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

• Label: 10.80-6.0.2-4-40.2
• 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:

$3, 5, 17$

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.

10.80-6.0.2-4-40.2.1

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