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

• Label: 12.50-2.0.2-25-50.18
• 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:

$2, 28, 32$

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.

12.50-2.0.2-25-50.18.1

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