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

• Label: 6.48-15.0.2-6-8.2
• 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:

$4, 8, 11$

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.

6.48-15.0.2-6-8.2.1

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