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

• Label: 7.56-4.0.2-4-28.1
• 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:

$3, 7, 16$

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.

7.56-4.0.2-4-28.1.1

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