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

• Label: 9.80-14.0.2-4-20.15
• 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:

$6, 10, 23$

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.

9.80-14.0.2-4-20.15.1

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