One refined passport of genus 10 with automorphism group $C_{42}$

• Label: 10.42-6.0.2-21-42.6
• Genus: \(10\)
• Quotient genus: \(0\)
• Group: \(C_{42}\)
• Signature: \([ 0; 2, 21, 42 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$10$
Quotient genus:	$0$
Group name:	$C_{42}$
Group identifier:	$[42,6]$
Signature:	$[ 0; 2, 21, 42 ]$

Conjugacy classes for this refined passport:

$2, 24, 33$

Jacobian variety group algebra decomposition:

$E\times A_{3}\times A_{6}$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,22) (2,23) (3,24) (4,25) (5,26) (6,27) (7,28) (8,29) (9,30) (10,31) (11,32) (12,33) (13,34) (14,35) (15,36) (16,37) (17,38) (18,39) (19,40) (20,41) (21,42)
Cyclic trigonal curve(s):	no

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

$y^2=x^{21}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.42-6.0.2-21-42.6.1

	(1,22) (2,23) (3,24) (4,25) (5,26) (6,27) (7,28) (8,29) (9,30) (10,31) (11,32) (12,33) (13,34) (14,35) (15,36) (16,37) (17,38) (18,39) (19,40) (20,41) (21,42)
	(1,11,21,3,13,16,5,8,18,7,10,20,2,12,15,4,14,17,6,9,19) (22,32,42,24,34,37,26,29,39,28,31,41,23,33,36,25,35,38,27,30,40)
	(1,40,9,27,17,35,4,36,12,23,20,31,7,39,8,26,16,34,3,42,11,22,19,30,6,38,14,25,15,33,2,41,10,28,18,29,5,37,13,24,21,32)