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

• Label: 8.64-53.0.2-4-32.6
• 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:

$3, 5, 17$

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.

8.64-53.0.2-4-32.6.1

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