Properties

Label 2.16.ah_bg
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x + 16 x^{2} )( 1 + 16 x^{2} )$
Frobenius angles:  $\pm0.160861246510$, $\pm0.5$
Angle rank:  $1$ (numerical)
Jacobians:  4

This isogeny class is not simple.

Newton polygon

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

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 170 69360 16756730 4276044000 1101267994250 281749132812240 72065710183970330 18446530487208984000 4722372370410814656170 1208927353846394074254000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 272 4090 65248 1050250 16793552 268465690 4294917568 68719562410 1099513023152

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah $\times$ 1.16.a and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{2^{4}}$
The base change of $A$ to $\F_{2^{8}}$ is 1.256.ar $\times$ 1.256.bg. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{8}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.h_bg$2$2.256.p_abg
2.16.ap_dk$4$(not in LMFDB)
2.16.ab_ay$4$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.h_bg$2$2.256.p_abg
2.16.ap_dk$4$(not in LMFDB)
2.16.ab_ay$4$(not in LMFDB)
2.16.b_ay$4$(not in LMFDB)
2.16.p_dk$4$(not in LMFDB)
2.16.al_ci$12$(not in LMFDB)
2.16.ad_e$12$(not in LMFDB)
2.16.d_e$12$(not in LMFDB)
2.16.l_ci$12$(not in LMFDB)