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

• Label: 9.72-5.0.2-4-36.7
• 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:

$4, 8, 19$

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.

9.72-5.0.2-4-36.7.1

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