Properties

Label 6.2.ai_bf_acw_eq_afs_hc
Base field $\F_{2}$
Dimension $6$
$p$-rank $2$
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:  $6$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$
  $1 - 8 x + 31 x^{2} - 74 x^{3} + 120 x^{4} - 148 x^{5} + 184 x^{6} - 296 x^{7} + 480 x^{8} - 592 x^{9} + 496 x^{10} - 256 x^{11} + 64 x^{12}$
Frobenius angles:  $\pm0.0693533547550$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.339907131295$, $\pm0.770553776540$
Angle rank:  $2$ (numerical)
Jacobians:  $0$

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

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $2$ $5500$ $848042$ $93500000$ $1153875382$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-5$ $3$ $19$ $47$ $35$ $51$ $79$ $159$ $523$ $1043$

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 $\F_{2^{4}}$.

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 3.2.ac_b_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 $\F_{2^{4}}$ is 1.16.i 3 $\times$ 3.16.g_r_ce. 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
6.2.ae_h_ag_i_abc_ce$2$(not in LMFDB)
6.2.ae_h_ac_ai_m_ai$2$(not in LMFDB)
6.2.a_ab_ac_i_ae_ai$2$(not in LMFDB)
6.2.a_ab_c_i_e_ai$2$(not in LMFDB)
6.2.e_h_c_ai_am_ai$2$(not in LMFDB)
6.2.e_h_g_i_bc_ce$2$(not in LMFDB)
6.2.i_bf_cw_eq_fs_hc$2$(not in LMFDB)
6.2.ac_b_e_ag_ae_q$3$(not in LMFDB)

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

TwistExtension degreeCommon base change
6.2.ae_h_ag_i_abc_ce$2$(not in LMFDB)
6.2.ae_h_ac_ai_m_ai$2$(not in LMFDB)
6.2.a_ab_ac_i_ae_ai$2$(not in LMFDB)
6.2.a_ab_c_i_e_ai$2$(not in LMFDB)
6.2.e_h_c_ai_am_ai$2$(not in LMFDB)
6.2.e_h_g_i_bc_ce$2$(not in LMFDB)
6.2.i_bf_cw_eq_fs_hc$2$(not in LMFDB)
6.2.ac_b_e_ag_ae_q$3$(not in LMFDB)
6.2.ag_r_abg_by_acy_ei$6$(not in LMFDB)
6.2.ac_b_ae_k_am_q$6$(not in LMFDB)
6.2.ac_b_a_c_e_aq$6$(not in LMFDB)
6.2.c_b_ae_ag_e_q$6$(not in LMFDB)
6.2.c_b_a_c_ae_aq$6$(not in LMFDB)
6.2.c_b_e_k_m_q$6$(not in LMFDB)
6.2.g_r_bg_by_cy_ei$6$(not in LMFDB)
6.2.ag_t_abo_cm_adk_eq$8$(not in LMFDB)
6.2.ae_d_k_au_ae_bo$8$(not in LMFDB)
6.2.ae_l_aw_bk_aca_cu$8$(not in LMFDB)
6.2.ac_ab_e_ae_a_i$8$(not in LMFDB)
6.2.ac_d_ae_i_aq_y$8$(not in LMFDB)
6.2.ac_d_a_a_i_ai$8$(not in LMFDB)
6.2.ac_h_am_u_abg_bo$8$(not in LMFDB)
6.2.a_af_ac_m_e_ay$8$(not in LMFDB)
6.2.a_af_c_m_ae_ay$8$(not in LMFDB)
6.2.a_d_ac_e_am_i$8$(not in LMFDB)
6.2.a_d_c_e_m_i$8$(not in LMFDB)
6.2.c_ab_ae_ae_a_i$8$(not in LMFDB)
6.2.c_d_a_a_ai_ai$8$(not in LMFDB)
6.2.c_d_e_i_q_y$8$(not in LMFDB)
6.2.c_h_m_u_bg_bo$8$(not in LMFDB)
6.2.e_d_ak_au_e_bo$8$(not in LMFDB)
6.2.e_l_w_bk_ca_cu$8$(not in LMFDB)
6.2.g_t_bo_cm_dk_eq$8$(not in LMFDB)
6.2.ae_f_c_ag_aq_bw$24$(not in LMFDB)
6.2.ae_j_as_be_abs_cm$24$(not in LMFDB)
6.2.ae_j_ao_w_abo_cm$24$(not in LMFDB)
6.2.ac_b_a_c_ai_q$24$(not in LMFDB)
6.2.ac_f_ai_o_ay_bg$24$(not in LMFDB)
6.2.a_ad_ac_k_a_aq$24$(not in LMFDB)
6.2.a_ad_c_k_a_aq$24$(not in LMFDB)
6.2.a_b_ac_ac_e_a$24$(not in LMFDB)
6.2.a_b_ac_g_ai_a$24$(not in LMFDB)
6.2.a_b_c_ac_ae_a$24$(not in LMFDB)
6.2.a_b_c_g_i_a$24$(not in LMFDB)
6.2.c_b_a_c_i_q$24$(not in LMFDB)
6.2.c_f_i_o_y_bg$24$(not in LMFDB)
6.2.e_f_ac_ag_q_bw$24$(not in LMFDB)
6.2.e_j_o_w_bo_cm$24$(not in LMFDB)
6.2.e_j_s_be_bs_cm$24$(not in LMFDB)