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

• Label: 5.40-5.0.2-4-20.8
• 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:

$4, 8, 15$

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.

5.40-5.0.2-4-20.8.1

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