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

• Label: 10.80-6.0.2-4-40.8
• 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:

$3, 5, 23$

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.

10.80-6.0.2-4-40.8.1

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