One refined passport of genus 9 with automorphism group $C_4\times D_9$

• Label: 9.72-5.0.2-4-36.9
• Genus: \(9\)
• Quotient genus: \(0\)
• Group: \(C_4\times D_9\)
• Signature: \([ 0; 2, 4, 36 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$9$
Quotient genus:	$0$
Group name:	$C_4\times D_9$
Group identifier:	$[72,5]$
Signature:	$[ 0; 2, 4, 36 ]$

Conjugacy classes for this refined passport:

$4, 8, 22$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{3}^{2}$
Corresponding character(s):	$5, 11, 19$

Other Data

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

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

$y^2=x(x^{18}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.72-5.0.2-4-36.9.1

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