Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x + 16 x^{2} )( 1 - 4 x + 16 x^{2} )$
Frobenius angles:  $\pm0.160861246510$, $\pm0.333333333333$
Angle rank:  $1$ (numerical)
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 130 65520 17280250 4326547680 1100192538250 281474121474000 72061311642105370 18447374928131997120 4722408399252751470250 1208926200925625332878000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 256 4218 66016 1049226 16777168 268449306 4295114176 68720086698 1099511974576

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah $\times$ 1.16.ae 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 $\F_{2^{12}}$ is 1.4096.ah $\times$ 1.4096.ey. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{12}}$.

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.ad_e$2$2.256.ab_jg
2.16.d_e$2$2.256.ab_jg
2.16.l_ci$2$2.256.ab_jg
2.16.b_ay$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.ad_e$2$2.256.ab_jg
2.16.d_e$2$2.256.ab_jg
2.16.l_ci$2$2.256.ab_jg
2.16.b_ay$3$(not in LMFDB)
2.16.ap_dk$6$(not in LMFDB)
2.16.ab_ay$6$(not in LMFDB)
2.16.p_dk$6$(not in LMFDB)
2.16.ah_bg$12$(not in LMFDB)
2.16.h_bg$12$(not in LMFDB)