Properties

Label 4.3.ah_y_acc_dv
Base Field $\F_{3}$
Dimension $4$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
L-polynomial:  $( 1 - 3 x + 3 x^{2} )^{2}( 1 - x + 3 x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.268536328535$, $\pm0.622727850897$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 9 7497 529200 67150629 5192572464 303286636800 23234300923311 1904096980028061 148884520287358800 12037866219491196672

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 9 27 117 342 783 2223 6741 19521 58464

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 2 $\times$ 2.3.ab_d and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{3}$
The base change of $A$ to $\F_{3^{6}}$ is 1.729.cc 2 $\times$ 2.729.acd_deb. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{3^{6}}$.
Remainder of endomorphism lattice by field

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
4.3.af_m_as_bb$2$(not in LMFDB)
4.3.ab_a_a_j$2$(not in LMFDB)
4.3.b_a_a_j$2$(not in LMFDB)
4.3.f_m_s_bb$2$(not in LMFDB)
4.3.h_y_cc_dv$2$(not in LMFDB)
4.3.ae_m_abb_cc$3$(not in LMFDB)
4.3.ab_a_a_j$3$(not in LMFDB)
4.3.ab_j_aj_bk$3$(not in LMFDB)
4.3.c_g_j_s$3$(not in LMFDB)
4.3.f_m_s_bb$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.3.af_m_as_bb$2$(not in LMFDB)
4.3.ab_a_a_j$2$(not in LMFDB)
4.3.b_a_a_j$2$(not in LMFDB)
4.3.f_m_s_bb$2$(not in LMFDB)
4.3.h_y_cc_dv$2$(not in LMFDB)
4.3.ae_m_abb_cc$3$(not in LMFDB)
4.3.ab_a_a_j$3$(not in LMFDB)
4.3.ab_j_aj_bk$3$(not in LMFDB)
4.3.c_g_j_s$3$(not in LMFDB)
4.3.f_m_s_bb$3$(not in LMFDB)
4.3.ab_g_ag_bb$4$(not in LMFDB)
4.3.b_g_g_bb$4$(not in LMFDB)
4.3.ac_g_aj_s$6$(not in LMFDB)
4.3.ab_a_a_j$6$(not in LMFDB)
4.3.b_j_j_bk$6$(not in LMFDB)
4.3.e_m_bb_cc$6$(not in LMFDB)
4.3.ab_ad_d_a$12$(not in LMFDB)
4.3.b_ad_ad_a$12$(not in LMFDB)
4.3.ab_d_ad_s$24$(not in LMFDB)
4.3.b_d_d_s$24$(not in LMFDB)