One refined passport of genus 4 with automorphism group $C_5:D_4$

• Label: 4.40-8.0.2-4-10.4
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(C_5:D_4\)
• Signature: \([ 0; 2, 4, 10 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$4$
Quotient genus:	$0$
Group name:	$C_5:D_4$
Group identifier:	$[40,8]$
Signature:	$[ 0; 2, 4, 10 ]$

Conjugacy classes for this refined passport:

$4, 5, 13$

Jacobian variety group algebra decomposition:	$A_{2}^{2}$
Corresponding character(s):	$9$

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:

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

4.40-8.0.2-4-10.4.1

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