Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.197201053961$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.652365995579$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 3 3375 79092 7171875 124264563 1067742000 26487260229 799929421875 25107150425292 1065956954484375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 6 17 50 76 63 94 178 341 966

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 2.2.ab_b 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 $\F_{2^{4}}$ is 1.16.i 3 $\times$ 2.16.j_bx. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{4}}$.
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_n_as_o_ai$2$(not in LMFDB)
5.2.ad_f_ag_o_ay$2$(not in LMFDB)
5.2.ab_b_c_g_ai$2$(not in LMFDB)
5.2.b_b_ac_g_i$2$(not in LMFDB)
5.2.d_f_g_o_y$2$(not in LMFDB)
5.2.f_n_s_o_i$2$(not in LMFDB)
5.2.h_z_cg_dy_fw$2$(not in LMFDB)
5.2.ab_b_c_a_e$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.af_n_as_o_ai$2$(not in LMFDB)
5.2.ad_f_ag_o_ay$2$(not in LMFDB)
5.2.ab_b_c_g_ai$2$(not in LMFDB)
5.2.b_b_ac_g_i$2$(not in LMFDB)
5.2.d_f_g_o_y$2$(not in LMFDB)
5.2.f_n_s_o_i$2$(not in LMFDB)
5.2.h_z_cg_dy_fw$2$(not in LMFDB)
5.2.ab_b_c_a_e$3$(not in LMFDB)
5.2.af_n_aba_bw_acy$6$(not in LMFDB)
5.2.ad_f_ag_i_am$6$(not in LMFDB)
5.2.ab_b_ag_i_ae$6$(not in LMFDB)
5.2.b_b_ac_a_ae$6$(not in LMFDB)
5.2.b_b_g_i_e$6$(not in LMFDB)
5.2.d_f_g_i_m$6$(not in LMFDB)
5.2.f_n_ba_bw_cy$6$(not in LMFDB)
5.2.af_p_abg_cg_adk$8$(not in LMFDB)
5.2.ad_b_g_ag_a$8$(not in LMFDB)
5.2.ad_h_ai_k_ai$8$(not in LMFDB)
5.2.ad_j_as_bi_abw$8$(not in LMFDB)
5.2.ab_ad_g_c_aq$8$(not in LMFDB)
5.2.ab_ab_a_ac_i$8$(not in LMFDB)
5.2.ab_d_ae_k_ai$8$(not in LMFDB)
5.2.ab_f_ac_k_a$8$(not in LMFDB)
5.2.ab_h_ai_w_ay$8$(not in LMFDB)
5.2.b_ad_ag_c_q$8$(not in LMFDB)
5.2.b_ab_a_ac_ai$8$(not in LMFDB)
5.2.b_d_e_k_i$8$(not in LMFDB)
5.2.b_f_c_k_a$8$(not in LMFDB)
5.2.b_h_i_w_y$8$(not in LMFDB)
5.2.d_b_ag_ag_a$8$(not in LMFDB)
5.2.d_h_i_k_i$8$(not in LMFDB)
5.2.d_j_s_bi_bw$8$(not in LMFDB)
5.2.f_p_bg_cg_dk$8$(not in LMFDB)
5.2.ad_d_a_e_am$24$(not in LMFDB)
5.2.ad_h_aq_bc_abo$24$(not in LMFDB)
5.2.ad_h_am_y_abk$24$(not in LMFDB)
5.2.ab_ab_e_e_am$24$(not in LMFDB)
5.2.ab_b_ac_e_a$24$(not in LMFDB)
5.2.ab_d_ae_e_ai$24$(not in LMFDB)
5.2.ab_d_a_i_ae$24$(not in LMFDB)
5.2.ab_f_ag_q_aq$24$(not in LMFDB)
5.2.b_ab_ae_e_m$24$(not in LMFDB)
5.2.b_b_c_e_a$24$(not in LMFDB)
5.2.b_d_a_i_e$24$(not in LMFDB)
5.2.b_d_e_e_i$24$(not in LMFDB)
5.2.b_f_g_q_q$24$(not in LMFDB)
5.2.d_d_a_e_m$24$(not in LMFDB)
5.2.d_h_m_y_bk$24$(not in LMFDB)
5.2.d_h_q_bc_bo$24$(not in LMFDB)