One refined passport of genus 9 with automorphism group $D_{10}:C_4$

• Label: 9.80-14.0.2-4-20.5
• Genus: \(9\)
• Quotient genus: \(0\)
• Group: \(D_{10}:C_4\)
• Signature: \([ 0; 2, 4, 20 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$9$
Quotient genus:	$0$
Group name:	$D_{10}:C_4$
Group identifier:	$[80,14]$
Signature:	$[ 0; 2, 4, 20 ]$

Conjugacy classes for this refined passport:

$5, 10, 19$

Jacobian variety group algebra decomposition:	$E\times A_{2}^{2}\times A_{2}^{2}$
Corresponding character(s):	$6, 12, 19$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,16) (2,17) (3,18) (4,19) (5,20) (6,11) (7,12) (8,13) (9,14) (10,15) (21,36) (22,37) (23,38) (24,39) (25,40) (26,31) (27,32) (28,33) (29,34) (30,35) (41,56) (42,57) (43,58) (44,59) (45,60) (46,51) (47,52) (48,53) (49,54) (50,55) (61,76) (62,77) (63,78) (64,79) (65,80) (66,71) (67,72) (68,73) (69,74) (70,75)
Cyclic trigonal curve(s):	no

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

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.80-14.0.2-4-20.5.1

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