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

• Label: 8.64-53.0.2-4-32.1
• 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:

$3, 5, 12$

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.

8.64-53.0.2-4-32.1.1

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