Properties

Label 2.625.adq_fda
Base field $\F_{5^{4}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 48 x + 625 x^{2} )( 1 - 46 x + 625 x^{2} )$
  $1 - 94 x + 3458 x^{2} - 58750 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0903344706017$, $\pm0.128188433698$
Angle rank:  $2$ (numerical)

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $335240$ $151839582720$ $59596911605204360$ $23283018837727720243200$ $9094947534077905730831256200$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $532$ $388706$ $244108948$ $152587592254$ $95367437054932$ $59604645205023266$ $37252903001126802388$ $23283064365887655467134$ $14551915228379959368778132$ $9094947017729585094940269026$

Jacobians and polarizations

This isogeny class contains a Jacobian, and hence is principally polarizable.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{5^{4}}$.

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.abw $\times$ 1.625.abu 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
2.625.ac_abkw$2$(not in LMFDB)
2.625.c_abkw$2$(not in LMFDB)
2.625.dq_fda$2$(not in LMFDB)

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

TwistExtension degreeCommon base change
2.625.ac_abkw$2$(not in LMFDB)
2.625.c_abkw$2$(not in LMFDB)
2.625.dq_fda$2$(not in LMFDB)
2.625.aci_cuw$4$(not in LMFDB)
2.625.abg_xi$4$(not in LMFDB)
2.625.bg_xi$4$(not in LMFDB)
2.625.ci_cuw$4$(not in LMFDB)