Properties

Label 4.5.am_cu_akq_bcf
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:  $( 1 - 3 x + 5 x^{2} )^{2}( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.265942140215$, $\pm0.265942140215$, $\pm0.384619558242$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 63 403137 321076224 165538130625 93198017193183 57988092160180224 36809102946159389727 23197544263794809120625 14538268526711324681567232 9095618997158239136593946097

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 26 162 678 3054 15194 77190 389190 1951290 9766346

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ad 2 $\times$ 2.5.ag_r and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{5}$
The base change of $A$ to $\F_{5^{6}}$ is 1.15625.afm 2 $\times$ 1.15625.acw 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5^{6}}$.
Remainder of endomorphism lattice by field

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.ag_s_abk_cp$2$(not in LMFDB)
4.5.a_a_am_n$2$(not in LMFDB)
4.5.a_a_m_n$2$(not in LMFDB)
4.5.g_s_bk_cp$2$(not in LMFDB)
4.5.m_cu_kq_bcf$2$(not in LMFDB)
4.5.ag_v_abq_dk$3$(not in LMFDB)
4.5.ad_d_m_ack$3$(not in LMFDB)
4.5.d_g_v_cg$3$(not in LMFDB)
4.5.j_bn_eq_lm$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ag_s_abk_cp$2$(not in LMFDB)
4.5.a_a_am_n$2$(not in LMFDB)
4.5.a_a_m_n$2$(not in LMFDB)
4.5.g_s_bk_cp$2$(not in LMFDB)
4.5.m_cu_kq_bcf$2$(not in LMFDB)
4.5.ag_v_abq_dk$3$(not in LMFDB)
4.5.ad_d_m_ack$3$(not in LMFDB)
4.5.d_g_v_cg$3$(not in LMFDB)
4.5.j_bn_eq_lm$3$(not in LMFDB)
4.5.ag_q_ay_bh$4$(not in LMFDB)
4.5.g_q_y_bh$4$(not in LMFDB)
4.5.aj_bn_aeq_lm$6$(not in LMFDB)
4.5.ad_g_av_cg$6$(not in LMFDB)
4.5.a_d_a_ca$6$(not in LMFDB)
4.5.d_d_am_ack$6$(not in LMFDB)
4.5.g_v_bq_dk$6$(not in LMFDB)
4.5.ag_r_as_m$12$(not in LMFDB)
4.5.ad_c_aj_bq$12$(not in LMFDB)
4.5.a_ad_a_ca$12$(not in LMFDB)
4.5.a_ab_a_bw$12$(not in LMFDB)
4.5.a_b_a_bw$12$(not in LMFDB)
4.5.d_c_j_bq$12$(not in LMFDB)
4.5.g_r_s_m$12$(not in LMFDB)
4.5.ak_bz_ags_ra$24$(not in LMFDB)
4.5.ah_y_acx_hu$24$(not in LMFDB)
4.5.ae_h_aq_bq$24$(not in LMFDB)
4.5.ae_j_ay_cg$24$(not in LMFDB)
4.5.ac_d_s_abm$24$(not in LMFDB)
4.5.ab_a_d_abm$24$(not in LMFDB)
4.5.b_a_ad_abm$24$(not in LMFDB)
4.5.c_d_as_abm$24$(not in LMFDB)
4.5.e_h_q_bq$24$(not in LMFDB)
4.5.e_j_y_cg$24$(not in LMFDB)
4.5.h_y_cx_hu$24$(not in LMFDB)
4.5.k_bz_gs_ra$24$(not in LMFDB)