Properties

Label 5.2.ag_q_av_i_i
Base field $\F_{2}$
Dimension $5$
$p$-rank $3$
Ordinary no
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$
  $1 - 6 x + 16 x^{2} - 21 x^{3} + 8 x^{4} + 8 x^{5} + 16 x^{6} - 84 x^{7} + 128 x^{8} - 96 x^{9} + 32 x^{10}$
Frobenius angles:  $\pm0.0889496890695$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.297004294965$, $\pm0.823081333977$
Angle rank:  $3$ (numerical)
Jacobians:  $0$

This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $2$ $800$ $106808$ $4360000$ $39237902$

Point counts of the (virtual) curve

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

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{4}}$.

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:
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)