Properties

Label 6.2.ai_bg_adj_hb_amh_sn
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:  $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0635622003031$, $\pm0.123548644961$, $\pm0.165221137389$, $\pm0.365221137389$, $\pm0.456881978294$, $\pm0.663562200303$
Angle rank:  $3$ (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 4009 141436 15190101 1005946931 70310098576 7593444454331 391558651249725 17823209075803324 1220422450820459359

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 5 4 13 30 68 198 341 508 1080

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 2.2.ad_f $\times$ 4.2.af_m_au_bd 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 $\F_{2^{30}}$ is 1.1073741824.acgor 2 $\times$ 2.1073741824.dfu_aggenfjn 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{30}}$.
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.ac_c_ad_d_ab_b$2$(not in LMFDB)
6.2.c_c_d_d_b_b$2$(not in LMFDB)
6.2.i_bg_dj_hb_mh_sn$2$(not in LMFDB)
6.2.af_l_ap_v_abo_cp$3$(not in LMFDB)
6.2.ac_c_ad_d_ab_b$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ac_c_ad_d_ab_b$2$(not in LMFDB)
6.2.c_c_d_d_b_b$2$(not in LMFDB)
6.2.i_bg_dj_hb_mh_sn$2$(not in LMFDB)
6.2.af_l_ap_v_abo_cp$3$(not in LMFDB)
6.2.ac_c_ad_d_ab_b$3$(not in LMFDB)
6.2.ad_c_d_ac_aj_v$5$(not in LMFDB)
6.2.ad_h_ar_bc_abs_ct$5$(not in LMFDB)
6.2.ad_h_ah_ac_ba_abx$5$(not in LMFDB)
6.2.f_l_p_v_bo_cp$6$(not in LMFDB)
6.2.d_c_ad_ac_j_v$10$(not in LMFDB)
6.2.d_h_h_ac_aba_abx$10$(not in LMFDB)
6.2.d_h_r_bc_bs_ct$10$(not in LMFDB)
6.2.af_n_az_bt_adc_ev$12$(not in LMFDB)
6.2.f_n_z_bt_dc_ev$12$(not in LMFDB)
6.2.a_ae_a_q_a_abh$15$(not in LMFDB)
6.2.a_b_af_b_af_r$15$(not in LMFDB)
6.2.a_b_f_b_f_r$15$(not in LMFDB)
6.2.d_c_ad_ac_j_v$15$(not in LMFDB)
6.2.d_h_h_ac_aba_abx$15$(not in LMFDB)
6.2.d_h_r_bc_bs_ct$15$(not in LMFDB)
6.2.ad_i_ap_bc_abt_cr$20$(not in LMFDB)
6.2.d_i_p_bc_bt_cr$20$(not in LMFDB)
6.2.a_ac_a_k_a_ap$60$(not in LMFDB)
6.2.a_c_a_k_a_p$60$(not in LMFDB)
6.2.a_d_af_f_ap_p$60$(not in LMFDB)
6.2.a_d_f_f_p_p$60$(not in LMFDB)
6.2.a_e_a_q_a_bh$60$(not in LMFDB)