Properties

Label 4.5.al_cj_aio_wi
Base Field $\F_{5}$
Dimension $4$
Ordinary No
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 28 x^{2} - 75 x^{3} + 140 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.117658111351$, $\pm0.147583617650$, $\pm0.327130732663$, $\pm0.462990021908$
Angle rank:  $4$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 74 407740 280608296 151261754240 95397532510834 60862715950229440 37778120833792126274 23401661133629045399040 14585586808425220946415848 9106486304538120500625312700

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 27 142 619 3125 15954 79221 392611 1957642 9778007

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae $\times$ 3.5.ah_bc_acx 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_f_c_au$2$(not in LMFDB)
4.5.d_f_ac_au$2$(not in LMFDB)
4.5.l_cj_io_wi$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ad_f_c_au$2$(not in LMFDB)
4.5.d_f_ac_au$2$(not in LMFDB)
4.5.l_cj_io_wi$2$(not in LMFDB)
4.5.aj_bv_agk_qo$4$(not in LMFDB)
4.5.af_t_acc_fa$4$(not in LMFDB)
4.5.f_t_cc_fa$4$(not in LMFDB)
4.5.j_bv_gk_qo$4$(not in LMFDB)