If an abelian variety $A$ is not simple, it is isogenous to a product of simple lower dimensional abelian varieties. These simple abelian varieties $B_i$ are the **isogeny factors** of $A$, and we say that $A$ decomposes (up to isogeny) into the product of the $B_i$'s:
$$A \sim B_1 \times \cdots \times B_n$$
Note that two elements of this product might be isogenous; in other words, elements of the decomposition may appear with multiplicity.

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**Knowl status:**

- Review status: reviewed
- Last edited by Kiran S. Kedlaya on 2019-05-04 20:31:44

**Referred to by:**

- av.fq.honda_tate
- av.simple
- lmfdb/abvar/fq/main.py (line 373)
- lmfdb/abvar/fq/main.py (lines 382-384)
- lmfdb/abvar/fq/main.py (line 396)
- lmfdb/abvar/fq/main.py (line 413)
- lmfdb/abvar/fq/main.py (line 430)
- lmfdb/abvar/fq/main.py (line 460)
- lmfdb/abvar/fq/templates/abvarfq-search-results.html (line 25)
- lmfdb/abvar/fq/templates/show-abvarfq.html (line 126)

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