## Invariants

Base field: | $\F_{2}$ |

Dimension: | $1$ |

Weil polynomial: | $1 - 2 x + 2 x^{2}$ |

Frobenius angles: | $\pm0.25$ |

Angle rank: | $0$ (numerical) |

Number field: | \(\Q(\sqrt{-1}) \) |

Galois group: | $C_2$ |

This isogeny class is simple.

## Newton polygon

This isogeny class is supersingular.

$p$-rank: | $0$ |

Slopes: | $[1/2, 1/2]$ |

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

$A(\F_{q^r})$ | 1 | 5 | 13 | 25 | 41 | 65 | 113 | 225 | 481 | 1025 |

$r$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

$C(\F_{q^r})$ | 1 | 5 | 13 | 25 | 41 | 65 | 113 | 225 | 481 | 1025 |

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.

# Additional information

This is the isogeny class of the Jacobian of a function field of class number 1. It also appears as a sporadic example in the classification of abelian varieties with one rational point.