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

• Label: 8.48-25.0.2-6-24.7
• 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:

$4, 11, 18$

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.

8.48-25.0.2-6-24.7.1

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