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

• Label: 8.48-25.0.2-6-24.6
• 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:

$4, 10, 21$

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.

8.48-25.0.2-6-24.6.1

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