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

• Label: 8.64-53.0.2-4-32.4
• 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:

$3, 5, 15$

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.

8.64-53.0.2-4-32.4.1

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