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

• Label: 10.42-6.0.2-21-42.8
• 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:

$2, 26, 39$

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.

10.42-6.0.2-21-42.8.1

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