Properties

Label 2.16.aj_bz
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 9 x + 51 x^{2} - 144 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.252176979752$, $\pm0.361066333219$
Angle rank:  $2$ (numerical)
Number field:  4.0.42625.1
Galois group:  $D_{4}$
Jacobians:  8

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 155 71455 17681780 4334531755 1099218828125 281350290819280 72051842202906455 18446710741535203155 4722368130496371258380 1208925191598773757109375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 278 4313 66138 1048298 16769783 268414028 4294959538 68719500713 1099511056598

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.42625.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.j_bz$2$2.256.v_ub