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

• Label: 5.40-5.0.2-4-20.4
• 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:

$3, 8, 16$

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.

5.40-5.0.2-4-20.4.1

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