One refined passport of genus 6 with automorphism group $C_7:D_4$

• Label: 6.56-7.0.2-4-14.4
• Genus: \(6\)
• Quotient genus: \(0\)
• Group: \(C_7:D_4\)
• Signature: \([ 0; 2, 4, 14 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$6$
Quotient genus:	$0$
Group name:	$C_7:D_4$
Group identifier:	$[56,7]$
Signature:	$[ 0; 2, 4, 14 ]$

Conjugacy classes for this refined passport:

$4, 5, 15$

Jacobian variety group algebra decomposition:	$A_{3}^{2}$
Corresponding character(s):	$6$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14) (15,22) (16,23) (17,24) (18,25) (19,26) (20,27) (21,28) (29,36) (30,37) (31,38) (32,39) (33,40) (34,41) (35,42) (43,50) (44,51) (45,52) (46,53) (47,54) (48,55) (49,56)
Cyclic trigonal curve(s):	no

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

$y^2=x^{14}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.56-7.0.2-4-14.4.1

	(1,29) (2,35) (3,34) (4,33) (5,32) (6,31) (7,30) (8,36) (9,42) (10,41) (11,40) (12,39) (13,38) (14,37) (15,50) (16,56) (17,55) (18,54) (19,53) (20,52) (21,51) (22,43) (23,49) (24,48) (25,47) (26,46) (27,45) (28,44)
	(1,48,8,55) (2,47,9,54) (3,46,10,53) (4,45,11,52) (5,44,12,51) (6,43,13,50) (7,49,14,56) (15,41,22,34) (16,40,23,33) (17,39,24,32) (18,38,25,31) (19,37,26,30) (20,36,27,29) (21,42,28,35)
	(1,17,5,21,2,18,6,15,3,19,7,16,4,20) (8,24,12,28,9,25,13,22,10,26,14,23,11,27) (29,45,33,49,30,46,34,43,31,47,35,44,32,48) (36,52,40,56,37,53,41,50,38,54,42,51,39,55)