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

• Label: 7.56-4.0.2-4-28.5
• 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:

$3, 8, 17$

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.

7.56-4.0.2-4-28.5.1

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