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

• Label: 8.48-25.0.2-6-24.5
• 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:

$4, 10, 19$

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.

8.48-25.0.2-6-24.5.1

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