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

• Label: 8.64-53.0.2-4-32.3
• 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:

$3, 5, 14$

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.

8.64-53.0.2-4-32.3.1

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