// Magma code for the lmfdb family of higher genus curves 10.80-6.0.2-4-40.4
// 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:=[80,6];
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:=[0,2,4,40];
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:=[[41, 45, 44, 43, 42, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 71, 75, 74, 73, 72, 76, 80, 79, 78, 77, 61, 65, 64, 63, 62, 66, 70, 69, 68, 67, 1, 5, 4, 3, 2, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 11, 15, 14, 13, 12, 31, 35, 34, 33, 32, 36, 40, 39, 38, 37, 21, 25, 24, 23, 22, 26, 30, 29, 28, 27], [70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 75, 74, 73, 72, 71, 80, 79, 78, 77, 76, 45, 44, 43, 42, 41, 50, 49, 48, 47, 46, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 35, 34, 33, 32, 31, 40, 39, 38, 37, 36, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [32, 33, 34, 35, 31, 37, 38, 39, 40, 36, 27, 28, 29, 30, 26, 22, 23, 24, 25, 21, 7, 8, 9, 10, 6, 2, 3, 4, 5, 1, 17, 18, 19, 20, 16, 12, 13, 14, 15, 11, 72, 73, 74, 75, 71, 77, 78, 79, 80, 76, 67, 68, 69, 70, 66, 62, 63, 64, 65, 61, 47, 48, 49, 50, 46, 42, 43, 44, 45, 41, 57, 58, 59, 60, 56, 52, 53, 54, 55, 51]];
cc:=[3,5,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 16, 17, 18, 19, 20, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 31, 32, 33, 34, 35, 46, 47, 48, 49, 50, 41, 42, 43, 44, 45, 56, 57, 58, 59, 60, 51, 52, 53, 54, 55, 66, 67, 68, 69, 70, 61, 62, 63, 64, 65, 76, 77, 78, 79, 80, 71, 72, 73, 74, 75];
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 >);
