Properties

Label 4.5.al_ci_aik_vz
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:  $( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.0878807261908$, $\pm0.384619558242$, $\pm0.450170915301$
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
$A(\F_{q^r})$ 63 343413 233700012 128379112029 87029776331568 59175145450918224 37623882916287319491 23355899060757619121325 14547860733152098732413852 9095463641330437680639848448

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 25 121 517 2840 15511 78899 391845 1952581 9766180

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 2.5.ag_r $\times$ 2.5.af_n 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 $\times$ 2.15625.gn_byxl. 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.ab_a_c_abd$2$(not in LMFDB)
4.5.b_a_ac_abd$2$(not in LMFDB)
4.5.l_ci_ik_vz$2$(not in LMFDB)
4.5.af_p_abj_cy$3$(not in LMFDB)
4.5.b_a_ac_abd$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ab_a_c_abd$2$(not in LMFDB)
4.5.b_a_ac_abd$2$(not in LMFDB)
4.5.l_ci_ik_vz$2$(not in LMFDB)
4.5.af_p_abj_cy$3$(not in LMFDB)
4.5.b_a_ac_abd$3$(not in LMFDB)
4.5.f_p_bj_cy$6$(not in LMFDB)
4.5.af_l_ap_y$12$(not in LMFDB)
4.5.f_l_p_y$12$(not in LMFDB)
4.5.aj_bp_afh_nq$24$(not in LMFDB)
4.5.ab_b_h_abu$24$(not in LMFDB)
4.5.b_b_ah_abu$24$(not in LMFDB)
4.5.j_bp_fh_nq$24$(not in LMFDB)