# GAP code for the lmfdb family of higher genus curves 7.18-2.0.6-9-18 # The results are stored in a list of records called 'data' # WARNING: The conjugacy class numbers may not be the same as those listed in lmfdb.org, as numberings in Magma and GAP may differ. If you need to connect this data to that posted on lmfdb.org, compare the variables 'passport_label' and 'gen_vector_labels'. data:=[]; # Generate data which is the same for all entries. gp_id:=[18,2]; signature:=[0,6,9,18]; genus:=7; r:=Length(signature)-1; g0:=signature[1]; dim:=3*g0-3+r; # Here we add an action to data. gen_vectors:=[[11, 12, 10, 14, 15, 13, 17, 18, 16, 2, 3, 1, 5, 6, 4, 8, 9, 7], [4, 5, 6, 7, 8, 9, 2, 3, 1, 13, 14, 15, 16, 17, 18, 11, 12, 10], [17, 18, 16, 12, 10, 11, 15, 13, 14, 8, 9, 7, 3, 1, 2, 6, 4, 5]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=1; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[11, 12, 10, 14, 15, 13, 17, 18, 16, 2, 3, 1, 5, 6, 4, 8, 9, 7], [7, 8, 9, 2, 3, 1, 5, 6, 4, 16, 17, 18, 11, 12, 10, 14, 15, 13], [14, 15, 13, 17, 18, 16, 12, 10, 11, 5, 6, 4, 8, 9, 7, 3, 1, 2]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=2; gen_vect_label:=1; braid_class:=1; topological_class:=[2, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[11, 12, 10, 14, 15, 13, 17, 18, 16, 2, 3, 1, 5, 6, 4, 8, 9, 7], [5, 6, 4, 8, 9, 7, 3, 1, 2, 14, 15, 13, 17, 18, 16, 12, 10, 11], [16, 17, 18, 11, 12, 10, 14, 15, 13, 7, 8, 9, 2, 3, 1, 5, 6, 4]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=3; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[11, 12, 10, 14, 15, 13, 17, 18, 16, 2, 3, 1, 5, 6, 4, 8, 9, 7], [8, 9, 7, 3, 1, 2, 6, 4, 5, 17, 18, 16, 12, 10, 11, 15, 13, 14], [13, 14, 15, 16, 17, 18, 11, 12, 10, 4, 5, 6, 7, 8, 9, 2, 3, 1]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=4; gen_vect_label:=1; braid_class:=1; topological_class:=[2, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[11, 12, 10, 14, 15, 13, 17, 18, 16, 2, 3, 1, 5, 6, 4, 8, 9, 7], [6, 4, 5, 9, 7, 8, 1, 2, 3, 15, 13, 14, 18, 16, 17, 10, 11, 12], [18, 16, 17, 10, 11, 12, 13, 14, 15, 9, 7, 8, 1, 2, 3, 4, 5, 6]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=5; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[11, 12, 10, 14, 15, 13, 17, 18, 16, 2, 3, 1, 5, 6, 4, 8, 9, 7], [9, 7, 8, 1, 2, 3, 4, 5, 6, 18, 16, 17, 10, 11, 12, 13, 14, 15], [15, 13, 14, 18, 16, 17, 10, 11, 12, 6, 4, 5, 9, 7, 8, 1, 2, 3]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=6; gen_vect_label:=1; braid_class:=1; topological_class:=[2, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[12, 10, 11, 15, 13, 14, 18, 16, 17, 3, 1, 2, 6, 4, 5, 9, 7, 8], [4, 5, 6, 7, 8, 9, 2, 3, 1, 13, 14, 15, 16, 17, 18, 11, 12, 10], [16, 17, 18, 11, 12, 10, 14, 15, 13, 7, 8, 9, 2, 3, 1, 5, 6, 4]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=7; gen_vect_label:=1; braid_class:=1; topological_class:=[2, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[12, 10, 11, 15, 13, 14, 18, 16, 17, 3, 1, 2, 6, 4, 5, 9, 7, 8], [7, 8, 9, 2, 3, 1, 5, 6, 4, 16, 17, 18, 11, 12, 10, 14, 15, 13], [13, 14, 15, 16, 17, 18, 11, 12, 10, 4, 5, 6, 7, 8, 9, 2, 3, 1]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=8; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[12, 10, 11, 15, 13, 14, 18, 16, 17, 3, 1, 2, 6, 4, 5, 9, 7, 8], [5, 6, 4, 8, 9, 7, 3, 1, 2, 14, 15, 13, 17, 18, 16, 12, 10, 11], [18, 16, 17, 10, 11, 12, 13, 14, 15, 9, 7, 8, 1, 2, 3, 4, 5, 6]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=9; gen_vect_label:=1; braid_class:=1; topological_class:=[2, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[12, 10, 11, 15, 13, 14, 18, 16, 17, 3, 1, 2, 6, 4, 5, 9, 7, 8], [8, 9, 7, 3, 1, 2, 6, 4, 5, 17, 18, 16, 12, 10, 11, 15, 13, 14], [15, 13, 14, 18, 16, 17, 10, 11, 12, 6, 4, 5, 9, 7, 8, 1, 2, 3]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=10; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[12, 10, 11, 15, 13, 14, 18, 16, 17, 3, 1, 2, 6, 4, 5, 9, 7, 8], [6, 4, 5, 9, 7, 8, 1, 2, 3, 15, 13, 14, 18, 16, 17, 10, 11, 12], [17, 18, 16, 12, 10, 11, 15, 13, 14, 8, 9, 7, 3, 1, 2, 6, 4, 5]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=11; gen_vect_label:=1; braid_class:=1; topological_class:=[2, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) ); # Here we add an action to data. gen_vectors:=[[12, 10, 11, 15, 13, 14, 18, 16, 17, 3, 1, 2, 6, 4, 5, 9, 7, 8], [9, 7, 8, 1, 2, 3, 4, 5, 6, 18, 16, 17, 10, 11, 12, 13, 14, 15], [14, 15, 13, 17, 18, 16, 12, 10, 11, 5, 6, 4, 8, 9, 7, 3, 1, 2]]; perm_list:= List([1..Length(gen_vectors)], x->PermList(gen_vectors[x])); S:=SymmetricGroup(gp_id[1]); G:=Subgroup(S,perm_list); passport_label:=12; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Add( data, rec( group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=perm_list, 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) );