One refined passport of genus 8 with automorphism group $C_3\times D_8$

• Label: 8.48-25.0.2-6-24.2
• Genus: \(8\)
• Quotient genus: \(0\)
• Group: \(C_3\times D_8\)
• Signature: \([ 0; 2, 6, 24 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$8$
Quotient genus:	$0$
Group name:	$C_3\times D_8$
Group identifier:	$[48,25]$
Signature:	$[ 0; 2, 6, 24 ]$

Conjugacy classes for this refined passport:

$3, 12, 21$

Jacobian variety group algebra decomposition:	$E\times E\times E^{2}\times A_{2}^{2}$
Corresponding character(s):	$5, 6, 14, 18$

Other Data

Hyperelliptic curve(s):	no
Cyclic trigonal curve(s):	yes
Trigonal automorphism:	(1,5,9) (2,6,10) (3,7,11) (4,8,12) (13,17,21) (14,18,22) (15,19,23) (16,20,24) (25,29,33) (26,30,34) (27,31,35) (28,32,36) (37,41,45) (38,42,46) (39,43,47) (40,44,48)

Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.48-25.0.2-6-24.2.1

	(1,13) (2,14) (3,16) (4,15) (5,17) (6,18) (7,20) (8,19) (9,21) (10,22) (11,24) (12,23) (25,37) (26,38) (27,40) (28,39) (29,41) (30,42) (31,44) (32,43) (33,45) (34,46) (35,48) (36,47)
	(1,29,9,25,5,33) (2,30,10,26,6,34) (3,32,11,28,7,36) (4,31,12,27,8,35) (13,43,21,39,17,47) (14,44,22,40,18,48) (15,41,23,37,19,45) (16,42,24,38,20,46)
	(1,45,8,40,10,42,3,47,5,37,12,44,2,46,7,39,9,41,4,48,6,38,11,43) (13,36,20,26,22,31,15,33,17,28,24,30,14,35,19,25,21,32,16,34,18,27,23,29)