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

• Label: 7.56-4.0.2-4-28.4
• 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:

$3, 8, 15$

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.

7.56-4.0.2-4-28.4.1

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