Properties

Label 5.2.ag_s_abl_ck_ado
Base field $\F_{2}$
Dimension $5$
$p$-rank $3$
Ordinary no
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$
  $1 - 6 x + 18 x^{2} - 37 x^{3} + 62 x^{4} - 92 x^{5} + 124 x^{6} - 148 x^{7} + 144 x^{8} - 96 x^{9} + 32 x^{10}$
Frobenius angles:  $\pm0.123548644961$, $\pm0.139386741866$, $\pm0.250000000000$, $\pm0.456881978294$, $\pm0.686170398078$
Angle rank:  $3$ (numerical)
Jacobians:  $0$
Isomorphism classes:  3

This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $2$ $1520$ $25688$ $1778400$ $55240202$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-3$ $5$ $6$ $25$ $47$ $86$ $193$ $273$ $474$ $1165$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{12}}$.

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ab_a 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 $\overline{\F}_{2}$
The base change of $A$ to $\F_{2^{12}}$ is 1.4096.h 2 $\times$ 1.4096.ey $\times$ 2.4096.agf_vki. The endomorphism algebra for each factor is:
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
5.2.ae_i_ah_ac_m$2$(not in LMFDB)
5.2.ac_c_af_k_am$2$(not in LMFDB)
5.2.a_a_ab_c_e$2$(not in LMFDB)
5.2.a_a_b_c_ae$2$(not in LMFDB)
5.2.c_c_f_k_m$2$(not in LMFDB)
5.2.e_i_h_ac_am$2$(not in LMFDB)
5.2.g_s_bl_ck_do$2$(not in LMFDB)
5.2.ad_d_ab_i_au$3$(not in LMFDB)
5.2.a_a_ab_c_e$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
5.2.ae_i_ah_ac_m$2$(not in LMFDB)
5.2.ac_c_af_k_am$2$(not in LMFDB)
5.2.a_a_ab_c_e$2$(not in LMFDB)
5.2.a_a_b_c_ae$2$(not in LMFDB)
5.2.c_c_f_k_m$2$(not in LMFDB)
5.2.e_i_h_ac_am$2$(not in LMFDB)
5.2.g_s_bl_ck_do$2$(not in LMFDB)
5.2.ad_d_ab_i_au$3$(not in LMFDB)
5.2.a_a_ab_c_e$3$(not in LMFDB)
5.2.ab_ab_f_e_am$6$(not in LMFDB)
5.2.b_ab_af_e_m$6$(not in LMFDB)
5.2.d_d_b_i_u$6$(not in LMFDB)
5.2.ae_k_av_bk_aca$8$(not in LMFDB)
5.2.ac_e_ad_a_e$8$(not in LMFDB)
5.2.c_e_d_a_ae$8$(not in LMFDB)
5.2.e_k_v_bk_ca$8$(not in LMFDB)
5.2.ad_f_ah_q_abc$12$(not in LMFDB)
5.2.ab_b_d_e_ae$12$(not in LMFDB)
5.2.b_b_ad_e_e$12$(not in LMFDB)
5.2.d_f_h_q_bc$12$(not in LMFDB)
5.2.ab_b_ad_g_ae$24$(not in LMFDB)
5.2.ab_d_af_k_am$24$(not in LMFDB)
5.2.b_b_d_g_e$24$(not in LMFDB)
5.2.b_d_f_k_m$24$(not in LMFDB)