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

• Label: 7.56-4.0.2-4-28.9
• 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:

$4, 7, 18$

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.

7.56-4.0.2-4-28.9.1

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