Properties

Label 2.625.ads_fgq
Base field $\F_{5^{4}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 96 x + 3552 x^{2} - 60000 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0487724642706$, $\pm0.118311861587$
Angle rank:  $2$ (numerical)
Number field:  4.0.1229056.2
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $334082$ $151764766468$ $59594450336321474$ $23282956846813150755856$ $9094946203907983996969941122$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $530$ $388514$ $244098866$ $152587185990$ $95367423107090$ $59604644778438242$ $37252902989257171634$ $23283064365584625012862$ $14551915228372869353694866$ $9094947017729435059194895394$

Jacobians and polarizations

This isogeny class contains a Jacobian, and hence is principally polarizable.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{5^{4}}$.

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.1229056.2.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.625.ds_fgq$2$(not in LMFDB)