Properties

Label 4.4.an_cy_aki_yq
Base field $\F_{2^{2}}$
Dimension $4$
$p$-rank $1$
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:  $\F_{2^{2}}$
Dimension:  $4$
L-polynomial:  $( 1 - 2 x )^{6}( 1 - x + 4 x^{2} )$
  $1 - 13 x + 76 x^{2} - 268 x^{3} + 640 x^{4} - 1072 x^{5} + 1216 x^{6} - 832 x^{7} + 256 x^{8}$
Frobenius angles:  $0$, $0$, $0$, $0$, $0$, $0$, $\pm0.419569376745$
Angle rank:  $1$ (numerical)

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

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4$ $17496$ $8941324$ $2733750000$ $855553548484$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-8$ $0$ $28$ $144$ $772$ $3720$ $15868$ $64224$ $258292$ $1040760$

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

Endomorphism algebra over $\F_{2^{2}}$
The isogeny class factors as 1.4.ae 3 $\times$ 1.4.ab and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

TwistExtension degreeCommon base change
4.4.al_ca_afs_mi$2$(not in LMFDB)
4.4.af_e_u_acm$2$(not in LMFDB)
4.4.ad_ae_m_a$2$(not in LMFDB)
4.4.d_ae_am_a$2$(not in LMFDB)
4.4.f_e_au_acm$2$(not in LMFDB)
4.4.l_ca_fs_mi$2$(not in LMFDB)
4.4.n_cy_ki_yq$2$(not in LMFDB)
4.4.ah_w_aca_ei$3$(not in LMFDB)
4.4.ab_e_aq_q$3$(not in LMFDB)
4.4.f_w_ce_fg$3$(not in LMFDB)

