Properties

Label 3.5.al_cd_agc
Base field $\F_{5}$
Dimension $3$
$p$-rank $3$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{5}$
Dimension:  $3$
L-polynomial:  $( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$
  $1 - 11 x + 55 x^{2} - 158 x^{3} + 275 x^{4} - 275 x^{5} + 125 x^{6}$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.265942140215$
Angle rank:  $2$ (numerical)
Jacobians:  $0$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $12$ $10800$ $2143296$ $276480000$ $32634675132$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-5$ $15$ $136$ $703$ $3335$ $16020$ $78731$ $391583$ $1955080$ $9769575$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{5}$.

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 1.5.ad and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

TwistExtension degreeCommon base change
3.5.af_h_ac$2$3.25.al_dv_atu
3.5.ad_ab_s$2$3.25.al_dv_atu
3.5.d_ab_as$2$3.25.al_dv_atu
3.5.f_h_c$2$3.25.al_dv_atu
3.5.l_cd_gc$2$3.25.al_dv_atu
3.5.b_e_h$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
3.5.af_h_ac$2$3.25.al_dv_atu
3.5.ad_ab_s$2$3.25.al_dv_atu
3.5.d_ab_as$2$3.25.al_dv_atu
3.5.f_h_c$2$3.25.al_dv_atu
3.5.l_cd_gc$2$3.25.al_dv_atu
3.5.b_e_h$3$(not in LMFDB)
3.5.aj_bp_aek$4$(not in LMFDB)
3.5.ah_bf_ade$4$(not in LMFDB)
3.5.af_n_aba$4$(not in LMFDB)
3.5.ad_f_ag$4$(not in LMFDB)
3.5.ad_l_as$4$(not in LMFDB)
3.5.ab_b_o$4$(not in LMFDB)
3.5.ab_h_c$4$(not in LMFDB)
3.5.b_b_ao$4$(not in LMFDB)
3.5.b_h_ac$4$(not in LMFDB)
3.5.d_f_g$4$(not in LMFDB)
3.5.d_l_s$4$(not in LMFDB)
3.5.f_n_ba$4$(not in LMFDB)
3.5.h_bf_de$4$(not in LMFDB)
3.5.j_bp_ek$4$(not in LMFDB)
3.5.ah_bc_acv$6$(not in LMFDB)
3.5.ab_e_ah$6$(not in LMFDB)
3.5.h_bc_cv$6$(not in LMFDB)
3.5.ad_ad_y$8$(not in LMFDB)
3.5.ad_n_ay$8$(not in LMFDB)
3.5.d_ad_ay$8$(not in LMFDB)
3.5.d_n_y$8$(not in LMFDB)
3.5.af_k_ar$12$(not in LMFDB)
3.5.ab_ac_x$12$(not in LMFDB)
3.5.b_ac_ax$12$(not in LMFDB)
3.5.f_k_r$12$(not in LMFDB)