Properties

Label 2.625.adq_fda
Base Field $\F_{5^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

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

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

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

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 335240 151839582720 59596911605204360 23283018837727720243200 9094947534077905730831256200 3552713704408601963154263877941760 1387778781396403997783818105108054549640 542101086254409874489939940370153755954380800 211758236813765824900156235508613898228490788065160 82718061255305520671211243365320087123033332751363545600

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

Decomposition and endomorphism algebra

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

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)