Properties

Label 4.5.al_ce_aha_ri
Base field $\F_{5}$
Dimension $4$
$p$-rank $3$
Ordinary no
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 23 x^{2} - 55 x^{3} + 115 x^{4} - 175 x^{5} + 125 x^{6} )$
  $1 - 11 x + 56 x^{2} - 182 x^{3} + 450 x^{4} - 910 x^{5} + 1400 x^{6} - 1375 x^{7} + 625 x^{8}$
Frobenius angles:  $\pm0.0441569735346$, $\pm0.147583617650$, $\pm0.210407616474$, $\pm0.568817170463$
Angle rank:  $4$ (numerical)

This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $54$ $270540$ $195495606$ $148498323840$ $101585855236734$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-5$ $17$ $97$ $609$ $3325$ $15929$ $77856$ $390641$ $1953637$ $9755557$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{5}$.

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae $\times$ 3.5.ah_x_acd and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

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_a_c_k$2$(not in LMFDB)
4.5.d_a_ac_k$2$(not in LMFDB)
4.5.l_ce_ha_ri$2$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
4.5.ad_a_c_k$2$(not in LMFDB)
4.5.d_a_ac_k$2$(not in LMFDB)
4.5.l_ce_ha_ri$2$(not in LMFDB)
4.5.aj_bq_afg_nc$4$(not in LMFDB)
4.5.af_o_abs_eq$4$(not in LMFDB)
4.5.f_o_bs_eq$4$(not in LMFDB)
4.5.j_bq_fg_nc$4$(not in LMFDB)