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

• Label: 7.64-38.0.2-4-16.8
• 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:

$5, 10, 21$

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.

7.64-38.0.2-4-16.8.1

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