One refined passport of genus 7 with automorphism group $D_8:C_4$

• Label: 7.64-38.0.2-4-16.10
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(D_8:C_4\)
• Signature: \([ 0; 2, 4, 16 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$7$
Quotient genus:	$0$
Group name:	$D_8:C_4$
Group identifier:	$[64,38]$
Signature:	$[ 0; 2, 4, 16 ]$

Conjugacy classes for this refined passport:

$6, 9, 17$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{2}^{2}$
Corresponding character(s):	$6, 12, 17$

Other Data

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

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

$y^2=x^{16}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

7.64-38.0.2-4-16.10.1

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