Properties

Label 5.2.ag_s_abk_cf_ade
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:  $( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0755571399449$, $\pm0.203216343788$, $\pm0.250000000000$, $\pm0.424442860055$, $\pm0.703216343788$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 2 1460 31226 2131600 38133362 1116954020 45547817842 962596454400 28494805076114 1124768298875300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 9 29 37 65 165 221 405 1025

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 4.2.ae_i_am_r 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 $\times$ 2.16.c_b 2 . 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.ac_c_ae_j_ao$2$(not in LMFDB)
5.2.c_c_e_j_o$2$(not in LMFDB)
5.2.g_s_bk_cf_de$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ac_c_ae_j_ao$2$(not in LMFDB)
5.2.c_c_e_j_o$2$(not in LMFDB)
5.2.g_s_bk_cf_de$2$(not in LMFDB)
5.2.ag_u_abw_dp_afq$8$(not in LMFDB)
5.2.ae_k_au_bh_abw$8$(not in LMFDB)
5.2.ae_m_abc_cb_adc$8$(not in LMFDB)
5.2.ac_a_e_ad_ac$8$(not in LMFDB)
5.2.ac_e_ai_n_ao$8$(not in LMFDB)
5.2.ac_e_ae_f_ac$8$(not in LMFDB)
5.2.a_a_a_ad_a$8$(not in LMFDB)
5.2.a_e_a_f_a$8$(not in LMFDB)
5.2.c_a_ae_ad_c$8$(not in LMFDB)
5.2.c_e_e_f_c$8$(not in LMFDB)
5.2.c_e_i_n_o$8$(not in LMFDB)
5.2.e_k_u_bh_bw$8$(not in LMFDB)
5.2.e_m_bc_cb_dc$8$(not in LMFDB)
5.2.g_u_bw_dp_fq$8$(not in LMFDB)
5.2.ae_h_ae_af_o$24$(not in LMFDB)
5.2.ac_d_ac_ab_i$24$(not in LMFDB)
5.2.a_ab_a_d_ac$24$(not in LMFDB)
5.2.a_ab_a_d_c$24$(not in LMFDB)
5.2.c_d_c_ab_ai$24$(not in LMFDB)
5.2.e_h_e_af_ao$24$(not in LMFDB)