One refined passport of genus 7 with automorphism group $C_3\times D_9$

• Label: 7.54-3.0.2-6-9.3
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_3\times D_9\)
• Signature: \([ 0; 2, 6, 9 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$7$
Quotient genus:	$0$
Group name:	$C_3\times D_9$
Group identifier:	$[54,3]$
Signature:	$[ 0; 2, 6, 9 ]$

Conjugacy classes for this refined passport:

$2, 8, 18$

Jacobian variety group algebra decomposition:	$E\times A_{3}^{2}$
Corresponding character(s):	$3, 10$

Other Data

Hyperelliptic curve(s):	no
Cyclic trigonal curve(s):	yes
Trigonal automorphism:	(1,10,19) (2,11,20) (3,12,21) (4,13,22) (5,14,23) (6,15,24) (7,16,25) (8,17,26) (9,18,27) (28,37,46) (29,38,47) (30,39,48) (31,40,49) (32,41,50) (33,42,51) (34,43,52) (35,44,53) (36,45,54)

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

$y^3=x^9-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

7.54-3.0.2-6-9.3.1

	(1,28) (2,30) (3,29) (4,35) (5,34) (6,36) (7,32) (8,31) (9,33) (10,37) (11,39) (12,38) (13,44) (14,43) (15,45) (16,41) (17,40) (18,42) (19,46) (20,48) (21,47) (22,53) (23,52) (24,54) (25,50) (26,49) (27,51)
	(1,44,19,35,10,53) (2,43,20,34,11,52) (3,45,21,36,12,54) (4,41,22,32,13,50) (5,40,23,31,14,49) (6,42,24,33,15,51) (7,38,25,29,16,47) (8,37,26,28,17,46) (9,39,27,30,18,48)
	(1,22,16,3,24,18,2,23,17) (4,25,12,6,27,11,5,26,10) (7,21,15,9,20,14,8,19,13) (28,49,43,30,51,45,29,50,44) (31,52,39,33,54,38,32,53,37) (34,48,42,36,47,41,35,46,40)