Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0435981566527$, $\pm0.123548644961$, $\pm0.329312442367$, $\pm0.456881978294$, $\pm0.527830414776$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $5$
Slopes:  $[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 1 1349 31996 352089 24621781 1208552912 34419317696 1064624536593 39582728628364 1278470195863379

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 8 8 0 21 74 129 248 575 1153

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 2.2.ad_f $\times$ 3.2.ae_j_ap 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 $\F_{2^{42}}$ is 1.4398046511104.ahxvrd 3 $\times$ 1.4398046511104.hpued 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{42}}$.
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.b_c_c_ac_ab$2$(not in LMFDB)
5.2.h_ba_cq_fg_ih$2$(not in LMFDB)
5.2.ae_i_al_n_ar$3$(not in LMFDB)
5.2.ab_c_ac_ac_b$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.b_c_c_ac_ab$2$(not in LMFDB)
5.2.h_ba_cq_fg_ih$2$(not in LMFDB)
5.2.ae_i_al_n_ar$3$(not in LMFDB)
5.2.ab_c_ac_ac_b$3$(not in LMFDB)
5.2.e_i_l_n_r$6$(not in LMFDB)
5.2.a_ac_c_d_af$7$(not in LMFDB)
5.2.a_f_af_k_at$7$(not in LMFDB)
5.2.ae_k_at_bf_abv$12$(not in LMFDB)
5.2.e_k_t_bf_bv$12$(not in LMFDB)
5.2.ag_q_aba_bh_abr$14$(not in LMFDB)
5.2.ag_x_acj_eu_ahp$14$(not in LMFDB)
5.2.ae_n_abd_cc_adf$14$(not in LMFDB)
5.2.ac_h_an_y_abl$14$(not in LMFDB)
5.2.a_ac_ac_d_f$14$(not in LMFDB)
5.2.a_f_f_k_t$14$(not in LMFDB)
5.2.c_h_n_y_bl$14$(not in LMFDB)
5.2.e_n_bd_cc_df$14$(not in LMFDB)
5.2.ad_f_al_t_az$21$(not in LMFDB)
5.2.a_ab_af_e_f$21$(not in LMFDB)
5.2.d_b_ae_g_z$21$(not in LMFDB)
5.2.d_f_b_al_az$21$(not in LMFDB)
5.2.d_i_k_n_l$21$(not in LMFDB)
5.2.g_q_ba_bh_br$21$(not in LMFDB)
5.2.g_x_cj_eu_hp$21$(not in LMFDB)
5.2.ae_h_af_ag_t$28$(not in LMFDB)
5.2.ac_b_ab_a_f$28$(not in LMFDB)
5.2.c_b_b_a_af$28$(not in LMFDB)
5.2.e_h_f_ag_at$28$(not in LMFDB)
5.2.af_n_az_bn_acd$42$(not in LMFDB)
5.2.ad_b_e_g_az$42$(not in LMFDB)
5.2.ad_f_ab_al_z$42$(not in LMFDB)
5.2.ad_i_ak_n_al$42$(not in LMFDB)
5.2.ac_b_ab_g_an$42$(not in LMFDB)
5.2.ab_b_b_ad_h$42$(not in LMFDB)
5.2.ab_e_ac_j_af$42$(not in LMFDB)
5.2.a_ab_f_e_af$42$(not in LMFDB)
5.2.b_b_ab_ad_ah$42$(not in LMFDB)
5.2.b_e_c_j_f$42$(not in LMFDB)
5.2.c_b_b_g_n$42$(not in LMFDB)
5.2.d_f_l_t_z$42$(not in LMFDB)
5.2.f_n_z_bn_cd$42$(not in LMFDB)
5.2.ad_d_ac_k_ax$84$(not in LMFDB)
5.2.ad_k_aq_bf_abl$84$(not in LMFDB)
5.2.ac_d_af_k_at$84$(not in LMFDB)
5.2.ab_ac_e_d_al$84$(not in LMFDB)
5.2.ab_a_c_b_af$84$(not in LMFDB)
5.2.ab_g_ae_t_al$84$(not in LMFDB)
5.2.a_b_af_e_af$84$(not in LMFDB)
5.2.a_b_f_e_f$84$(not in LMFDB)
5.2.b_ac_ae_d_l$84$(not in LMFDB)
5.2.b_a_ac_b_f$84$(not in LMFDB)
5.2.b_g_e_t_l$84$(not in LMFDB)
5.2.c_d_f_k_t$84$(not in LMFDB)
5.2.d_d_c_k_x$84$(not in LMFDB)
5.2.d_k_q_bf_bl$84$(not in LMFDB)