## Family Information

Genus: | 4 |

Quotient genus: | 0 |

Group name: | $\SL(2,3)$ |

Group identifier: | [24,3] |

Signature: | $[ 0; 3, 4, 6 ]$ |

Conjugacy classes for this refined passport: | 3, 5, 7 |

Jacobian variety group algebra decomposition: | $A_{2}\times E^{2}$ |

Corresponding character(s): | 4, 5 |

## Other Data

Hyperelliptic curve(s): | Yes |

Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) |

Cyclic trigonal curve(s): | No |

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

$y^2=x(x^4-1)(x^4+2i\\sqrt{3}x^2+1)$ |

## Generating vector(s)

Displaying the unique generating vector for this refined passport.

4.24-3.0.3-4-6.1.1

(1,9,17) (2,10,18) (3,15,21) (4,16,22) (5,11,23) (6,12,24) (7,13,19) (8,14,20) | |

(1,4,2,3) (5,8,6,7) (9,12,10,11) (13,16,14,15) (17,20,18,19) (21,24,22,23) | |

(1,21,11,2,22,12) (3,18,14,4,17,13) (5,19,10,6,20,9) (7,24,15,8,23,16) |