Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0693533547550$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.339907131295$, $\pm0.770553776540$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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 1100 65234 3740000 28143302 896967500 26886431938 844596720000 38112217374998 1149689065827500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 3 15 39 27 51 95 191 555 1043

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 3.2.ac_b_a 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.g_r_ce. 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_b_a_g_aq$2$(not in LMFDB)
5.2.ac_b_e_ac_a$2$(not in LMFDB)
5.2.c_b_ae_ac_a$2$(not in LMFDB)
5.2.c_b_a_g_q$2$(not in LMFDB)
5.2.g_r_bc_be_bg$2$(not in LMFDB)
5.2.a_ab_c_a_ai$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ac_b_a_g_aq$2$(not in LMFDB)
5.2.ac_b_e_ac_a$2$(not in LMFDB)
5.2.c_b_ae_ac_a$2$(not in LMFDB)
5.2.c_b_a_g_q$2$(not in LMFDB)
5.2.g_r_bc_be_bg$2$(not in LMFDB)
5.2.a_ab_c_a_ai$3$(not in LMFDB)
5.2.ae_h_ak_q_ay$6$(not in LMFDB)
5.2.a_ab_ac_a_i$6$(not in LMFDB)
5.2.e_h_k_q_y$6$(not in LMFDB)
5.2.ae_j_ao_s_ay$8$(not in LMFDB)
5.2.ac_ad_i_c_aq$8$(not in LMFDB)
5.2.ac_f_ai_k_aq$8$(not in LMFDB)
5.2.a_b_ac_c_ai$8$(not in LMFDB)
5.2.a_b_c_c_i$8$(not in LMFDB)
5.2.c_ad_ai_c_q$8$(not in LMFDB)
5.2.c_f_i_k_q$8$(not in LMFDB)
5.2.e_j_o_s_y$8$(not in LMFDB)
5.2.a_ab_ac_a_i$12$(not in LMFDB)
5.2.ac_ab_e_e_aq$24$(not in LMFDB)
5.2.ac_d_ae_i_aq$24$(not in LMFDB)
5.2.c_ab_ae_e_q$24$(not in LMFDB)
5.2.c_d_e_i_q$24$(not in LMFDB)