One refined passport of genus 5 with automorphism group $C_4\times D_5$

• Label: 5.40-5.0.2-4-20.6
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_4\times D_5\)
• Signature: \([ 0; 2, 4, 20 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$5$
Quotient genus:	$0$
Group name:	$C_4\times D_5$
Group identifier:	$[40,5]$
Signature:	$[ 0; 2, 4, 20 ]$

Conjugacy classes for this refined passport:

$4, 7, 16$

Jacobian variety group algebra decomposition:	$E\times A_{2}^{2}$
Corresponding character(s):	$6, 13$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) (21,26) (22,27) (23,28) (24,29) (25,30) (31,36) (32,37) (33,38) (34,39) (35,40)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x(x^{10}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

5.40-5.0.2-4-20.6.1

	(1,26) (2,30) (3,29) (4,28) (5,27) (6,21) (7,25) (8,24) (9,23) (10,22) (11,36) (12,40) (13,39) (14,38) (15,37) (16,31) (17,35) (18,34) (19,33) (20,32)
	(1,33,6,38) (2,32,7,37) (3,31,8,36) (4,35,9,40) (5,34,10,39) (11,28,16,23) (12,27,17,22) (13,26,18,21) (14,30,19,25) (15,29,20,24)
	(1,14,7,20,3,11,9,17,5,13,6,19,2,15,8,16,4,12,10,18) (21,34,27,40,23,31,29,37,25,33,26,39,22,35,28,36,24,32,30,38)