48, 54, 51, 37, 43, 40, 38, 44, 41, 39, 45, 42], [40, 39, 44, 45, 41, 37, 38, 43, 42, 49, 48, 53, 54, 50, 46, 47, 52, 51, 67, 66, 71, 72, 68, 64, 65, 70, 69, 58, 57, 62, 63, 59, 55, 56, 61, 60, 13, 12, 17, 18, 14, 10, 11, 16, 15, 4, 3, 8, 9, 5, 1, 2, 7, 6, 22, 21, 26, 27, 23, 19, 20, 25, 24, 31, 30, 35, 36, 32, 28, 29, 34, 33], [63, 56, 58, 55, 60, 62, 59, 61, 57, 72, 65, 67, 64, 69, 71, 68, 70, 66, 45, 38, 40, 37, 42, 44, 41, 43, 39, 54, 47, 49, 46, 51, 53, 50, 52, 48, 36, 29, 31, 28, 33, 35, 32, 34, 30, 27, 20, 22, 19, 24, 26, 23, 25, 21, 18, 11, 13, 10, 15, 17, 14, 16, 12, 9, 2, 4, 1, 6, 8, 5, 7, 3]];
cc:=[4,5,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=3;
full_auto:=[432,734];
full_sign:=[0,2,3,8];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[19, 25, 22, 20, 26, 23, 21, 27, 24, 28, 34, 31, 29, 35, 32, 30, 36, 33, 10, 16, 13, 11, 17, 14, 12, 18, 15, 1, 7, 4, 2, 8, 5, 3, 9, 6, 55, 61, 58, 56, 62, 59, 57, 63, 60, 64, 70, 67, 65, 71, 68, 66, 72, 69, 46, 52, 49, 47, 53, 50, 48, 54, 51, 37, 43, 40, 38, 44, 41, 39, 45, 42], [45, 41, 37, 38, 43, 42, 40, 39, 44, 54, 50, 46, 47, 52, 51, 49, 48, 53, 72, 68, 64, 65, 70, 69, 67, 66, 71, 63, 59, 55, 56, 61, 60, 58, 57, 62, 18, 14, 10, 11, 16, 15, 13, 12, 17, 9, 5, 1, 2, 7, 6, 4, 3, 8, 27, 23, 19, 20, 25, 24, 22, 21, 26, 36, 32, 28, 29, 34, 33, 31, 30, 35], [61, 57, 59, 56, 58, 63, 60, 62, 55, 70, 66, 68, 65, 67, 72, 69, 71, 64, 43, 39, 41, 38, 40, 45, 42, 44, 37, 52, 48, 50, 47, 49, 54, 51, 53, 46, 34, 30, 32, 29, 31, 36, 33, 35, 28, 25, 21, 23, 20, 22, 27, 24, 26, 19, 16, 12, 14, 11, 13, 18, 15, 17, 10, 7, 3, 5, 2, 4, 9, 6, 8, 1]];
cc:=[4,5,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=4;
full_auto:=[432,734];
full_sign:=[0,2,3,8];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);
