Properties

Label 5.2.ah_bb_acv_ft_ajd
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:  $( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$
Frobenius angles:  $\pm0.123548644961$, $\pm0.123548644961$, $\pm0.384973271919$, $\pm0.456881978294$, $\pm0.456881978294$
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
$A(\F_{q^r})$ 2 2888 80864 467856 20317462 1868281856 69047017342 1408741551648 35385170776928 1200850669604168

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 10 14 2 16 100 220 322 518 1090

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ab $\times$ 2.2.ad_f 2 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 $\F_{2^{6}}$ is 1.64.aj $\times$ 1.64.l 4 . The endomorphism algebra for each factor is:
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
5.2.af_p_abj_cn_adv$2$(not in LMFDB)
5.2.ab_d_ab_ab_d$2$(not in LMFDB)
5.2.b_d_b_ab_ad$2$(not in LMFDB)
5.2.f_p_bj_cn_dv$2$(not in LMFDB)
5.2.h_bb_cv_ft_jd$2$(not in LMFDB)
5.2.ae_j_an_o_ap$3$(not in LMFDB)
5.2.ab_a_c_f_aj$3$(not in LMFDB)
5.2.ab_d_ab_ab_d$3$(not in LMFDB)
5.2.c_d_f_i_j$3$(not in LMFDB)
5.2.f_p_bj_cn_dv$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.af_p_abj_cn_adv$2$(not in LMFDB)
5.2.ab_d_ab_ab_d$2$(not in LMFDB)
5.2.b_d_b_ab_ad$2$(not in LMFDB)
5.2.f_p_bj_cn_dv$2$(not in LMFDB)
5.2.h_bb_cv_ft_jd$2$(not in LMFDB)
5.2.ae_j_an_o_ap$3$(not in LMFDB)
5.2.ab_a_c_f_aj$3$(not in LMFDB)
5.2.ab_d_ab_ab_d$3$(not in LMFDB)
5.2.c_d_f_i_j$3$(not in LMFDB)
5.2.f_p_bj_cn_dv$3$(not in LMFDB)
5.2.ab_b_b_af_d$4$(not in LMFDB)
5.2.b_b_ab_af_ad$4$(not in LMFDB)
5.2.ac_h_ai_t_ar$5$(not in LMFDB)
5.2.d_c_ad_ag_ah$5$(not in LMFDB)
5.2.ac_d_af_i_aj$6$(not in LMFDB)
5.2.b_a_ac_f_j$6$(not in LMFDB)
5.2.e_j_n_o_p$6$(not in LMFDB)
5.2.af_k_af_au_bx$10$(not in LMFDB)
5.2.ad_c_d_ag_h$10$(not in LMFDB)
5.2.a_f_a_p_ab$10$(not in LMFDB)
5.2.a_f_a_p_b$10$(not in LMFDB)
5.2.c_h_i_t_r$10$(not in LMFDB)
5.2.f_k_f_au_abx$10$(not in LMFDB)
5.2.ae_l_av_bi_abx$12$(not in LMFDB)
5.2.ac_f_aj_q_ax$12$(not in LMFDB)
5.2.ab_c_a_h_ah$12$(not in LMFDB)
5.2.ab_e_ac_n_aj$12$(not in LMFDB)
5.2.b_c_a_h_h$12$(not in LMFDB)
5.2.b_e_c_n_j$12$(not in LMFDB)
5.2.c_f_j_q_x$12$(not in LMFDB)
5.2.e_l_v_bi_bx$12$(not in LMFDB)
5.2.ag_u_abw_dm_afj$15$(not in LMFDB)
5.2.af_k_af_au_bx$15$(not in LMFDB)
5.2.a_f_a_p_ab$15$(not in LMFDB)
5.2.e_k_w_bo_cj$15$(not in LMFDB)
5.2.ab_c_a_ah_h$24$(not in LMFDB)
5.2.b_c_a_ah_ah$24$(not in LMFDB)
5.2.ae_k_aw_bo_acj$30$(not in LMFDB)
5.2.g_u_bw_dm_fj$30$(not in LMFDB)