Properties

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

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x )^{2}( 1 - 46 x + 625 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.128188433698$
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 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
$A(\F_{q^r})$ 334080 151763189760 59594309672567040 23282949931463587921920 9094945953144959085213446400 3552713671475126028465738890772480 1387778780757989861339566093792094972160 542101086242729415562632792537803191159357440 211758236813562392174376399740850992152295496280320 82718061255302130586102535275755088212492586679753932800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 530 388510 244098290 152587140670 95367420477650 59604644652491230 37252902983989503410 23283064365385983576190 14551915228365979578311570 9094947017729212351140651550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.aby $\times$ 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.ae_abok$2$(not in LMFDB)
2.625.e_abok$2$(not in LMFDB)
2.625.ds_fgo$2$(not in LMFDB)
2.625.av_dw$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.ae_abok$2$(not in LMFDB)
2.625.e_abok$2$(not in LMFDB)
2.625.ds_fgo$2$(not in LMFDB)
2.625.av_dw$3$(not in LMFDB)
2.625.act_doi$6$(not in LMFDB)
2.625.v_dw$6$(not in LMFDB)
2.625.ct_doi$6$(not in LMFDB)