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

• Label: 7.64-38.0.2-4-16.16
• 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:

$6, 10, 22$

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.

7.64-38.0.2-4-16.16.1

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