Properties

Label 6.2.aj_bq_aff_ms_ayp_bmn
Base Field $\F_{2}$
Dimension $6$
Ordinary Yes
$p$-rank $6$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

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

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $6$
Slopes:  $[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]$

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 6859 438976 5000211 887503681 192699928576 10722223798651 342104081183019 17854072924596544 1381721358424021399

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 8 9 -4 24 131 246 308 513 1208

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 2.2.ad_f 3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-3}, \sqrt{5})\)$)$
Endomorphism algebra over $\overline{\F}_{2}$
The base change of $A$ to $\F_{2^{6}}$ is 1.64.l 6 and its endomorphism algebra is $\mathrm{M}_{6}($\(\Q(\sqrt{-15}) \)$)$
All geometric endomorphisms are defined over $\F_{2^{6}}$.
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.ad_g_aj_g_d_ah$2$(not in LMFDB)
6.2.d_g_j_g_ad_ah$2$(not in LMFDB)
6.2.j_bq_ff_ms_yp_bmn$2$(not in LMFDB)
6.2.ag_s_abk_cc_aco_df$3$(not in LMFDB)
6.2.ad_d_a_d_ap_bd$3$(not in LMFDB)
6.2.ad_g_aj_g_d_ah$3$(not in LMFDB)
6.2.a_ad_a_p_a_az$3$(not in LMFDB)
6.2.a_a_a_a_a_l$3$(not in LMFDB)
6.2.d_d_a_d_p_bd$3$(not in LMFDB)
6.2.d_g_j_g_ad_ah$3$(not in LMFDB)
6.2.g_s_bk_cc_co_df$3$(not in LMFDB)
6.2.j_bq_ff_ms_yp_bmn$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ad_g_aj_g_d_ah$2$(not in LMFDB)
6.2.d_g_j_g_ad_ah$2$(not in LMFDB)
6.2.j_bq_ff_ms_yp_bmn$2$(not in LMFDB)
6.2.ag_s_abk_cc_aco_df$3$(not in LMFDB)
6.2.ad_d_a_d_ap_bd$3$(not in LMFDB)
6.2.ad_g_aj_g_d_ah$3$(not in LMFDB)
6.2.a_ad_a_p_a_az$3$(not in LMFDB)
6.2.a_a_a_a_a_l$3$(not in LMFDB)
6.2.d_d_a_d_p_bd$3$(not in LMFDB)
6.2.d_g_j_g_ad_ah$3$(not in LMFDB)
6.2.g_s_bk_cc_co_df$3$(not in LMFDB)
6.2.j_bq_ff_ms_yp_bmn$3$(not in LMFDB)
6.2.ad_e_ad_ae_p_ax$4$(not in LMFDB)
6.2.d_e_d_ae_ap_ax$4$(not in LMFDB)
6.2.ae_m_az_bt_acr_dx$5$(not in LMFDB)
6.2.b_ad_af_a_g_l$5$(not in LMFDB)
6.2.d_g_j_g_ad_ah$6$(not in LMFDB)
6.2.a_a_aj_a_a_bj$9$(not in LMFDB)
6.2.a_a_j_a_a_bj$9$(not in LMFDB)
6.2.ah_v_abf_g_cu_agb$10$(not in LMFDB)
6.2.ac_g_al_v_abh_cb$10$(not in LMFDB)
6.2.ab_ad_f_a_ag_l$10$(not in LMFDB)
6.2.c_g_l_v_bh_cb$10$(not in LMFDB)
6.2.e_m_z_bt_cr_dx$10$(not in LMFDB)
6.2.h_v_bf_g_acu_agb$10$(not in LMFDB)
6.2.ag_u_abw_do_afu_in$12$(not in LMFDB)
6.2.ad_f_ag_l_av_bj$12$(not in LMFDB)
6.2.ad_h_am_x_abn_cj$12$(not in LMFDB)
6.2.a_ac_a_c_a_af$12$(not in LMFDB)
6.2.a_ab_a_l_a_ah$12$(not in LMFDB)
6.2.a_a_a_a_a_al$12$(not in LMFDB)
6.2.a_b_a_l_a_h$12$(not in LMFDB)
6.2.a_c_a_c_a_f$12$(not in LMFDB)
6.2.a_d_a_p_a_z$12$(not in LMFDB)
6.2.d_f_g_l_v_bj$12$(not in LMFDB)
6.2.d_h_m_x_bn_cj$12$(not in LMFDB)
6.2.g_u_bw_do_fu_in$12$(not in LMFDB)
6.2.ai_bh_adr_if_apa_xb$15$(not in LMFDB)
6.2.ah_v_abf_g_cu_agb$15$(not in LMFDB)
6.2.af_m_au_be_abt_cn$15$(not in LMFDB)
6.2.ae_d_l_av_aj_cb$15$(not in LMFDB)
6.2.ac_d_af_d_a_ab$15$(not in LMFDB)
6.2.ac_g_al_v_abh_cb$15$(not in LMFDB)
6.2.ab_ad_f_a_ag_l$15$(not in LMFDB)
6.2.ab_d_ab_j_ag_x$15$(not in LMFDB)
6.2.b_d_b_j_g_x$15$(not in LMFDB)
6.2.c_d_f_d_a_ab$15$(not in LMFDB)
6.2.c_g_l_v_bh_cb$15$(not in LMFDB)
6.2.e_d_al_av_j_cb$15$(not in LMFDB)
6.2.e_m_z_bt_cr_dx$15$(not in LMFDB)
6.2.f_m_u_be_bt_cn$15$(not in LMFDB)
6.2.h_v_bf_g_acu_agb$15$(not in LMFDB)
6.2.i_bh_dr_if_pa_xb$15$(not in LMFDB)
6.2.ad_f_ag_ad_v_abj$24$(not in LMFDB)
6.2.a_ab_a_ad_a_h$24$(not in LMFDB)
6.2.a_b_a_ad_a_ah$24$(not in LMFDB)
6.2.d_f_g_ad_av_abj$24$(not in LMFDB)
6.2.af_o_abe_ce_adr_fn$60$(not in LMFDB)
6.2.ae_f_d_an_f_l$60$(not in LMFDB)
6.2.ab_f_ad_r_ak_bp$60$(not in LMFDB)
6.2.b_f_d_r_k_bp$60$(not in LMFDB)
6.2.e_f_ad_an_af_l$60$(not in LMFDB)
6.2.f_o_be_ce_dr_fn$60$(not in LMFDB)