Properties

Label 5.2.ag_r_abb_ba_ay
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.132091856901$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.309487084859$, $\pm0.780459932197$
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 1575 111033 6181875 44988603 1224138825 27759090936 869771266875 38981319187473 1175636550020625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 3 18 47 42 72 102 199 567 1068

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 3.2.ac_b_b 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.o_dx_sl. 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_b_g_aq$2$(not in LMFDB)
5.2.ac_b_d_c_ai$2$(not in LMFDB)
5.2.c_b_ad_c_i$2$(not in LMFDB)
5.2.c_b_ab_g_q$2$(not in LMFDB)
5.2.g_r_bb_ba_y$2$(not in LMFDB)
5.2.a_ab_d_c_ag$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ac_b_b_g_aq$2$(not in LMFDB)
5.2.ac_b_d_c_ai$2$(not in LMFDB)
5.2.c_b_ad_c_i$2$(not in LMFDB)
5.2.c_b_ab_g_q$2$(not in LMFDB)
5.2.g_r_bb_ba_y$2$(not in LMFDB)
5.2.a_ab_d_c_ag$3$(not in LMFDB)
5.2.ae_h_aj_o_aw$6$(not in LMFDB)
5.2.a_ab_ad_c_g$6$(not in LMFDB)
5.2.e_h_j_o_w$6$(not in LMFDB)
5.2.ae_j_an_q_au$8$(not in LMFDB)
5.2.ac_ad_j_c_au$8$(not in LMFDB)
5.2.ac_f_ah_k_am$8$(not in LMFDB)
5.2.a_b_ab_e_ae$8$(not in LMFDB)
5.2.a_b_b_e_e$8$(not in LMFDB)
5.2.c_ad_aj_c_u$8$(not in LMFDB)
5.2.c_f_h_k_m$8$(not in LMFDB)
5.2.e_j_n_q_u$8$(not in LMFDB)
5.2.a_ab_d_c_ag$12$(not in LMFDB)
5.2.ac_ab_f_e_as$24$(not in LMFDB)
5.2.ac_d_ad_i_ao$24$(not in LMFDB)
5.2.c_ab_af_e_s$24$(not in LMFDB)
5.2.c_d_d_i_o$24$(not in LMFDB)