Properties

Label 4.5.al_ch_ahx_ue
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 9 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.235523574971$, $\pm0.521566933142$
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
$A(\F_{q^r})$ 68 360400 252268916 159798476800 104455895241728 62590163252952400 37542139214220476372 23275134774468653875200 14565881008837190764198724 9097810705223061110824960000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 23 127 655 3410 16391 78731 390495 1954999 9768698

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ad_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.af_l_at_bs$2$(not in LMFDB)
4.5.ad_d_d_ae$2$(not in LMFDB)
4.5.d_d_ad_ae$2$(not in LMFDB)
4.5.f_l_t_bs$2$(not in LMFDB)
4.5.l_ch_hx_ue$2$(not in LMFDB)
4.5.b_i_i_bd$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.af_l_at_bs$2$(not in LMFDB)
4.5.ad_d_d_ae$2$(not in LMFDB)
4.5.d_d_ad_ae$2$(not in LMFDB)
4.5.f_l_t_bs$2$(not in LMFDB)
4.5.l_ch_hx_ue$2$(not in LMFDB)
4.5.b_i_i_bd$3$(not in LMFDB)
4.5.aj_bt_afx_pc$4$(not in LMFDB)
4.5.ah_bj_aej_lk$4$(not in LMFDB)
4.5.af_r_abx_ey$4$(not in LMFDB)
4.5.ad_j_ap_bg$4$(not in LMFDB)
4.5.ad_p_abh_ea$4$(not in LMFDB)
4.5.ab_f_h_i$4$(not in LMFDB)
4.5.ab_l_b_ce$4$(not in LMFDB)
4.5.b_f_ah_i$4$(not in LMFDB)
4.5.b_l_ab_ce$4$(not in LMFDB)
4.5.d_j_p_bg$4$(not in LMFDB)
4.5.d_p_bh_ea$4$(not in LMFDB)
4.5.f_r_bx_ey$4$(not in LMFDB)
4.5.h_bj_ej_lk$4$(not in LMFDB)
4.5.j_bt_fx_pc$4$(not in LMFDB)
4.5.ah_bg_aea_kj$6$(not in LMFDB)
4.5.ab_i_ai_bd$6$(not in LMFDB)
4.5.h_bg_ea_kj$6$(not in LMFDB)
4.5.ad_b_j_aw$8$(not in LMFDB)
4.5.ad_r_abn_es$8$(not in LMFDB)
4.5.d_b_aj_aw$8$(not in LMFDB)
4.5.d_r_bn_es$8$(not in LMFDB)
4.5.af_o_abo_dx$12$(not in LMFDB)
4.5.ab_c_q_at$12$(not in LMFDB)
4.5.b_c_aq_at$12$(not in LMFDB)
4.5.f_o_bo_dx$12$(not in LMFDB)