// Magma code for the lmfdb family of higher genus curves 8.72-8.0.2-4-18
// 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:=[72,8];
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:=[0,2,4,18];
genus:=8;
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:=[[37, 39, 38, 44, 43, 45, 41, 40, 42, 46, 48, 47, 53, 52, 54, 50, 49, 51, 64, 66, 65, 71, 70, 72, 68, 67, 69, 55, 57, 56, 62, 61, 63, 59, 58, 60, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15, 28, 30, 29, 35, 34, 36, 32, 31, 33, 19, 21, 20, 26, 25, 27, 23, 22, 24], [62, 61, 63, 59, 58, 60, 56, 55, 57, 71, 70, 72, 68, 67, 69, 65, 64, 66, 53, 52, 54, 50, 49, 51, 47, 46, 48, 44, 43, 45, 41, 40, 42, 38, 37, 39, 26, 25, 27, 23, 22, 24, 20, 19, 21, 35, 34, 36, 32, 31, 33, 29, 28, 30, 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3], [22, 23, 24, 25, 26, 27, 21, 19, 20, 31, 32, 33, 34, 35, 36, 30, 28, 29, 4, 5, 6, 7, 8, 9, 3, 1, 2, 13, 14, 15, 16, 17, 18, 12, 10, 11, 58, 59, 60, 61, 62, 63, 57, 55, 56, 67, 68, 69, 70, 71, 72, 66, 64, 65, 40, 41, 42, 43, 44, 45, 39, 37, 38, 49, 50, 51, 52, 53, 54, 48, 46, 47]];
cc:=[4,6,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27, 46, 47, 48, 49, 50, 51, 52, 53, 54, 37, 38, 39, 40, 41, 42, 43, 44, 45, 64, 65, 66, 67, 68, 69, 70, 71, 72, 55, 56, 57, 58, 59, 60, 61, 62, 63];
is_cyclic_trigonal:=false;
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, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[37, 39, 38, 44, 43, 45, 41, 40, 42, 46, 48, 47, 53, 52, 54, 50, 49, 51, 64, 66, 65, 71, 70, 72, 68, 67, 69, 55, 57, 56, 62, 61, 63, 59, 58, 60, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15, 28, 30, 29, 35, 34, 36, 32, 31, 33, 19, 21, 20, 26, 25, 27, 23, 22, 24], [60, 59, 58, 57, 56, 55, 61, 63, 62, 69, 68, 67, 66, 65, 64, 70, 72, 71, 51, 50, 49, 48, 47, 46, 52, 54, 53, 42, 41, 40, 39, 38, 37, 43, 45, 44, 24, 23, 22, 21, 20, 19, 25, 27, 26, 33, 32, 31, 30, 29, 28, 34, 36, 35, 15, 14, 13, 12, 11, 10, 16, 18, 17, 6, 5, 4, 3, 2, 1, 7, 9, 8], [27, 25, 26, 20, 21, 19, 23, 24, 22, 36, 34, 35, 29, 30, 28, 32, 33, 31, 9, 7, 8, 2, 3, 1, 5, 6, 4, 18, 16, 17, 11, 12, 10, 14, 15, 13, 63, 61, 62, 56, 57, 55, 59, 60, 58, 72, 70, 71, 65, 66, 64, 68, 69, 67, 45, 43, 44, 38, 39, 37, 41, 42, 40, 54, 52, 53, 47, 48, 46, 50, 51, 49]];
cc:=[4,6,17];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27, 46, 47, 48, 49, 50, 51, 52, 53, 54, 37, 38, 39, 40, 41, 42, 43, 44, 45, 64, 65, 66, 67, 68, 69, 70, 71, 72, 55, 56, 57, 58, 59, 60, 61, 62, 63];
is_cyclic_trigonal:=false;
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, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[37, 39, 38, 44, 43, 45, 41, 40, 42, 46, 48, 47, 53, 52, 54, 50, 49, 51, 64, 66, 65, 71, 70, 72, 68, 67, 69, 55, 57, 56, 62, 61, 63, 59, 58, 60, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15, 28, 30, 29, 35, 34, 36, 32, 31, 33, 19, 21, 20, 26, 25, 27, 23, 22, 24], [61, 63, 62, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 52, 54, 53, 49, 51, 50, 46, 48, 47, 43, 45, 44, 40, 42, 41, 37, 39, 38, 25, 27, 26, 22, 24, 23, 19, 21, 20, 34, 36, 35, 31, 33, 32, 28, 30, 29, 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2], [23, 24, 22, 26, 27, 25, 19, 20, 21, 32, 33, 31, 35, 36, 34, 28, 29, 30, 5, 6, 4, 8, 9, 7, 1, 2, 3, 14, 15, 13, 17, 18, 16, 10, 11, 12, 59, 60, 58, 62, 63, 61, 55, 56, 57, 68, 69, 67, 71, 72, 70, 64, 65, 66, 41, 42, 40, 44, 45, 43, 37, 38, 39, 50, 51, 49, 53, 54, 52, 46, 47, 48]];
cc:=[4,6,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27, 46, 47, 48, 49, 50, 51, 52, 53, 54, 37, 38, 39, 40, 41, 42, 43, 44, 45, 64, 65, 66, 67, 68, 69, 70, 71, 72, 55, 56, 57, 58, 59, 60, 61, 62, 63];
