Properties

Label 3.16.av_hn_abnb
Base Field $\F_{2^{4}}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 16 x^{2} )^{3}$
Frobenius angles:  $\pm0.160861246510$, $\pm0.160861246510$, $\pm0.160861246510$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 1000 13824000 68417929000 284371070976000 1158452071890625000 4729246818274054656000 19349349617882459638009000 79232664195372087170924544000 324519767412018097477971305521000 1329225450601162408904302776000000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 206 4076 66206 1053596 16801646 268526156 4295211326 68719733756 1099509522446

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah 3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-15}) \)$)$
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
3.16.ah_ab_ep$2$(not in LMFDB)
3.16.h_ab_aep$2$(not in LMFDB)
3.16.v_hn_bnb$2$(not in LMFDB)
3.16.a_a_ah$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ah_ab_ep$2$(not in LMFDB)
3.16.h_ab_aep$2$(not in LMFDB)
3.16.v_hn_bnb$2$(not in LMFDB)
3.16.a_a_ah$3$(not in LMFDB)
3.16.ah_bh_aep$4$(not in LMFDB)
3.16.h_bh_ep$4$(not in LMFDB)
3.16.ao_du_arn$6$(not in LMFDB)
3.16.a_a_h$6$(not in LMFDB)
3.16.o_du_rn$6$(not in LMFDB)