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

TwistExtension degreeCommon base change
4.4.al_ca_afs_mi$2$(not in LMFDB)
4.4.af_e_u_acm$2$(not in LMFDB)
4.4.ad_ae_m_a$2$(not in LMFDB)
4.4.d_ae_am_a$2$(not in LMFDB)
4.4.f_e_au_acm$2$(not in LMFDB)
4.4.l_ca_fs_mi$2$(not in LMFDB)
4.4.n_cy_ki_yq$2$(not in LMFDB)
4.4.ah_w_aca_ei$3$(not in LMFDB)
4.4.ab_e_aq_q$3$(not in LMFDB)
4.4.f_w_ce_fg$3$(not in LMFDB)
4.4.aj_bo_aeu_lc$4$(not in LMFDB)
4.4.ah_y_acq_ge$4$(not in LMFDB)
4.4.af_u_aci_ey$4$(not in LMFDB)
4.4.ad_m_abk_cm$4$(not in LMFDB)
4.4.ab_a_e_abg$4$(not in LMFDB)
4.4.ab_q_am_ds$4$(not in LMFDB)
4.4.b_a_ae_abg$4$(not in LMFDB)
4.4.b_q_m_ds$4$(not in LMFDB)
4.4.d_m_bk_cm$4$(not in LMFDB)
4.4.f_u_ci_ey$4$(not in LMFDB)
4.4.h_y_cq_ge$4$(not in LMFDB)
4.4.j_bo_eu_lc$4$(not in LMFDB)
4.4.ad_g_ai_a$5$(not in LMFDB)
4.4.al_cg_aho_rw$6$(not in LMFDB)
4.4.aj_bm_aee_jg$6$(not in LMFDB)
4.4.aj_bs_afo_my$6$(not in LMFDB)
4.4.ah_bc_adc_gu$6$(not in LMFDB)
4.4.ah_bi_aea_jo$6$(not in LMFDB)
4.4.af_k_abc_dc$6$(not in LMFDB)
4.4.af_q_abo_dc$6$(not in LMFDB)
4.4.af_w_ace_fg$6$(not in LMFDB)
4.4.ad_c_m_abw$6$(not in LMFDB)
4.4.ad_i_ay_bw$6$(not in LMFDB)
4.4.ad_o_ay_cu$6$(not in LMFDB)
4.4.ab_ac_e_aq$6$(not in LMFDB)
4.4.ab_e_q_aq$6$(not in LMFDB)
4.4.ab_k_ai_ce$6$(not in LMFDB)
4.4.b_ac_ae_aq$6$(not in LMFDB)
4.4.b_e_aq_aq$6$(not in LMFDB)
4.4.b_e_q_q$6$(not in LMFDB)
4.4.b_k_i_ce$6$(not in LMFDB)
4.4.d_c_am_abw$6$(not in LMFDB)
4.4.d_i_y_bw$6$(not in LMFDB)
4.4.d_o_y_cu$6$(not in LMFDB)
4.4.f_k_bc_dc$6$(not in LMFDB)
4.4.f_q_bo_dc$6$(not in LMFDB)
4.4.h_w_ca_ei$6$(not in LMFDB)
4.4.h_bc_dc_gu$6$(not in LMFDB)
4.4.h_bi_ea_jo$6$(not in LMFDB)
4.4.j_bm_ee_jg$6$(not in LMFDB)
4.4.j_bs_fo_my$6$(not in LMFDB)
4.4.l_cg_ho_rw$6$(not in LMFDB)
4.4.af_m_au_bg$8$(not in LMFDB)
4.4.ad_e_am_bg$8$(not in LMFDB)
4.4.ab_i_ae_bg$8$(not in LMFDB)
4.4.b_i_e_bg$8$(not in LMFDB)
4.4.d_e_m_bg$8$(not in LMFDB)
4.4.f_m_u_bg$8$(not in LMFDB)
4.4.ab_e_i_ai$9$(not in LMFDB)
4.4.ah_ba_acu_ge$10$(not in LMFDB)
4.4.af_o_abo_ds$10$(not in LMFDB)
4.4.ab_c_ai_a$10$(not in LMFDB)
4.4.b_c_i_a$10$(not in LMFDB)
4.4.d_g_i_a$10$(not in LMFDB)
4.4.f_o_bo_ds$10$(not in LMFDB)
4.4.h_ba_cu_ge$10$(not in LMFDB)
4.4.ah_be_ado_ia$12$(not in LMFDB)
4.4.af_i_a_aq$12$(not in LMFDB)
4.4.af_s_aca_ei$12$(not in LMFDB)
4.4.af_y_acm_ge$12$(not in LMFDB)
4.4.ad_a_a_q$12$(not in LMFDB)
4.4.ad_g_a_ai$12$(not in LMFDB)
4.4.ad_k_abc_bw$12$(not in LMFDB)
4.4.ad_q_abg_ds$12$(not in LMFDB)
4.4.ad_s_abk_ei$12$(not in LMFDB)
4.4.ab_c_a_i$12$(not in LMFDB)
4.4.ab_e_a_a$12$(not in LMFDB)
4.4.ab_g_au_q$12$(not in LMFDB)
4.4.ab_m_ai_cm$12$(not in LMFDB)
4.4.ab_o_am_dc$12$(not in LMFDB)
4.4.b_c_a_i$12$(not in LMFDB)
4.4.b_e_a_a$12$(not in LMFDB)
4.4.b_g_u_q$12$(not in LMFDB)
4.4.b_m_i_cm$12$(not in LMFDB)
4.4.b_o_m_dc$12$(not in LMFDB)
4.4.d_a_a_q$12$(not in LMFDB)
4.4.d_g_a_ai$12$(not in LMFDB)
4.4.d_k_bc_bw$12$(not in LMFDB)
4.4.d_q_bg_ds$12$(not in LMFDB)
4.4.d_s_bk_ei$12$(not in LMFDB)
4.4.f_i_a_aq$12$(not in LMFDB)
4.4.f_s_ca_ei$12$(not in LMFDB)
4.4.f_y_cm_ge$12$(not in LMFDB)
4.4.h_be_do_ia$12$(not in LMFDB)
4.4.d_m_bc_cu$15$(not in LMFDB)
4.4.ab_e_ai_i$18$(not in LMFDB)
4.4.b_e_ai_ai$18$(not in LMFDB)
4.4.b_e_i_i$18$(not in LMFDB)
4.4.ad_o_abg_dc$20$(not in LMFDB)
4.4.ab_k_aq_bw$20$(not in LMFDB)
4.4.b_k_q_bw$20$(not in LMFDB)
4.4.d_o_bg_dc$20$(not in LMFDB)
4.4.ad_k_am_bg$24$(not in LMFDB)
4.4.ab_g_ae_bg$24$(not in LMFDB)
4.4.b_g_e_bg$24$(not in LMFDB)
4.4.d_k_m_bg$24$(not in LMFDB)
4.4.af_u_aca_eq$30$(not in LMFDB)
4.4.ad_m_abc_cu$30$(not in LMFDB)
4.4.ab_i_am_bo$30$(not in LMFDB)
4.4.ab_i_e_y$30$(not in LMFDB)
4.4.b_i_ae_y$30$(not in LMFDB)
4.4.b_i_m_bo$30$(not in LMFDB)
4.4.f_u_ca_eq$30$(not in LMFDB)