Properties

Label 5.2.ag_s_abi_bw_acm
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $0$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.111901318694$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.359194778829$, $\pm0.729359314356$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $0$
Slopes:  $[1/3, 1/3, 1/3, 1/2, 1/2, 1/2, 1/2, 2/3, 2/3, 2/3]$

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 2025 65403 4505625 39491733 927087525 36600767913 955088870625 36862172735193 1220220502700625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 15 41 37 53 137 225 537 1105

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 3.2.ac_c_ac 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_bw_jg. 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_c_ac_i_aq$2$(not in LMFDB)
5.2.ac_c_c_a_a$2$(not in LMFDB)
5.2.c_c_ac_a_a$2$(not in LMFDB)
5.2.c_c_c_i_q$2$(not in LMFDB)
5.2.g_s_bi_bw_cm$2$(not in LMFDB)
5.2.a_a_c_a_ae$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ac_c_ac_i_aq$2$(not in LMFDB)
5.2.ac_c_c_a_a$2$(not in LMFDB)
5.2.c_c_ac_a_a$2$(not in LMFDB)
5.2.c_c_c_i_q$2$(not in LMFDB)
5.2.g_s_bi_bw_cm$2$(not in LMFDB)
5.2.a_a_c_a_ae$3$(not in LMFDB)
5.2.ae_i_ao_y_abk$6$(not in LMFDB)
5.2.a_a_ac_a_e$6$(not in LMFDB)
5.2.e_i_o_y_bk$6$(not in LMFDB)
5.2.ae_k_as_bc_abo$8$(not in LMFDB)
5.2.ac_ac_g_a_ai$8$(not in LMFDB)
5.2.ac_g_ak_q_ay$8$(not in LMFDB)
5.2.a_c_ac_e_ai$8$(not in LMFDB)
5.2.a_c_c_e_i$8$(not in LMFDB)
5.2.c_ac_ag_a_i$8$(not in LMFDB)
5.2.c_g_k_q_y$8$(not in LMFDB)
5.2.e_k_s_bc_bo$8$(not in LMFDB)
5.2.ac_a_c_e_am$24$(not in LMFDB)
5.2.ac_e_ag_m_au$24$(not in LMFDB)
5.2.c_a_ac_e_m$24$(not in LMFDB)
5.2.c_e_g_m_u$24$(not in LMFDB)