is_cyclic_trigonal:=false;
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, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[37, 39, 38, 44, 43, 45, 41, 40, 42, 46, 48, 47, 53, 52, 54, 50, 49, 51, 64, 66, 65, 71, 70, 72, 68, 67, 69, 55, 57, 56, 62, 61, 63, 59, 58, 60, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15, 28, 30, 29, 35, 34, 36, 32, 31, 33, 19, 21, 20, 26, 25, 27, 23, 22, 24], [59, 58, 60, 56, 55, 57, 63, 62, 61, 68, 67, 69, 65, 64, 66, 72, 71, 70, 50, 49, 51, 47, 46, 48, 54, 53, 52, 41, 40, 42, 38, 37, 39, 45, 44, 43, 23, 22, 24, 20, 19, 21, 27, 26, 25, 32, 31, 33, 29, 28, 30, 36, 35, 34, 14, 13, 15, 11, 10, 12, 18, 17, 16, 5, 4, 6, 2, 1, 3, 9, 8, 7], [25, 26, 27, 21, 19, 20, 24, 22, 23, 34, 35, 36, 30, 28, 29, 33, 31, 32, 7, 8, 9, 3, 1, 2, 6, 4, 5, 16, 17, 18, 12, 10, 11, 15, 13, 14, 61, 62, 63, 57, 55, 56, 60, 58, 59, 70, 71, 72, 66, 64, 65, 69, 67, 68, 43, 44, 45, 39, 37, 38, 42, 40, 41, 52, 53, 54, 48, 46, 47, 51, 49, 50]];
cc:=[4,6,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27, 46, 47, 48, 49, 50, 51, 52, 53, 54, 37, 38, 39, 40, 41, 42, 43, 44, 45, 64, 65, 66, 67, 68, 69, 70, 71, 72, 55, 56, 57, 58, 59, 60, 61, 62, 63];
is_cyclic_trigonal:=false;
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, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[37, 39, 38, 44, 43, 45, 41, 40, 42, 46, 48, 47, 53, 52, 54, 50, 49, 51, 64, 66, 65, 71, 70, 72, 68, 67, 69, 55, 57, 56, 62, 61, 63, 59, 58, 60, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15, 28, 30, 29, 35, 34, 36, 32, 31, 33, 19, 21, 20, 26, 25, 27, 23, 22, 24], [63, 62, 61, 60, 59, 58, 57, 56, 55, 72, 71, 70, 69, 68, 67, 66, 65, 64, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 27, 26, 25, 24, 23, 22, 21, 20, 19, 36, 35, 34, 33, 32, 31, 30, 29, 28, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [24, 22, 23, 27, 25, 26, 20, 21, 19, 33, 31, 32, 36, 34, 35, 29, 30, 28, 6, 4, 5, 9, 7, 8, 2, 3, 1, 15, 13, 14, 18, 16, 17, 11, 12, 10, 60, 58, 59, 63, 61, 62, 56, 57, 55, 69, 67, 68, 72, 70, 71, 65, 66, 64, 42, 40, 41, 45, 43, 44, 38, 39, 37, 51, 49, 50, 54, 52, 53, 47, 48, 46]];
cc:=[4,6,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27, 46, 47, 48, 49, 50, 51, 52, 53, 54, 37, 38, 39, 40, 41, 42, 43, 44, 45, 64, 65, 66, 67, 68, 69, 70, 71, 72, 55, 56, 57, 58, 59, 60, 61, 62, 63];
is_cyclic_trigonal:=false;
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, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[37, 39, 38, 44, 43, 45, 41, 40, 42, 46, 48, 47, 53, 52, 54, 50, 49, 51, 64, 66, 65, 71, 70, 72, 68, 67, 69, 55, 57, 56, 62, 61, 63, 59, 58, 60, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15, 28, 30, 29, 35, 34, 36, 32, 31, 33, 19, 21, 20, 26, 25, 27, 23, 22, 24], [58, 60, 59, 55, 57, 56, 62, 61, 63, 67, 69, 68, 64, 66, 65, 71, 70, 72, 49, 51, 50, 46, 48, 47, 53, 52, 54, 40, 42, 41, 37, 39, 38, 44, 43, 45, 22, 24, 23, 19, 21, 20, 26, 25, 27, 31, 33, 32, 28, 30, 29, 35, 34, 36, 13, 15, 14, 10, 12, 11, 17, 16, 18, 4, 6, 5, 1, 3, 2, 8, 7, 9], [26, 27, 25, 19, 20, 21, 22, 23, 24, 35, 36, 34, 28, 29, 30, 31, 32, 33, 8, 9, 7, 1, 2, 3, 4, 5, 6, 17, 18, 16, 10, 11, 12, 13, 14, 15, 62, 63, 61, 55, 56, 57, 58, 59, 60, 71, 72, 70, 64, 65, 66, 67, 68, 69, 44, 45, 43, 37, 38, 39, 40, 41, 42, 53, 54, 52, 46, 47, 48, 49, 50, 51]];
cc:=[4,6,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27, 46, 47, 48, 49, 50, 51, 52, 53, 54, 37, 38, 39, 40, 41, 42, 43, 44, 45, 64, 65, 66, 67, 68, 69, 70, 71, 72, 55, 56, 57, 58, 59, 60, 61, 62, 63];
is_cyclic_trigonal:=false;
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, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);
