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

• Label: 10.42-6.0.2-21-42.7
• 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:

$2, 25, 40$

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.

10.42-6.0.2-21-42.7.1

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