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

• Label: 6.48-15.0.2-6-8.4
• 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:

$4, 9, 11$

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.

6.48-15.0.2-6-8.4.1

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