## Family Information

Genus: | 2 |

Group name: | $D_4$ |

Group identifier: | [8,3] |

Signature: | $[ 0; 2, 2, 2, 4 ]$ |

Conjugacy classes for this refined passport: | 2, 3, 4, 5 |

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

Corresponding character(s): | 5 |

## Other Data

Hyperelliptic curve(s): | Yes |

Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) |

Cyclic trigonal curve(s): | No |

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

$y^2=x(x^{4}+a_{1}x^{2}+1)$ | |

$y^2=(x^{2}-1)(x^{4}+a_{1}x^{2}+1)$ |

## Generating Vector(s)

Displaying the unique generating vector for this refined passport.

2.8-3.0.2-2-2-4.1.1

(1,2) (3,4) (5,6) (7,8) | |

(1,3) (2,4) (5,7) (6,8) | |

(1,5) (2,6) (3,8) (4,7) | |

(1,8,2,7) (3,5,4,6) |