Properties

Label 5.2.ag_s_abh_bs_ace
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.161334789180$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.327009058845$, $\pm0.739882802642$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 4 2600 100048 6890000 53126324 1040499200 32604824284 849412980000 35849268493168 1174955063165000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 18 49 47 62 123 193 522 1065

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 3.2.ac_c_ab 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 2 $\times$ 3.16.q_ey_yp. 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_ab_i_aq$2$(not in LMFDB)
5.2.ac_c_b_e_ai$2$(not in LMFDB)
5.2.c_c_ab_e_i$2$(not in LMFDB)
5.2.c_c_b_i_q$2$(not in LMFDB)
5.2.g_s_bh_bs_ce$2$(not in LMFDB)
5.2.a_a_d_c_ac$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ac_c_ab_i_aq$2$(not in LMFDB)
5.2.ac_c_b_e_ai$2$(not in LMFDB)
5.2.c_c_ab_e_i$2$(not in LMFDB)
5.2.c_c_b_i_q$2$(not in LMFDB)
5.2.g_s_bh_bs_ce$2$(not in LMFDB)
5.2.a_a_d_c_ac$3$(not in LMFDB)
5.2.ae_i_an_w_abi$6$(not in LMFDB)
5.2.a_a_ad_c_c$6$(not in LMFDB)
5.2.e_i_n_w_bi$6$(not in LMFDB)
5.2.ae_k_ar_ba_abk$8$(not in LMFDB)
5.2.ac_ac_h_a_am$8$(not in LMFDB)
5.2.ac_g_aj_q_au$8$(not in LMFDB)
5.2.a_c_ab_g_ae$8$(not in LMFDB)
5.2.a_c_b_g_e$8$(not in LMFDB)
5.2.c_ac_ah_a_m$8$(not in LMFDB)
5.2.c_g_j_q_u$8$(not in LMFDB)
5.2.e_k_r_ba_bk$8$(not in LMFDB)
5.2.a_a_ad_c_c$12$(not in LMFDB)
5.2.ac_a_d_e_ao$24$(not in LMFDB)
5.2.ac_e_af_m_as$24$(not in LMFDB)
5.2.c_a_ad_e_o$24$(not in LMFDB)
5.2.c_e_f_m_s$24$(not in LMFDB)