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

• Label: 6.56-7.0.2-4-14.3
• 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:

$4, 5, 14$

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.

6.56-7.0.2-4-14.3.1

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