Properties

Label 5.2.ag_q_av_i_i
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0889496890695$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.297004294965$, $\pm0.823081333977$
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
$A(\F_{q^r})$ 2 800 106808 4360000 39237902 1196249600 21135172186 910446480000 35876430274568 1212843550820000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 1 18 41 37 70 67 209 522 1101

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 3.2.ac_a_d 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.i_bo_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.ac_a_d_e_aq$2$(not in LMFDB)
5.2.ac_a_f_a_ai$2$(not in LMFDB)
5.2.c_a_af_a_i$2$(not in LMFDB)
5.2.c_a_ad_e_q$2$(not in LMFDB)
5.2.g_q_v_i_ai$2$(not in LMFDB)
5.2.a_ac_d_c_ak$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ac_a_d_e_aq$2$(not in LMFDB)
5.2.ac_a_f_a_ai$2$(not in LMFDB)
5.2.c_a_af_a_i$2$(not in LMFDB)
5.2.c_a_ad_e_q$2$(not in LMFDB)
5.2.g_q_v_i_ai$2$(not in LMFDB)
5.2.a_ac_d_c_ak$3$(not in LMFDB)
5.2.ac_a_d_e_aq$4$(not in LMFDB)
5.2.ac_a_f_a_ai$4$(not in LMFDB)
5.2.c_a_af_a_i$4$(not in LMFDB)
5.2.c_a_ad_e_q$4$(not in LMFDB)
5.2.g_q_v_i_ai$4$(not in LMFDB)
5.2.ae_g_af_g_ak$6$(not in LMFDB)
5.2.a_ac_ad_c_k$6$(not in LMFDB)
5.2.e_g_f_g_k$6$(not in LMFDB)
5.2.ae_i_aj_g_ae$8$(not in LMFDB)
5.2.ac_ae_l_e_abc$8$(not in LMFDB)
5.2.ac_e_af_e_ae$8$(not in LMFDB)
5.2.a_a_ab_c_ae$8$(not in LMFDB)
5.2.a_a_b_c_e$8$(not in LMFDB)
5.2.c_ae_al_e_bc$8$(not in LMFDB)
5.2.c_e_f_e_e$8$(not in LMFDB)
5.2.e_i_j_g_e$8$(not in LMFDB)
5.2.ae_g_af_g_ak$12$(not in LMFDB)
5.2.a_ac_ad_c_k$12$(not in LMFDB)
5.2.a_ac_d_c_ak$12$(not in LMFDB)
5.2.e_g_f_g_k$12$(not in LMFDB)
5.2.ac_ac_h_e_aw$24$(not in LMFDB)
5.2.ac_c_ab_e_ak$24$(not in LMFDB)
5.2.c_ac_ah_e_w$24$(not in LMFDB)
5.2.c_c_b_e_k$24$(not in LMFDB)