Properties

Label 4.5.al_ci_aig_vi
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 71 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.111887224672$, $\pm0.147583617650$, $\pm0.292466693033$, $\pm0.493752400559$
Angle rank:  $4$ (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
$A(\F_{q^r})$ 70 378700 261994390 152413116800 98529792816350 61266667616927500 37498238315499418240 23306761596246922483200 14588230530131581136310070 9112190427730262575095767500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 25 133 625 3225 16057 78640 391025 1957993 9784125

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae $\times$ 3.5.ah_bb_act 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.ad_e_c_ao$2$(not in LMFDB)
4.5.d_e_ac_ao$2$(not in LMFDB)
4.5.l_ci_ig_vi$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ad_e_c_ao$2$(not in LMFDB)
4.5.d_e_ac_ao$2$(not in LMFDB)
4.5.l_ci_ig_vi$2$(not in LMFDB)
4.5.aj_bu_age_pw$4$(not in LMFDB)
4.5.af_s_aca_ey$4$(not in LMFDB)
4.5.f_s_ca_ey$4$(not in LMFDB)
4.5.j_bu_ge_pw$4$(not in LMFDB)