# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 60 306000 219018060 158238720000 106436408884800 62860964749362000 37723253866119092940 23415883237073387520000 14587645433752853450921340 9090152629464840455232000000

 $r$ 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: 1.5.ae 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-1})$$$)$ 2.5.ad_h : 4.0.48069.2.
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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)