Properties

Label 4.5.am_cp_ajc_xg
Base Field $\F_{5}$
Dimension $4$
Ordinary Yes
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 20 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.103885594917$, $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.516810247272$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 44 259600 206947136 144877568000 101344979199244 62729484748902400 37865824253945399756 23405215805135290368000 14603329963432731221966144 9106643109419934768670090000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 16 102 592 3314 16426 79402 392672 1960014 9778176

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ae_j and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ae_d_e_ae$2$(not in LMFDB)
4.5.ae_d_m_abk$2$(not in LMFDB)
4.5.e_d_am_abk$2$(not in LMFDB)
4.5.e_d_ae_ae$2$(not in LMFDB)
4.5.m_cp_jc_xg$2$(not in LMFDB)
4.5.a_e_ai_al$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ae_d_e_ae$2$(not in LMFDB)
4.5.ae_d_m_abk$2$(not in LMFDB)
4.5.e_d_am_abk$2$(not in LMFDB)
4.5.e_d_ae_ae$2$(not in LMFDB)
4.5.m_cp_jc_xg$2$(not in LMFDB)
4.5.a_e_ai_al$3$(not in LMFDB)
4.5.ak_bz_agu_rk$4$(not in LMFDB)
4.5.ai_bn_afc_my$4$(not in LMFDB)
4.5.ag_t_ace_fs$4$(not in LMFDB)
4.5.ae_p_abs_ea$4$(not in LMFDB)
4.5.ac_d_a_am$4$(not in LMFDB)
4.5.ac_d_i_abc$4$(not in LMFDB)
4.5.a_h_au_q$4$(not in LMFDB)
4.5.a_h_u_q$4$(not in LMFDB)
4.5.c_d_ai_abc$4$(not in LMFDB)
4.5.c_d_a_am$4$(not in LMFDB)
4.5.e_p_bs_ea$4$(not in LMFDB)
4.5.g_t_ce_fs$4$(not in LMFDB)
4.5.i_bn_fc_my$4$(not in LMFDB)
4.5.k_bz_gu_rk$4$(not in LMFDB)
4.5.ai_bk_aeq_lx$6$(not in LMFDB)
4.5.a_e_i_al$6$(not in LMFDB)
4.5.i_bk_eq_lx$6$(not in LMFDB)
4.5.ae_b_m_aw$8$(not in LMFDB)
4.5.ae_r_aca_es$8$(not in LMFDB)
4.5.e_b_am_aw$8$(not in LMFDB)
4.5.e_r_ca_es$8$(not in LMFDB)
4.5.ag_q_abs_er$12$(not in LMFDB)
4.5.ac_a_m_abn$12$(not in LMFDB)
4.5.c_a_am_abn$12$(not in LMFDB)
4.5.g_q_bs_er$12$(not in LMFDB)