One refined passport of genus 12 with automorphism group $C_{50}$

• Label: 12.50-2.0.2-25-50.20
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(C_{50}\)
• Signature: \([ 0; 2, 25, 50 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$C_{50}$
Group identifier:	$[50,2]$
Signature:	$[ 0; 2, 25, 50 ]$

Conjugacy classes for this refined passport:

$2, 30, 31$

Jacobian variety group algebra decomposition:

$A_{10}\times A_{2}$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,26) (2,27) (3,28) (4,29) (5,30) (6,31) (7,32) (8,33) (9,34) (10,35) (11,36) (12,37) (13,38) (14,39) (15,40) (16,41) (17,42) (18,43) (19,44) (20,45) (21,46) (22,47) (23,48) (24,49) (25,50)
Cyclic trigonal curve(s):	no

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

$y^2=x^{25}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.50-2.0.2-25-50.20.1

	(1,26) (2,27) (3,28) (4,29) (5,30) (6,31) (7,32) (8,33) (9,34) (10,35) (11,36) (12,37) (13,38) (14,39) (15,40) (16,41) (17,42) (18,43) (19,44) (20,45) (21,46) (22,47) (23,48) (24,49) (25,50)
	(1,25,20,15,10,5,24,19,14,9,4,23,18,13,8,3,22,17,12,7,2,21,16,11,6) (26,50,45,40,35,30,49,44,39,34,29,48,43,38,33,28,47,42,37,32,27,46,41,36,31)
	(1,31,11,41,21,27,7,37,17,47,3,33,13,43,23,29,9,39,19,49,5,35,15,45,25,26,6,36,16,46,2,32,12,42,22,28,8,38,18,48,4,34,14,44,24,30,10,40,20,50)