Properties

Label 2.625.adt_fim
Base Field $\F_{5^{4}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x )^{2}( 1 - 47 x + 625 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.110824686604$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 333504 151726977792 59593183840124928 23282924033616449080320 9094945470272953332640023744 3552713664112294973059395017244672 1387778780673206929525437879489281988288 542101086242306040340621284561503887086858240 211758236813575081126396704350644278179168450985984 82718061255302668143228043611353054683575428530146269952

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 529 388417 244093678 152586970945 95367415414369 59604644528963422 37252902981713628913 23283064365367799748865 14551915228366851556454734 9094947017729271456171660577

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.aby $\times$ 1.625.abv 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.ad_abqi$2$(not in LMFDB)
2.625.d_abqi$2$(not in LMFDB)
2.625.dt_fim$2$(not in LMFDB)
2.625.aw_cx$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.ad_abqi$2$(not in LMFDB)
2.625.d_abqi$2$(not in LMFDB)
2.625.dt_fim$2$(not in LMFDB)
2.625.aw_cx$3$(not in LMFDB)
2.625.acu_dph$6$(not in LMFDB)
2.625.w_cx$6$(not in LMFDB)
2.625.cu_dph$6$(not in LMFDB)