Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 4 x )^{2}( 1 - 10 x + 55 x^{2} - 160 x^{3} + 256 x^{4} )$
Frobenius angles:  $0$, $0$, $\pm0.203888329072$, $\pm0.352056944208$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 1278 15399900 69407657298 281738952914400 1151273353973692158 4719658364717363531100 19340723763427235881587138 79226803614675742178238000000 324516064130818486839763842790638 1329222780364668270507849413405497500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 235 4139 65599 1047079 16767595 268406459 4294893631 68718949559 1099507313675

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 2.16.ak_cd 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
3.16.ac_aj_eq$2$(not in LMFDB)
3.16.c_aj_aeq$2$(not in LMFDB)
3.16.s_fv_bdg$2$(not in LMFDB)
3.16.ag_bf_adw$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ac_aj_eq$2$(not in LMFDB)
3.16.c_aj_aeq$2$(not in LMFDB)
3.16.s_fv_bdg$2$(not in LMFDB)
3.16.ag_bf_adw$3$(not in LMFDB)
3.16.ak_ct_ami$4$(not in LMFDB)
3.16.k_ct_mi$4$(not in LMFDB)
3.16.ao_eh_auu$6$(not in LMFDB)
3.16.g_bf_dw$6$(not in LMFDB)
3.16.o_eh_uu$6$(not in LMFDB)