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

• Label: 10.42-6.0.2-21-42.5
• 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:

$2, 23, 34$

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.

10.42-6.0.2-21-42.5.1

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