# Properties

 Genus $$4$$ Quotient Genus $$0$$ Group $$C_3\times S_4$$ Signature $$[ 0; 2, 3, 12 ]$$ Generating Vectors $$1$$

# Learn more about

## Family Information

 Genus: 4 Quotient Genus: 0 Group name: $C_3\times S_4$ Group identifier: [72,42] Signature: $[ 0; 2, 3, 12 ]$
 Conjugacy classes for this refined passport: 3, 8, 14

 Jacobian variety group algebra decomposition: $E\times E^{3}$ Corresponding character(s): 4, 12

## Other Data

 Hyperelliptic curve(s): No Cyclic trigonal curve(s): Yes Trigonal automorphism: (1,13,25) (2,14,26) (3,15,27) (4,16,28) (5,17,29) (6,18,30) (7,19,31) (8,20,32) (9,21,33) (10,22,34) (11,23,35) (12,24,36) (37,49,61) (38,50,62) (39,51,63) (40,52,64) (41,53,65) (42,54,66) (43,55,67) (44,56,68) (45,57,69) (46,58,70) (47,59,71) (48,60,72)

 Equation(s) of curve(s) in this refined passport:
 $y^3 = x(x^4-1)$

## Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.72-42.0.2-3-12.2.1

 (1,37) (2,39) (3,38) (4,40) (5,45) (6,47) (7,46) (8,48) (9,41) (10,43) (11,42) (12,44) (13,49) (14,51) (15,50) (16,52) (17,57) (18,59) (19,58) (20,60) (21,53) (22,55) (23,54) (24,56) (25,61) (26,63) (27,62) (28,64) (29,69) (30,71) (31,70) (32,72) (33,65) (34,67) (35,66) (36,68) (1,36,19) (2,34,18) (3,33,20) (4,35,17) (5,28,23) (6,26,22) (7,25,24) (8,27,21) (9,32,15) (10,30,14) (11,29,16) (12,31,13) (37,72,55) (38,70,54) (39,69,56) (40,71,53) (41,64,59) (42,62,58) (43,61,60) (44,63,57) (45,68,51) (46,66,50) (47,65,52) (48,67,49) (1,58,27,48,13,70,3,60,25,46,15,72) (2,59,28,45,14,71,4,57,26,47,16,69) (5,54,31,44,17,66,7,56,29,42,19,68) (6,55,32,41,18,67,8,53,30,43,20,65) (9,50,35,40,21,62,11,52,33,38,23,64) (10,51,36,37,22,63,12,49,34,39,24,61)