Properties

Label 2.625.ado_ezi
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:  $( 1 - 48 x + 625 x^{2} )( 1 - 44 x + 625 x^{2} )$
Frobenius angles:  $\pm0.0903344706017$, $\pm0.157542425424$
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
$A(\F_{q^r})$ 336396 151909705680 59598962701730028 23283061464588750028800 9094948199552013841188153516 3552713711304593534384790445644240 1387778781396351426561625058962084201548 542101086252185722669976788052334631924531200 211758236813695820277483083910747035232560438447436 82718061255304015637765950724351496568052393796752552400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388886 244117350 152587871614 95367444032934 59604645320718806 37252903001125391190 23283064365792128873854 14551915228375148687738934 9094947017729419614762939926

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.abw $\times$ 1.625.abs 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_abhe$2$(not in LMFDB)
2.625.e_abhe$2$(not in LMFDB)
2.625.do_ezi$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.ae_abhe$2$(not in LMFDB)
2.625.e_abhe$2$(not in LMFDB)
2.625.do_ezi$2$(not in LMFDB)
2.625.acg_ctu$4$(not in LMFDB)
2.625.abe_yk$4$(not in LMFDB)
2.625.be_yk$4$(not in LMFDB)
2.625.cg_ctu$4$(not in LMFDB)