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

• Label: 9.72-5.0.2-4-36.11
• 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:

$4, 9, 23$

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.

9.72-5.0.2-4-36.11.1

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