Properties

Label 5.2.ah_ba_acn_eu_ahk
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.147012170705$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.341962716420$, $\pm0.600633654388$
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
$A(\F_{q^r})$ 3 3825 86697 3538125 78877563 994848075 26085841176 1135175563125 36400837975749 1083629820189375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 8 17 36 61 59 94 268 530 983

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 3.2.ad_g_aj 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.d_bq_db. 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.ad_g_aj_q_ay$2$(not in LMFDB)
5.2.ab_c_b_e_a$2$(not in LMFDB)
5.2.b_c_ab_e_a$2$(not in LMFDB)
5.2.d_g_j_q_y$2$(not in LMFDB)
5.2.h_ba_cn_eu_hk$2$(not in LMFDB)
5.2.ab_c_b_ac_g$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ad_g_aj_q_ay$2$(not in LMFDB)
5.2.ab_c_b_e_a$2$(not in LMFDB)
5.2.b_c_ab_e_a$2$(not in LMFDB)
5.2.d_g_j_q_y$2$(not in LMFDB)
5.2.h_ba_cn_eu_hk$2$(not in LMFDB)
5.2.ab_c_b_ac_g$3$(not in LMFDB)
5.2.af_o_abf_cg_adm$6$(not in LMFDB)
5.2.b_c_ab_ac_ag$6$(not in LMFDB)
5.2.f_o_bf_cg_dm$6$(not in LMFDB)
5.2.af_q_abl_cs_aee$8$(not in LMFDB)
5.2.ad_c_d_ai_m$8$(not in LMFDB)
5.2.ad_k_av_bo_aci$8$(not in LMFDB)
5.2.ab_e_af_k_am$8$(not in LMFDB)
5.2.b_e_f_k_m$8$(not in LMFDB)
5.2.d_c_ad_ai_am$8$(not in LMFDB)
5.2.d_k_v_bo_ci$8$(not in LMFDB)
5.2.f_q_bl_cs_ee$8$(not in LMFDB)
5.2.ad_e_ad_e_ag$24$(not in LMFDB)
5.2.ad_i_ap_bc_abq$24$(not in LMFDB)
5.2.d_e_d_e_g$24$(not in LMFDB)
5.2.d_i_p_bc_bq$24$(not in LMFDB)