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

• Label: 10.80-6.0.2-4-40.3
• 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:

$3, 5, 18$

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.

10.80-6.0.2-4-40.3.1

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