Properties

Label 3.16.at_gh_abfs
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:  $( 1 - 4 x )^{2}( 1 - 11 x + 59 x^{2} - 176 x^{3} + 256 x^{4} )$
Frobenius angles:  $0$, $0$, $\pm0.133878927982$, $\pm0.347077071791$
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
$A(\F_{q^r})$ 1161 14599575 68032644876 280282363458075 1150297296203146311 4719711176171189125200 19342248765590222946866349 79229949044965879176813834675 324520349399954424887225543759124 1329226922797812775716769917551964375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 222 4057 65258 1046188 16767783 268427626 4295064146 68719857001 1099510740222

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 2.16.al_ch 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.ad_an_eq$2$(not in LMFDB)
3.16.d_an_aeq$2$(not in LMFDB)
3.16.t_gh_bfs$2$(not in LMFDB)
3.16.ah_bf_aem$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ad_an_eq$2$(not in LMFDB)
3.16.d_an_aeq$2$(not in LMFDB)
3.16.t_gh_bfs$2$(not in LMFDB)
3.16.ah_bf_aem$3$(not in LMFDB)
3.16.al_cx_ano$4$(not in LMFDB)
3.16.l_cx_no$4$(not in LMFDB)
3.16.ap_ep_awq$6$(not in LMFDB)
3.16.h_bf_em$6$(not in LMFDB)
3.16.p_ep_wq$6$(not in LMFDB)