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. You can browse further statistics or create your own.

Browse

By dimension:	1  2  3  4  5  6
By base field cardinality:	2  3  4  5  7  8  9  16  17  19  23  25  27-211  223-1024
Some interesting isogeny classes or a random isogeny class
A table by dimension and base field.

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	(Geometrically) Squarefree
Number of Jacobians		e.g. 6	Number of hyperelliptic Jacobians		e.g. 6
Degree of endomorphism_field		e.g. 6-12, 168	Angle rank		e.g. 3
Number of twists		e.g. 390	Max twist degree		e.g. 16
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		e.g. 1-3	Distinct factors		e.g. 2 or 1-3
Dimension 2 factors		e.g. 1-3	Distinct factors		e.g. 2 or 1-3
Dimension 3 factors		e.g. 2	Distinct factors		e.g. 2 or 0-1
Dimension 4 factors		e.g. 2			e.g. 0 or 1
Dimension 5 factors		e.g. 2			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 names
Results to display

Display:

Find

Label or polynomial
	e.g. 2.16.am_cn or 1 - x + 2x^2 or x^2 - x + 2