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

• Label: 7.64-41.0.2-4-16.2
• 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:	$[64,41]$
Signature:	$[ 0; 2, 4, 16 ]$

Conjugacy classes for this refined passport:

$4, 8, 16$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times E^{4}$
Corresponding character(s):	$7, 12, 15$

Other Data

Hyperelliptic curve(s):	no
Cyclic trigonal curve(s):	no

Generating vector(s)

Displaying the unique generating vector for this refined passport.

7.64-41.0.2-4-16.2.1

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