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

• Label: 7.64-38.0.2-4-16.7
• 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:

$5, 10, 19$

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.

7.64-38.0.2-4-16.7.1

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