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

• Label: 7.64-38.0.2-4-16.3
• 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:

$5, 9, 20$

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.

7.64-38.0.2-4-16.3.1

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