Properties

Label 4.5.al_ch_ahz_um
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 26 x^{2} - 68 x^{3} + 130 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.0605820805461$, $\pm0.147583617650$, $\pm0.287119770935$, $\pm0.511693182811$
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
$A(\F_{q^r})$ 64 340480 236305216 145954242560 97099396455424 60419585726456320 37120951071118044992 23226689054721740636160 14577807273559580351296576 9108081009512793909929574400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 23 121 599 3180 15839 77849 389679 1956595 9779718

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae $\times$ 3.5.ah_ba_acq 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_d_b_am$2$(not in LMFDB)
4.5.d_d_ab_am$2$(not in LMFDB)
4.5.l_ch_hz_um$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ad_d_b_am$2$(not in LMFDB)
4.5.d_d_ab_am$2$(not in LMFDB)
4.5.l_ch_hz_um$2$(not in LMFDB)
4.5.aj_bt_afz_pg$4$(not in LMFDB)
4.5.af_r_abz_eu$4$(not in LMFDB)
4.5.f_r_bz_eu$4$(not in LMFDB)
4.5.j_bt_fz_pg$4$(not in LMFDB)