## Invariants

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

Dimension: | $2$ |

L-polynomial: | $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )$ |

Frobenius angles: | $\pm0.384973271919$, $\pm0.615026728081$ |

Angle rank: | $1$ (numerical) |

Jacobians: | 0 |

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

$p$-rank: | $2$ |

Slopes: | $[0, 0, 1, 1]$ |

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

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

$A(\F_{q^r})$ | 8 | 64 | 56 | 256 | 968 | 3136 | 16472 | 82944 | 263144 | 937024 |

Point counts of the (virtual) curve

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

$C(\F_{q^r})$ | 3 | 11 | 9 | 15 | 33 | 47 | 129 | 319 | 513 | 911 |

## Decomposition and endomorphism algebra

**Endomorphism algebra over $\F_{2}$**

The isogeny class factors as 1.2.ab $\times$ 1.2.b and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |

**Endomorphism algebra over $\overline{\F}_{2}$**

The base change of $A$ to $\F_{2^{2}}$ is 1.4.d^{ 2 } and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-7}) \)$)$ |

## Base change

This is a primitive isogeny class.