One refined passport of genus 6 with automorphism group $C_3:D_8$

• Label: 6.48-15.0.2-6-8.1
• Genus: \(6\)
• Quotient genus: \(0\)
• Group: \(C_3:D_8\)
• Signature: \([ 0; 2, 6, 8 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$6$
Quotient genus:	$0$
Group name:	$C_3:D_8$
Group identifier:	$[48,15]$
Signature:	$[ 0; 2, 6, 8 ]$

Conjugacy classes for this refined passport:

$4, 8, 10$

Jacobian variety group algebra decomposition:	$E^{2}\times A_{2}^{2}$
Corresponding character(s):	$8, 12$

Other Data

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

Equation(s) of curve(s) in this refined passport:

$y^3=(x^4-1)^2(x^4+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.48-15.0.2-6-8.1.1

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