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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
"n/a" means that the isogeny classes of abelian varieties of this dimension over this field are not in the database yet.

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Base field cardinality range:
Dimension range:

Find a specific isogeny class by LMFDB label


e.g. 2.16.am_cn

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