Properties

Label 5.2.ag_p_aq_af_be
Base field $\F_{2}$
Dimension $5$
$p$-rank $4$
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:  $( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$
  $1 - 6 x + 15 x^{2} - 16 x^{3} - 5 x^{4} + 30 x^{5} - 10 x^{6} - 64 x^{7} + 120 x^{8} - 96 x^{9} + 32 x^{10}$
Frobenius angles:  $\pm0.0247483856139$, $\pm0.177336015878$, $\pm0.250000000000$, $\pm0.344002682545$, $\pm0.858081718947$
Angle rank:  $2$ (numerical)
Jacobians:  $0$
Isomorphism classes:  1

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

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $1$ $305$ $65572$ $1923025$ $27087101$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-3$ $-1$ $15$ $27$ $27$ $65$ $81$ $259$ $447$ $959$

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 $\F_{2^{12}}$.

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 4.2.ae_f_c_al 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 $\F_{2^{12}}$ is 1.4096.ey $\times$ 2.4096.ahm_zkj 2 . 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_ab_e_d_ao$2$(not in LMFDB)
5.2.c_ab_ae_d_o$2$(not in LMFDB)
5.2.g_p_q_af_abe$2$(not in LMFDB)
5.2.a_a_c_b_g$3$(not in LMFDB)
5.2.a_d_c_h_g$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
5.2.ac_ab_e_d_ao$2$(not in LMFDB)
5.2.c_ab_ae_d_o$2$(not in LMFDB)
5.2.g_p_q_af_abe$2$(not in LMFDB)
5.2.a_a_c_b_g$3$(not in LMFDB)
5.2.a_d_c_h_g$3$(not in LMFDB)
5.2.ae_l_aw_bn_acg$4$(not in LMFDB)
5.2.a_d_ac_h_ag$4$(not in LMFDB)
5.2.a_d_c_h_g$4$(not in LMFDB)
5.2.e_l_w_bn_cg$4$(not in LMFDB)
5.2.ae_i_ak_j_ak$6$(not in LMFDB)
5.2.ae_l_aw_bn_acg$6$(not in LMFDB)
5.2.a_a_ac_b_ag$6$(not in LMFDB)
5.2.a_d_ac_h_ag$6$(not in LMFDB)
5.2.e_i_k_j_k$6$(not in LMFDB)
5.2.e_l_w_bn_cg$6$(not in LMFDB)
5.2.ae_h_ag_ab_i$8$(not in LMFDB)
5.2.ac_h_am_x_abg$8$(not in LMFDB)
5.2.c_h_m_x_bg$8$(not in LMFDB)
5.2.e_h_g_ab_ai$8$(not in LMFDB)
5.2.ac_ac_i_b_as$24$(not in LMFDB)
5.2.ac_e_ag_f_ai$24$(not in LMFDB)
5.2.ac_g_ai_r_as$24$(not in LMFDB)
5.2.a_ac_a_b_a$24$(not in LMFDB)
5.2.a_g_a_r_a$24$(not in LMFDB)
5.2.c_ac_ai_b_s$24$(not in LMFDB)
5.2.c_e_g_f_i$24$(not in LMFDB)
5.2.c_g_i_r_s$24$(not in LMFDB)