Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 4 x )^{2}( 1 - 7 x + 16 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.160861246510$
Angle rank:  $1$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 90 54000 16233210 4276044000 1099117082250 281474121474000 72056913100240410 18446530487208984000 4722336341568877842090 1208922742163319108750000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 208 3962 65248 1048202 16777168 268432922 4294917568 68719038122 1099508828848

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 1.16.ah and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{4}}$.

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.ab_ay$2$2.256.abx_boq
2.16.b_ay$2$2.256.abx_boq
2.16.p_dk$2$2.256.abx_boq
2.16.ad_e$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.ab_ay$2$2.256.abx_boq
2.16.b_ay$2$2.256.abx_boq
2.16.p_dk$2$2.256.abx_boq
2.16.ad_e$3$(not in LMFDB)
2.16.ah_bg$4$(not in LMFDB)
2.16.h_bg$4$(not in LMFDB)
2.16.al_ci$6$(not in LMFDB)
2.16.d_e$6$(not in LMFDB)
2.16.l_ci$6$(not in LMFDB)