Properties

Label 2.5.ac_a
Base Field $\F_{5}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{5}$
Dimension:  $2$
L-polynomial:  $1 - 2 x - 10 x^{3} + 25 x^{4}$
Frobenius angles:  $\pm0.0841889326552$, $\pm0.673328138963$
Angle rank:  $2$ (numerical)
Number field:  4.0.38720.3
Galois group:  $D_{4}$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14 532 11438 393680 9826894 240358132 6142944878 153012392960 3813285458654 95461966344052

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 22 88 630 3144 15382 78628 391710 1952404 9775302

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The endomorphism algebra of this simple isogeny class is 4.0.38720.3.
All geometric endomorphisms are defined over $\F_{5}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.5.c_a$2$2.25.ae_k