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

• Label: 7.56-4.0.2-4-28.2
• 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:

$3, 7, 19$

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.

7.56-4.0.2-4-28.2.1

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