# Properties

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

# Related objects

## 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, 7, 15

 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.

4.72-42.0.2-3-12.1.1

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