// Magma code for the lmfdb family of higher genus curves 10.30-4.0.3-30-30
// 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:=[30,4];
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:=[0,3,30,30];
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:=[[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 16, 17, 18, 19, 20], [22, 23, 24, 25, 21, 27, 28, 29, 30, 26, 17, 18, 19, 20, 16, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 2, 3, 4, 5, 1], [25, 21, 22, 23, 24, 30, 26, 27, 28, 29, 20, 16, 17, 18, 19, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 5, 1, 2, 3, 4]];
cc:=[3,23,28];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[60,10];
full_sign:=[0,2,6,30];
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:=[[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 16, 17, 18, 19, 20], [23, 24, 25, 21, 22, 28, 29, 30, 26, 27, 18, 19, 20, 16, 17, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 3, 4, 5, 1, 2], [24, 25, 21, 22, 23, 29, 30, 26, 27, 28, 19, 20, 16, 17, 18, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 4, 5, 1, 2, 3]];
cc:=[3,24,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
full_auto:=[60,10];
full_sign:=[0,2,6,30];
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:=[[11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 26, 27, 28, 29, 30, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [27, 28, 29, 30, 26, 17, 18, 19, 20, 16, 22, 23, 24, 25, 21, 12, 13, 14, 15, 11, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6], [30, 26, 27, 28, 29, 20, 16, 17, 18, 19, 25, 21, 22, 23, 24, 15, 11, 12, 13, 14, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9]];
cc:=[4,25,30];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
full_auto:=[60,10];
full_sign:=[0,2,6,30];
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:=[[11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 26, 27, 28, 29, 30, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [28, 29, 30, 26, 27, 18, 19, 20, 16, 17, 23, 24, 25, 21, 22, 13, 14, 15, 11, 12, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7], [29, 30, 26, 27, 28, 19, 20, 16, 17, 18, 24, 25, 21, 22, 23, 14, 15, 11, 12, 13, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8]];
cc:=[4,27,29];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
full_auto:=[60,10];
full_sign:=[0,2,6,30];
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>);
