One refined passport of genus 7 with automorphism group $C_4\times D_7$

• Label: 7.56-4.0.2-4-28.7
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_4\times D_7\)
• Signature: \([ 0; 2, 4, 28 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$7$
Quotient genus:	$0$
Group name:	$C_4\times D_7$
Group identifier:	$[56,4]$
Signature:	$[ 0; 2, 4, 28 ]$

Conjugacy classes for this refined passport:

$4, 7, 15$

Jacobian variety group algebra decomposition:	$E\times A_{3}^{2}$
Corresponding character(s):	$5, 15$

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:

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

7.56-4.0.2-4-28.7.1

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