One refined passport of genus 7 with automorphism group $C_3\times D_7$

• Label: 7.42-4.0.2-6-21.1
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_3\times D_7\)
• Signature: \([ 0; 2, 6, 21 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$7$
Quotient genus:	$0$
Group name:	$C_3\times D_7$
Group identifier:	$[42,4]$
Signature:	$[ 0; 2, 6, 21 ]$

Conjugacy classes for this refined passport:

$2, 5, 11$

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

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

$y^3=x^8-x$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

7.42-4.0.2-6-21.1.1

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