Properties

Label 5.2.ah_ba_acp_fd_aic
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.123548644961$, $\pm0.174442860055$, $\pm0.250000000000$, $\pm0.456881978294$, $\pm0.546783656212$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 2 2660 61256 957600 69424562 2281173440 39982829098 1029278275200 35222880982952 1154645016587300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 8 11 16 56 113 150 240 515 1048

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ac_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 $\overline{\F}_{2}$
The base change of $A$ to $\F_{2^{12}}$ is 1.4096.h 2 $\times$ 1.4096.ey $\times$ 2.4096.adu_hrl. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{12}}$.
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.ad_g_al_r_aw$2$(not in LMFDB)
5.2.ad_g_ah_f_ac$2$(not in LMFDB)
5.2.ab_c_ab_b_g$2$(not in LMFDB)
5.2.b_c_b_b_ag$2$(not in LMFDB)
5.2.d_g_h_f_c$2$(not in LMFDB)
5.2.d_g_l_r_w$2$(not in LMFDB)
5.2.h_ba_cp_fd_ic$2$(not in LMFDB)
5.2.ae_i_ak_n_as$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ad_g_al_r_aw$2$(not in LMFDB)
5.2.ad_g_ah_f_ac$2$(not in LMFDB)
5.2.ab_c_ab_b_g$2$(not in LMFDB)
5.2.b_c_b_b_ag$2$(not in LMFDB)
5.2.d_g_h_f_c$2$(not in LMFDB)
5.2.d_g_l_r_w$2$(not in LMFDB)
5.2.h_ba_cp_fd_ic$2$(not in LMFDB)
5.2.ae_i_ak_n_as$3$(not in LMFDB)
5.2.a_a_ac_f_c$6$(not in LMFDB)
5.2.a_a_c_f_ac$6$(not in LMFDB)
5.2.e_i_k_n_s$6$(not in LMFDB)
5.2.af_q_abn_cx_aem$8$(not in LMFDB)
5.2.ab_e_ad_d_ae$8$(not in LMFDB)
5.2.b_e_d_d_e$8$(not in LMFDB)
5.2.f_q_bn_cx_em$8$(not in LMFDB)
5.2.ae_k_as_bf_abu$12$(not in LMFDB)
5.2.a_c_ac_h_ac$12$(not in LMFDB)
5.2.a_c_c_h_c$12$(not in LMFDB)
5.2.e_k_s_bf_bu$12$(not in LMFDB)
5.2.ac_e_ag_j_ai$24$(not in LMFDB)
5.2.ac_g_ak_t_ay$24$(not in LMFDB)
5.2.c_e_g_j_i$24$(not in LMFDB)
5.2.c_g_k_t_y$24$(not in LMFDB)