Properties

Label 5.2.ah_z_ach_ec_age
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.105278500939$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.316838792568$, $\pm0.641249159631$
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
$A(\F_{q^r})$ 2 2300 51038 3910000 72017402 763018100 26336547722 1076814000000 34196345458262 1244370684807500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 6 14 38 56 42 94 254 500 1126

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 3.2.ad_f_ah 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.f_br_fn. 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_f_ah_o_ay$2$(not in LMFDB)
5.2.ab_b_d_c_a$2$(not in LMFDB)
5.2.b_b_ad_c_a$2$(not in LMFDB)
5.2.d_f_h_o_y$2$(not in LMFDB)
5.2.h_z_ch_ec_ge$2$(not in LMFDB)
5.2.ab_b_b_ac_c$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ad_f_ah_o_ay$2$(not in LMFDB)
5.2.ab_b_d_c_a$2$(not in LMFDB)
5.2.b_b_ad_c_a$2$(not in LMFDB)
5.2.d_f_h_o_y$2$(not in LMFDB)
5.2.h_z_ch_ec_ge$2$(not in LMFDB)
5.2.ab_b_b_ac_c$3$(not in LMFDB)
5.2.h_z_ch_ec_ge$4$(not in LMFDB)
5.2.af_n_abb_by_ada$6$(not in LMFDB)
5.2.b_b_ab_ac_ac$6$(not in LMFDB)
5.2.f_n_bb_by_da$6$(not in LMFDB)
5.2.af_p_abh_ci_ado$8$(not in LMFDB)
5.2.ad_b_f_ag_e$8$(not in LMFDB)
5.2.ad_j_at_bi_aca$8$(not in LMFDB)
5.2.ab_d_af_i_am$8$(not in LMFDB)
5.2.b_d_f_i_m$8$(not in LMFDB)
5.2.d_b_af_ag_ae$8$(not in LMFDB)
5.2.d_j_t_bi_ca$8$(not in LMFDB)
5.2.f_p_bh_ci_do$8$(not in LMFDB)
5.2.ad_d_ab_e_ak$24$(not in LMFDB)
5.2.ad_h_an_y_abm$24$(not in LMFDB)
5.2.d_d_b_e_k$24$(not in LMFDB)
5.2.d_h_n_y_bm$24$(not in LMFDB)