One refined passport of genus 10 with automorphism group $C_{40}:C_2$

• Label: 10.80-6.0.2-4-40.1
• Genus: \(10\)
• Quotient genus: \(0\)
• Group: \(C_{40}:C_2\)
• Signature: \([ 0; 2, 4, 40 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$10$
Quotient genus:	$0$
Group name:	$C_{40}:C_2$
Group identifier:	$[80,6]$
Signature:	$[ 0; 2, 4, 40 ]$

Conjugacy classes for this refined passport:

$3, 5, 16$

Jacobian variety group algebra decomposition:	$E^{2}\times A_{4}^{2}$
Corresponding character(s):	$10, 16$

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) (41,46) (42,47) (43,48) (44,49) (45,50) (51,56) (52,57) (53,58) (54,59) (55,60) (61,66) (62,67) (63,68) (64,69) (65,70) (71,76) (72,77) (73,78) (74,79) (75,80)
Cyclic trigonal curve(s):	no

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

$y^2=x(x^{20}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.80-6.0.2-4-40.1.1

	(1,41) (2,45) (3,44) (4,43) (5,42) (6,46) (7,50) (8,49) (9,48) (10,47) (11,56) (12,60) (13,59) (14,58) (15,57) (16,51) (17,55) (18,54) (19,53) (20,52) (21,71) (22,75) (23,74) (24,73) (25,72) (26,76) (27,80) (28,79) (29,78) (30,77) (31,61) (32,65) (33,64) (34,63) (35,62) (36,66) (37,70) (38,69) (39,68) (40,67)
	(1,67,6,62) (2,66,7,61) (3,70,8,65) (4,69,9,64) (5,68,10,63) (11,72,16,77) (12,71,17,76) (13,75,18,80) (14,74,19,79) (15,73,20,78) (21,42,26,47) (22,41,27,46) (23,45,28,50) (24,44,29,49) (25,43,30,48) (31,57,36,52) (32,56,37,51) (33,60,38,55) (34,59,39,54) (35,58,40,53)
	(1,35,19,23,7,36,15,29,3,32,16,25,9,38,12,26,5,34,18,22,6,40,14,28,2,31,20,24,8,37,11,30,4,33,17,21,10,39,13,27) (41,75,59,63,47,76,55,69,43,72,56,65,49,78,52,66,45,74,58,62,46,80,54,68,42,71,60,64,48,77,51,70,44,73,57,61,50,79,53,67)