Isogeny Classes of Abelian Varieties over Finite Fields

The database currently contains 2,945,722 isogeny classes of abelian varieties of dimension up to 6 over finite fields.

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Browse isogeny classes of abelian varieties over finite fields

By dimension: 1  2  3  4  5  6 

By base field cardinality: 2  3  4  5  7-16  17-25  27-211  223-1024 

Some interesting isogeny classes: 2.64.a_abp   2.167.a_hi   4.2.ad_c_a_b   6.2.ak_cb_ahg_sy_abme_ciq   6.2.ag_r_abd_bg_ay_u  

A table by dimension and base field

Find a specific isogeny class by label

Cardinality of the base field		e.g. 81 or 3-49	Primitive
Characteristic of the base field		e.g. 3 or 2-5	Simple
Dimension		e.g. 2 or 3-5	Geometrically simple
Initial coefficients		e.g. [2, -1, 3, 9]	Principally polarizable
$p$-rank		e.g. 2	Jacobian
$p$-rank deficit		e.g. 2
Number of Jacobians		e.g. 6	Number of Hyperelliptic Jacobians
Degree of endomorphism_field		e.g. 6-12, 168	Angle rank
Number of twists		e.g. 390	Max twist degree
Slopes of Newton polygon				e.g. [0,0,1/2]
Point counts of the variety				e.g. [75,7125]
Point counts of the curve				e.g. [9,87]
Simple factors				e.g. 1.2.b,1.2.b,2.2.a_b
Use geometric decomposition in the following inputs
Dimension 1 factors		Distinct factors		e.g. 2 or 1-3
Dimension 2 factors		Distinct factors		e.g. 2 or 1-3
Dimension 3 factors		Distinct factors		e.g. 2 or 0-1
Dimension 4 factors				e.g. 0 or 1
Dimension 5 factors				e.g. 0 or 1
Number field				e.g. 4.0.29584.2 or Qzeta8
Galois group				e.g. C4, or 8T12, a list of group labels
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