Properties

Label 5.2.ai_bh_ado_hj_alu
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$
Frobenius angles:  $\pm0.123548644961$, $\pm0.123548644961$, $\pm0.250000000000$, $\pm0.456881978294$, $\pm0.456881978294$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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 1805 75088 731025 37864361 2168541440 54945865913 1100579337225 32857658578576 1271561917711025

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 7 13 11 35 109 191 259 481 1147

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 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 $\F_{2^{12}}$ is 1.4096.h 4 $\times$ 1.4096.ey. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{12}}$.
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.ae_j_aq_x_abe$2$(not in LMFDB)
5.2.ac_d_ac_ab_g$2$(not in LMFDB)
5.2.c_d_c_ab_ag$2$(not in LMFDB)
5.2.e_j_q_x_be$2$(not in LMFDB)
5.2.i_bh_do_hj_lu$2$(not in LMFDB)
5.2.af_m_ar_r_as$3$(not in LMFDB)
5.2.ac_a_e_f_as$3$(not in LMFDB)
5.2.ac_d_ac_ab_g$3$(not in LMFDB)
5.2.b_a_b_f_g$3$(not in LMFDB)
5.2.e_j_q_x_be$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ae_j_aq_x_abe$2$(not in LMFDB)
5.2.ac_d_ac_ab_g$2$(not in LMFDB)
5.2.c_d_c_ab_ag$2$(not in LMFDB)
5.2.e_j_q_x_be$2$(not in LMFDB)
5.2.i_bh_do_hj_lu$2$(not in LMFDB)
5.2.af_m_ar_r_as$3$(not in LMFDB)
5.2.ac_a_e_f_as$3$(not in LMFDB)
5.2.ac_d_ac_ab_g$3$(not in LMFDB)
5.2.b_a_b_f_g$3$(not in LMFDB)
5.2.e_j_q_x_be$3$(not in LMFDB)
5.2.ac_b_c_af_g$4$(not in LMFDB)
5.2.c_b_ac_af_ag$4$(not in LMFDB)
5.2.ad_i_am_v_aba$5$(not in LMFDB)
5.2.c_ac_ah_b_o$5$(not in LMFDB)
5.2.ab_a_ab_f_ag$6$(not in LMFDB)
5.2.c_a_ae_f_s$6$(not in LMFDB)
5.2.f_m_r_r_s$6$(not in LMFDB)
5.2.ag_v_acc_ed_agm$8$(not in LMFDB)
5.2.a_b_a_af_a$8$(not in LMFDB)
5.2.a_d_a_ab_a$8$(not in LMFDB)
5.2.g_v_cc_ed_gm$8$(not in LMFDB)
5.2.ag_o_aj_abb_cs$10$(not in LMFDB)
5.2.ac_ac_h_b_ao$10$(not in LMFDB)
5.2.ab_e_ae_n_ak$10$(not in LMFDB)
5.2.b_e_e_n_k$10$(not in LMFDB)
5.2.d_i_m_v_ba$10$(not in LMFDB)
5.2.g_o_j_abb_acs$10$(not in LMFDB)
5.2.af_o_abb_br_ack$12$(not in LMFDB)
5.2.ac_c_a_h_ao$12$(not in LMFDB)
5.2.ac_e_ae_n_as$12$(not in LMFDB)
5.2.ab_c_ad_h_ak$12$(not in LMFDB)
5.2.b_c_d_h_k$12$(not in LMFDB)
5.2.c_c_a_h_o$12$(not in LMFDB)
5.2.c_e_e_n_s$12$(not in LMFDB)
5.2.f_o_bb_br_ck$12$(not in LMFDB)
5.2.ah_z_acj_el_agw$15$(not in LMFDB)
5.2.ag_o_aj_abb_cs$15$(not in LMFDB)
5.2.ab_e_ae_n_ak$15$(not in LMFDB)
5.2.d_f_j_p_w$15$(not in LMFDB)
5.2.ad_g_aj_l_am$24$(not in LMFDB)
5.2.ad_i_ap_z_abk$24$(not in LMFDB)
5.2.ac_c_a_ah_o$24$(not in LMFDB)
5.2.a_a_a_f_a$24$(not in LMFDB)
5.2.a_c_a_ah_a$24$(not in LMFDB)
5.2.a_c_a_h_a$24$(not in LMFDB)
5.2.a_e_a_n_a$24$(not in LMFDB)
5.2.c_c_a_ah_ao$24$(not in LMFDB)
5.2.d_g_j_l_m$24$(not in LMFDB)
5.2.d_i_p_z_bk$24$(not in LMFDB)
5.2.ad_f_aj_p_aw$30$(not in LMFDB)
5.2.h_z_cj_el_gw$30$(not in LMFDB)
5.2.ae_g_ab_an_bc$40$(not in LMFDB)
5.2.ab_g_ae_r_ai$40$(not in LMFDB)
5.2.b_g_e_r_i$40$(not in LMFDB)
5.2.e_g_b_an_abc$40$(not in LMFDB)
5.2.af_p_abj_cn_adw$120$(not in LMFDB)
5.2.f_p_bj_cn_dw$120$(not in LMFDB)