Properties

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

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.00978468837242$, $\pm0.190215311628$, $\pm0.250000000000$, $\pm0.409784688372$, $\pm0.609784688372$
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 1205 24583 1090525 38101136 918297965 28940657243 1030791493125 27499042761151 885180832006400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 6 8 18 41 54 108 242 386 781

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 4.2.af_n_az_bn 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 $\F_{2^{20}}$ is 1.1048576.acmj 4 $\times$ 1.1048576.dau. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{20}}$.
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.ad_f_aj_p_aw$2$(not in LMFDB)
5.2.d_f_j_p_w$2$(not in LMFDB)
5.2.h_z_cj_el_gw$2$(not in LMFDB)
5.2.ab_e_ae_n_ak$3$(not in LMFDB)
5.2.c_ac_ah_b_o$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ad_f_aj_p_aw$2$(not in LMFDB)
5.2.d_f_j_p_w$2$(not in LMFDB)
5.2.h_z_cj_el_gw$2$(not in LMFDB)
5.2.ab_e_ae_n_ak$3$(not in LMFDB)
5.2.c_ac_ah_b_o$3$(not in LMFDB)
5.2.ac_a_e_f_as$5$(not in LMFDB)
5.2.d_f_j_p_w$5$(not in LMFDB)
5.2.ag_o_aj_abb_cs$6$(not in LMFDB)
5.2.ad_i_am_v_aba$6$(not in LMFDB)
5.2.ac_ac_h_b_ao$6$(not in LMFDB)
5.2.b_e_e_n_k$6$(not in LMFDB)
5.2.d_i_m_v_ba$6$(not in LMFDB)
5.2.g_o_j_abb_acs$6$(not in LMFDB)
5.2.af_p_abj_cn_adw$8$(not in LMFDB)
5.2.f_p_bj_cn_dw$8$(not in LMFDB)
5.2.c_a_ae_f_s$10$(not in LMFDB)
5.2.ai_bh_ado_hj_alu$15$(not in LMFDB)
5.2.ag_o_aj_abb_cs$15$(not in LMFDB)
5.2.af_m_ar_r_as$15$(not in LMFDB)
5.2.ad_i_am_v_aba$15$(not in LMFDB)
5.2.ac_d_ac_ab_g$15$(not in LMFDB)
5.2.ab_e_ae_n_ak$15$(not in LMFDB)
5.2.b_a_b_f_g$15$(not in LMFDB)
5.2.e_j_q_x_be$15$(not in LMFDB)
5.2.ac_c_a_h_ao$20$(not in LMFDB)
5.2.ac_e_ae_n_as$20$(not in LMFDB)
5.2.c_c_a_h_o$20$(not in LMFDB)
5.2.c_e_e_n_s$20$(not in LMFDB)
5.2.ae_g_ab_an_bc$24$(not in LMFDB)
5.2.ab_g_ae_r_ai$24$(not in LMFDB)
5.2.b_g_e_r_i$24$(not in LMFDB)
5.2.e_g_b_an_abc$24$(not in LMFDB)
5.2.ae_j_aq_x_abe$30$(not in LMFDB)
5.2.ab_a_ab_f_ag$30$(not in LMFDB)
5.2.ab_e_ae_n_ak$30$(not in LMFDB)
5.2.c_d_c_ab_ag$30$(not in LMFDB)
5.2.f_m_r_r_s$30$(not in LMFDB)
5.2.i_bh_do_hj_lu$30$(not in LMFDB)
5.2.ac_c_a_ah_o$40$(not in LMFDB)
5.2.a_a_a_f_a$40$(not in LMFDB)
5.2.a_c_a_ah_a$40$(not in LMFDB)
5.2.a_c_a_h_a$40$(not in LMFDB)
5.2.a_e_a_n_a$40$(not in LMFDB)
5.2.c_c_a_ah_ao$40$(not in LMFDB)
5.2.af_o_abb_br_ack$60$(not in LMFDB)
5.2.ac_b_c_af_g$60$(not in LMFDB)
5.2.ab_c_ad_h_ak$60$(not in LMFDB)
5.2.b_c_d_h_k$60$(not in LMFDB)
5.2.c_b_ac_af_ag$60$(not in LMFDB)
5.2.f_o_bb_br_ck$60$(not in LMFDB)
5.2.ag_v_acc_ed_agm$120$(not in LMFDB)
5.2.ad_g_aj_l_am$120$(not in LMFDB)
5.2.ad_i_ap_z_abk$120$(not in LMFDB)
5.2.a_b_a_af_a$120$(not in LMFDB)
5.2.a_d_a_ab_a$120$(not in LMFDB)
5.2.d_g_j_l_m$120$(not in LMFDB)
5.2.d_i_p_z_bk$120$(not in LMFDB)
5.2.g_v_cc_ed_gm$120$(not in LMFDB)