Properties

Label 4.5.am_ct_akj_bbk
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 8 x + 34 x^{2} - 93 x^{3} + 170 x^{4} - 200 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.101435245160$, $\pm0.147583617650$, $\pm0.306436956418$, $\pm0.413672014132$
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
$A(\F_{q^r})$ 58 365980 289808194 156569171840 94128265961138 59931647673780220 37696051384494647986 23438944479771914595840 14584359406912159084235392 9101614396243900551995791900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 24 147 640 3084 15711 79052 393232 1957476 9772784

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae $\times$ 3.5.ai_bi_adp 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.ae_h_d_abg$2$(not in LMFDB)
4.5.e_h_ad_abg$2$(not in LMFDB)
4.5.m_ct_kj_bbk$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ae_h_d_abg$2$(not in LMFDB)
4.5.e_h_ad_abg$2$(not in LMFDB)
4.5.m_ct_kj_bbk$2$(not in LMFDB)
4.5.ak_cd_aht_ug$4$(not in LMFDB)
4.5.ag_x_acn_fy$4$(not in LMFDB)
4.5.g_x_cn_fy$4$(not in LMFDB)
4.5.k_cd_ht_ug$4$(not in LMFDB)