Properties

Label 5.2.ai_bi_ads_hs_ami
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $0$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$
Frobenius angles:  $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.5$
Angle rank:  $0$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 3 5625 257049 3515625 93250113 1445900625 21033109569 576650390625 27459819020673 1202052237890625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 9 25 41 65 81 65 97 385 1089

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 4 $\times$ 1.2.a 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 $\F_{2^{8}}$ is 1.256.abg 5 and its endomorphism algebra is $\mathrm{M}_{5}(B)$, where $B$ is the quaternion algebra over \(\Q\) ramified at $2$ and $\infty$.
All geometric endomorphisms are defined over $\F_{2^{8}}$.
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_k_aq_y_abg$2$(not in LMFDB)
5.2.a_c_a_i_a$2$(not in LMFDB)
5.2.e_k_q_y_bg$2$(not in LMFDB)
5.2.i_bi_ds_hs_mi$2$(not in LMFDB)
5.2.ac_e_a_ae_q$3$(not in LMFDB)
5.2.e_k_y_bs_cm$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ae_k_aq_y_abg$2$(not in LMFDB)
5.2.a_c_a_i_a$2$(not in LMFDB)
5.2.e_k_q_y_bg$2$(not in LMFDB)
5.2.i_bi_ds_hs_mi$2$(not in LMFDB)
5.2.ac_e_a_ae_q$3$(not in LMFDB)
5.2.e_k_y_bs_cm$3$(not in LMFDB)
5.2.c_e_e_a_a$5$(not in LMFDB)
5.2.ag_u_abw_do_afo$6$(not in LMFDB)
5.2.ae_k_ay_bs_acm$6$(not in LMFDB)
5.2.ac_e_ai_m_aq$6$(not in LMFDB)
5.2.a_c_a_ae_a$6$(not in LMFDB)
5.2.c_e_a_ae_aq$6$(not in LMFDB)
5.2.c_e_i_m_q$6$(not in LMFDB)
5.2.g_u_bw_do_fo$6$(not in LMFDB)
5.2.ak_by_age_nw_awu$8$(not in LMFDB)
5.2.ag_o_ai_abg_dc$8$(not in LMFDB)
5.2.ag_s_abg_bo_abw$8$(not in LMFDB)
5.2.ag_w_ace_ei_agu$8$(not in LMFDB)
5.2.ae_g_a_aq_bg$8$(not in LMFDB)
5.2.ae_o_abg_cm_ads$8$(not in LMFDB)
5.2.ac_ag_q_i_abw$8$(not in LMFDB)
5.2.ac_ac_i_a_aq$8$(not in LMFDB)
5.2.ac_c_a_ai_q$8$(not in LMFDB)
5.2.ac_c_a_i_aq$8$(not in LMFDB)
5.2.ac_g_ai_q_aq$8$(not in LMFDB)
5.2.ac_k_aq_bo_abw$8$(not in LMFDB)
5.2.a_ag_a_i_a$8$(not in LMFDB)
5.2.a_ac_a_a_a$8$(not in LMFDB)
5.2.a_c_a_ai_a$8$(not in LMFDB)
5.2.a_g_a_q_a$8$(not in LMFDB)
5.2.a_k_a_bo_a$8$(not in LMFDB)
5.2.c_ag_aq_i_bw$8$(not in LMFDB)
5.2.c_ac_ai_a_q$8$(not in LMFDB)
5.2.c_c_a_ai_aq$8$(not in LMFDB)
5.2.c_c_a_i_q$8$(not in LMFDB)
5.2.c_g_i_q_q$8$(not in LMFDB)
5.2.c_k_q_bo_bw$8$(not in LMFDB)
5.2.e_g_a_aq_abg$8$(not in LMFDB)
5.2.e_o_bg_cm_ds$8$(not in LMFDB)
5.2.g_o_i_abg_adc$8$(not in LMFDB)
5.2.g_s_bg_bo_bw$8$(not in LMFDB)
5.2.g_w_ce_ei_gu$8$(not in LMFDB)
5.2.k_by_ge_nw_wu$8$(not in LMFDB)
5.2.ac_e_ae_a_a$10$(not in LMFDB)
5.2.ac_c_a_a_a$16$(not in LMFDB)
5.2.a_c_a_a_a$16$(not in LMFDB)
5.2.c_c_a_a_a$16$(not in LMFDB)
5.2.ai_bg_adg_gi_ajw$24$(not in LMFDB)
5.2.ag_q_au_e_q$24$(not in LMFDB)
