Properties

Label 4.5.al_cj_ain_we
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 11 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.300933478836$, $\pm0.472779926746$
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
$A(\F_{q^r})$ 76 418000 288734716 157943808000 98651495818816 61458772341538000 37682909808445408156 23329649713854578688000 14571525193312758813944236 9105474366436704604480000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 27 145 647 3230 16107 79025 391407 1955755 9776922

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ad_l 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_n_abj_ds$2$(not in LMFDB)
4.5.ad_f_d_aq$2$(not in LMFDB)
4.5.d_f_ad_aq$2$(not in LMFDB)
4.5.f_n_bj_ds$2$(not in LMFDB)
4.5.l_cj_in_we$2$(not in LMFDB)
4.5.b_k_q_bz$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.af_n_abj_ds$2$(not in LMFDB)
4.5.ad_f_d_aq$2$(not in LMFDB)
4.5.d_f_ad_aq$2$(not in LMFDB)
4.5.f_n_bj_ds$2$(not in LMFDB)
4.5.l_cj_in_we$2$(not in LMFDB)
4.5.b_k_q_bz$3$(not in LMFDB)
4.5.aj_bv_agj_qm$4$(not in LMFDB)
4.5.ah_bl_aer_mm$4$(not in LMFDB)
4.5.af_t_acb_fc$4$(not in LMFDB)
4.5.ad_l_abb_cq$4$(not in LMFDB)
4.5.ad_r_abh_em$4$(not in LMFDB)
4.5.ab_h_l_m$4$(not in LMFDB)
4.5.ab_n_ah_dg$4$(not in LMFDB)
4.5.b_h_al_m$4$(not in LMFDB)
4.5.b_n_h_dg$4$(not in LMFDB)
4.5.d_l_bb_cq$4$(not in LMFDB)
4.5.d_r_bh_em$4$(not in LMFDB)
4.5.f_t_cb_fc$4$(not in LMFDB)
4.5.h_bl_er_mm$4$(not in LMFDB)
4.5.j_bv_gj_qm$4$(not in LMFDB)
4.5.ah_bi_aei_lf$6$(not in LMFDB)
4.5.ab_k_aq_bz$6$(not in LMFDB)
4.5.h_bi_ei_lf$6$(not in LMFDB)
4.5.ad_d_j_abm$8$(not in LMFDB)
4.5.ad_t_abn_fi$8$(not in LMFDB)
4.5.d_d_aj_abm$8$(not in LMFDB)
4.5.d_t_bn_fi$8$(not in LMFDB)
4.5.af_q_abs_dv$12$(not in LMFDB)
4.5.ab_e_u_av$12$(not in LMFDB)
4.5.b_e_au_av$12$(not in LMFDB)
4.5.f_q_bs_dv$12$(not in LMFDB)