There are finitely many isogeny classes of abelian varieties over a finite field, if the dimension of the abelian variety and the cardinality of the base field are fixed. They are classified by their Weil polynomial, from which many invariants may be computed.

## Browse isogeny classes of abelian varieties over finite fields

A random isogeny class from the database.

### By field of definition and dimension:

The table below gives the number of isogeny classes of abelian varieties of dimension $g$ defined over the field $\F_q$.

Dimension | Cardinality of base field \(q\) | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2 | 3 | 4 | 5 | 7 | 8 | 9 | 11 | 13 | 16 | 17 | 19 | 23 | 25 | 27 | |

1 | 5 | 7 | 9 | 9 | 11 | 9 | 13 | 13 | 15 | 13 | 17 | 17 | 19 | 20 | 17 |

2 | 35 | 63 | 91 | 129 | 207 | 167 | 285 | 401 | 513 | 457 | 765 | 897 | 1193 | 1273 | 1125 |

3 | 215 | 677 | 1397 | 2953 | 7979 | 7623 | 15459 | 30543 | 50371 | n/a | n/a | n/a | n/a | n/a | n/a |

4 | 1645 | 10963 | 38160 | 132839 | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a |

5 | 14325 | 267465 | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a |

6 | 164937 | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a |