Properties

Label 2.16.ao_dd
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:  $( 1 - 7 x + 16 x^{2} )^{2}$
Frobenius angles:  $\pm0.160861246510$, $\pm0.160861246510$
Angle rank:  $1$ (numerical)
Jacobians:  1

This isogeny class is not 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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 100 57600 16728100 4324377600 1103025062500 281748310329600 72073826707176100 18447442819965849600 4722378257821885008100 1208924276393377476000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 223 4083 65983 1051923 16793503 268495923 4295129983 68719648083 1099510224223

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-15}) \)$)$
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.a_ar$2$2.256.abi_bev
2.16.o_dd$2$2.256.abi_bev
2.16.h_bh$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.a_ar$2$2.256.abi_bev
2.16.o_dd$2$2.256.abi_bev
2.16.h_bh$3$(not in LMFDB)
2.16.a_r$4$(not in LMFDB)
2.16.ah_bh$6$(not in LMFDB)