Properties

Label 4.5.al_cf_ahh_se
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 7 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.177952114464$, $\pm0.556618995437$
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
$A(\F_{q^r})$ 60 306000 219018060 158238720000 106436408884800 62860964749362000 37723253866119092940 23415883237073387520000 14587645433752853450921340 9090152629464840455232000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 19 109 647 3470 16459 79109 392847 1957915 9760474

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ad_h 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_j_ad_ai$2$(not in LMFDB)
4.5.ad_b_d_i$2$(not in LMFDB)
4.5.d_b_ad_i$2$(not in LMFDB)
4.5.f_j_d_ai$2$(not in LMFDB)
4.5.l_cf_hh_se$2$(not in LMFDB)
4.5.b_g_a_h$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.af_j_ad_ai$2$(not in LMFDB)
4.5.ad_b_d_i$2$(not in LMFDB)
4.5.d_b_ad_i$2$(not in LMFDB)
4.5.f_j_d_ai$2$(not in LMFDB)
4.5.l_cf_hh_se$2$(not in LMFDB)
4.5.b_g_a_h$3$(not in LMFDB)
4.5.aj_br_afl_ns$4$(not in LMFDB)
4.5.ah_bh_aeb_ki$4$(not in LMFDB)
4.5.af_p_abt_eu$4$(not in LMFDB)
4.5.ad_h_ad_ae$4$(not in LMFDB)
4.5.ad_n_abh_do$4$(not in LMFDB)
4.5.ab_d_d_e$4$(not in LMFDB)
4.5.ab_j_j_bc$4$(not in LMFDB)
4.5.b_d_ad_e$4$(not in LMFDB)
4.5.b_j_aj_bc$4$(not in LMFDB)
4.5.d_h_d_ae$4$(not in LMFDB)
4.5.d_n_bh_do$4$(not in LMFDB)
4.5.f_p_bt_eu$4$(not in LMFDB)
4.5.h_bh_eb_ki$4$(not in LMFDB)
4.5.j_br_fl_ns$4$(not in LMFDB)
4.5.ah_be_ads_jn$6$(not in LMFDB)
4.5.ab_g_a_h$6$(not in LMFDB)
4.5.h_be_ds_jn$6$(not in LMFDB)
4.5.ad_ab_j_ag$8$(not in LMFDB)
4.5.ad_p_abn_ec$8$(not in LMFDB)
4.5.d_ab_aj_ag$8$(not in LMFDB)
4.5.d_p_bn_ec$8$(not in LMFDB)
4.5.af_m_abk_dz$12$(not in LMFDB)
4.5.ab_a_m_ar$12$(not in LMFDB)
4.5.b_a_am_ar$12$(not in LMFDB)
4.5.f_m_bk_dz$12$(not in LMFDB)