One refined passport of genus 8 with automorphism group $\SD_{64}$

• Label: 8.64-53.0.2-4-32.5
• Genus: \(8\)
• Quotient genus: \(0\)
• Group: \(\SD_{64}\)
• Signature: \([ 0; 2, 4, 32 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$8$
Quotient genus:	$0$
Group name:	$\SD_{64}$
Group identifier:	$[64,53]$
Signature:	$[ 0; 2, 4, 32 ]$

Conjugacy classes for this refined passport:

$3, 5, 16$

Jacobian variety group algebra decomposition:	$A_{4}^{2}$
Corresponding character(s):	$12$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) (33,34) (35,36) (37,38) (39,40) (41,42) (43,44) (45,46) (47,48) (49,50) (51,52) (53,54) (55,56) (57,58) (59,60) (61,62) (63,64)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x(x^{16}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.64-53.0.2-4-32.5.1

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