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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 34 62 91 128 206 166 285 400 512 457 764 896 1192 1273 1124
3 210 670 1397 2944 7968 7614 15459 30530 50356 n/a n/a n/a n/a n/a n/a
4 1610 10900 38160 132710 n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a
5 14110 266788 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 163292 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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cardinality of the base field range:
dimension range:

Find a specific isogeny class by LMFDB label


e.g. 2.16.am_cn

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