Properties

Label 2.625.ado_ezd
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:  $( 1 - 49 x + 625 x^{2} )( 1 - 43 x + 625 x^{2} )$
Frobenius angles:  $\pm0.0637685608585$, $\pm0.170463428383$
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
$A(\F_{q^r})$ 336391 151905765825 59598625703581888 23283045886763785505625 9094947679704005460682452991 3552713697338350150689668151705600 1387778781078692401589796220056514049263 542101086245928974960116970885078365534475625 211758236813588739509881050636883247271221964865216 82718061255302454695965997198025275049032278585159616625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388876 244115970 152587769524 95367438581934 59604645086404126 37252902992598296670 23283064365523403605924 14551915228367790153420834 9094947017729247987397006876

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.abx $\times$ 1.625.abr 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.ag_abgz$2$(not in LMFDB)
2.625.g_abgz$2$(not in LMFDB)
2.625.do_ezd$2$(not in LMFDB)