Properties

Label 2.625.adp_fba
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:  $( 1 - 49 x + 625 x^{2} )( 1 - 44 x + 625 x^{2} )$
Frobenius angles:  $\pm0.0637685608585$, $\pm0.157542425424$
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
$A(\F_{q^r})$ 335814 151871881500 59597697578914584 23283028828261319256000 9094947477498274450749792054 3552713696983468149860835257856000 1387778781136443116268666121080408643974 542101086247837190884400326435064803815264000 211758236813628960063579859486460063298823237552344 82718061255303087453497691509313846358017174372166537500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 533 388789 244112168 152587657729 95367436461653 59604645080450194 37252902994148530613 23283064365605360855809 14551915228370554088825048 9094947017729317559823372949

Decomposition and endomorphism algebra

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