5.2.ag_s_abo_cy_aeq$24$(not in LMFDB)
5.2.ag_u_abs_cy_aei$24$(not in LMFDB)
5.2.ae_e_e_am_q$24$(not in LMFDB)
5.2.ae_g_ae_e_ai$24$(not in LMFDB)
5.2.ae_i_am_u_abg$24$(not in LMFDB)
5.2.ae_i_ai_e_a$24$(not in LMFDB)
5.2.ae_i_ae_am_bg$24$(not in LMFDB)
5.2.ae_k_au_bk_ace$24$(not in LMFDB)
5.2.ae_m_abc_ca_adc$24$(not in LMFDB)
5.2.ae_m_ay_bs_acm$24$(not in LMFDB)
5.2.ac_ae_m_e_abg$24$(not in LMFDB)
5.2.ac_ac_i_e_ay$24$(not in LMFDB)
5.2.ac_a_a_ae_q$24$(not in LMFDB)
5.2.ac_a_e_ae_a$24$(not in LMFDB)
5.2.ac_a_e_e_aq$24$(not in LMFDB)
5.2.ac_c_ai_m_ai$24$(not in LMFDB)
5.2.ac_c_ae_e_a$24$(not in LMFDB)
5.2.ac_c_a_ae_i$24$(not in LMFDB)
5.2.ac_c_a_e_ai$24$(not in LMFDB)
5.2.ac_e_ae_e_a$24$(not in LMFDB)
5.2.ac_e_ae_m_aq$24$(not in LMFDB)
5.2.ac_g_am_u_abg$24$(not in LMFDB)
5.2.ac_g_ai_u_ay$24$(not in LMFDB)
5.2.ac_i_aq_bc_abw$24$(not in LMFDB)
5.2.ac_i_am_bc_abg$24$(not in LMFDB)
5.2.a_ae_ae_e_q$24$(not in LMFDB)
5.2.a_ae_a_e_a$24$(not in LMFDB)
5.2.a_ae_e_e_aq$24$(not in LMFDB)
5.2.a_ac_ae_e_i$24$(not in LMFDB)
5.2.a_ac_a_e_a$24$(not in LMFDB)
5.2.a_ac_e_e_ai$24$(not in LMFDB)
5.2.a_a_ae_e_a$24$(not in LMFDB)
5.2.a_a_a_ae_a$24$(not in LMFDB)
5.2.a_a_a_e_a$24$(not in LMFDB)
5.2.a_a_e_e_a$24$(not in LMFDB)
5.2.a_c_ae_e_ai$24$(not in LMFDB)
5.2.a_c_a_e_a$24$(not in LMFDB)
5.2.a_c_e_e_i$24$(not in LMFDB)
5.2.a_e_ae_e_aq$24$(not in LMFDB)
5.2.a_e_a_e_a$24$(not in LMFDB)
5.2.a_e_a_m_a$24$(not in LMFDB)
5.2.a_e_e_e_q$24$(not in LMFDB)
5.2.a_g_a_u_a$24$(not in LMFDB)
5.2.a_i_a_bc_a$24$(not in LMFDB)
5.2.c_ae_am_e_bg$24$(not in LMFDB)
5.2.c_ac_ai_e_y$24$(not in LMFDB)
5.2.c_a_ae_ae_a$24$(not in LMFDB)
5.2.c_a_ae_e_q$24$(not in LMFDB)
5.2.c_a_a_ae_aq$24$(not in LMFDB)
5.2.c_c_a_ae_ai$24$(not in LMFDB)
5.2.c_c_a_e_i$24$(not in LMFDB)
5.2.c_c_e_e_a$24$(not in LMFDB)
5.2.c_c_i_m_i$24$(not in LMFDB)
5.2.c_e_e_e_a$24$(not in LMFDB)
5.2.c_e_e_m_q$24$(not in LMFDB)
5.2.c_g_i_u_y$24$(not in LMFDB)
5.2.c_g_m_u_bg$24$(not in LMFDB)
5.2.c_i_m_bc_bg$24$(not in LMFDB)
5.2.c_i_q_bc_bw$24$(not in LMFDB)
5.2.e_e_ae_am_aq$24$(not in LMFDB)
5.2.e_g_e_e_i$24$(not in LMFDB)
5.2.e_i_e_am_abg$24$(not in LMFDB)
5.2.e_i_i_e_a$24$(not in LMFDB)
5.2.e_i_m_u_bg$24$(not in LMFDB)
5.2.e_k_u_bk_ce$24$(not in LMFDB)
5.2.e_m_y_bs_cm$24$(not in LMFDB)
5.2.e_m_bc_ca_dc$24$(not in LMFDB)
5.2.g_q_u_e_aq$24$(not in LMFDB)
5.2.g_s_bo_cy_eq$24$(not in LMFDB)
5.2.g_u_bs_cy_ei$24$(not in LMFDB)
5.2.i_bg_dg_gi_jw$24$(not in LMFDB)
5.2.ae_i_ai_a_i$40$(not in LMFDB)
5.2.ac_a_e_a_ai$40$(not in LMFDB)
5.2.ac_e_ae_i_ai$40$(not in LMFDB)
5.2.a_a_a_a_ai$40$(not in LMFDB)
5.2.a_a_a_a_a$40$(not in LMFDB)
5.2.a_a_a_a_i$40$(not in LMFDB)
5.2.a_e_a_i_a$40$(not in LMFDB)
5.2.c_a_ae_a_i$40$(not in LMFDB)
5.2.c_e_e_i_i$40$(not in LMFDB)
5.2.e_i_i_a_ai$40$(not in LMFDB)