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

• Label: 10.42-6.0.2-21-42.3
• 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:

$2, 21, 35$

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.

10.42-6.0.2-21-42.3.1

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