Properties

Label 5.2.ah_y_aca_dg_aeq
Base field $\F_{2}$
Dimension $5$
$p$-rank $1$
Ordinary no
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - x - 2 x^{3} + 4 x^{4} )$
  $1 - 7 x + 24 x^{2} - 52 x^{3} + 84 x^{4} - 120 x^{5} + 168 x^{6} - 208 x^{7} + 192 x^{8} - 112 x^{9} + 32 x^{10}$
Frobenius angles:  $\pm0.139386741866$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.686170398078$
Angle rank:  $2$ (numerical)
Jacobians:  $0$

This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $2$ $2000$ $57122$ $6500000$ $96627242$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-4$ $4$ $14$ $48$ $66$ $64$ $122$ $192$ $410$ $1104$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{4}}$.

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 2.2.ab_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 $\F_{2^{4}}$ is 1.16.i 3 $\times$ 2.16.h_bo. The endomorphism algebra for each factor is:
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_m_am_ae_y$2$(not in LMFDB)
5.2.ad_e_ae_m_ay$2$(not in LMFDB)
5.2.ab_a_e_e_ai$2$(not in LMFDB)
5.2.b_a_ae_e_i$2$(not in LMFDB)
5.2.d_e_e_m_y$2$(not in LMFDB)
5.2.f_m_m_ae_ay$2$(not in LMFDB)
5.2.h_y_ca_dg_eq$2$(not in LMFDB)
5.2.ab_a_c_a_a$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
5.2.af_m_am_ae_y$2$(not in LMFDB)
5.2.ad_e_ae_m_ay$2$(not in LMFDB)
5.2.ab_a_e_e_ai$2$(not in LMFDB)
5.2.b_a_ae_e_i$2$(not in LMFDB)
5.2.d_e_e_m_y$2$(not in LMFDB)
5.2.f_m_m_ae_ay$2$(not in LMFDB)
5.2.h_y_ca_dg_eq$2$(not in LMFDB)
5.2.ab_a_c_a_a$3$(not in LMFDB)
5.2.af_m_aw_bo_acm$6$(not in LMFDB)
5.2.ad_e_ac_a_a$6$(not in LMFDB)
5.2.ab_a_ag_i_a$6$(not in LMFDB)
5.2.b_a_ac_a_a$6$(not in LMFDB)
5.2.b_a_g_i_a$6$(not in LMFDB)
5.2.d_e_c_a_a$6$(not in LMFDB)
5.2.f_m_w_bo_cm$6$(not in LMFDB)
5.2.af_o_abc_bw_acu$8$(not in LMFDB)
5.2.ad_a_i_ae_ai$8$(not in LMFDB)
5.2.ad_g_ae_a_i$8$(not in LMFDB)
5.2.ad_i_aq_bc_abo$8$(not in LMFDB)
5.2.ab_ae_i_e_ay$8$(not in LMFDB)
5.2.ab_ac_a_a_i$8$(not in LMFDB)
5.2.ab_c_ae_i_ai$8$(not in LMFDB)
5.2.ab_e_a_e_i$8$(not in LMFDB)
5.2.ab_g_ai_q_ay$8$(not in LMFDB)
5.2.b_ae_ai_e_y$8$(not in LMFDB)
5.2.b_ac_a_a_ai$8$(not in LMFDB)
5.2.b_c_e_i_i$8$(not in LMFDB)
5.2.b_e_a_e_ai$8$(not in LMFDB)
5.2.b_g_i_q_y$8$(not in LMFDB)
5.2.d_a_ai_ae_i$8$(not in LMFDB)
5.2.d_g_e_a_ai$8$(not in LMFDB)
5.2.d_i_q_bc_bo$8$(not in LMFDB)
5.2.f_o_bc_bw_cu$8$(not in LMFDB)
5.2.ad_e_ac_a_a$12$(not in LMFDB)
5.2.ad_c_c_e_aq$24$(not in LMFDB)
5.2.ad_g_ao_y_abg$24$(not in LMFDB)
5.2.ad_g_ak_u_abg$24$(not in LMFDB)
5.2.ab_ac_g_e_aq$24$(not in LMFDB)
5.2.ab_a_ac_e_a$24$(not in LMFDB)
5.2.ab_c_ac_a_a$24$(not in LMFDB)
5.2.ab_c_c_e_a$24$(not in LMFDB)
5.2.ab_e_ag_m_aq$24$(not in LMFDB)
5.2.b_ac_ag_e_q$24$(not in LMFDB)
5.2.b_a_c_e_a$24$(not in LMFDB)
5.2.b_c_ac_e_a$24$(not in LMFDB)
5.2.b_c_c_a_a$24$(not in LMFDB)
5.2.b_e_g_m_q$24$(not in LMFDB)
5.2.d_c_ac_e_q$24$(not in LMFDB)
5.2.d_g_k_u_bg$24$(not in LMFDB)
5.2.d_g_o_y_bg$24$(not in LMFDB)