Properties

Label 2.49.av_hy
Base Field $\F_{7^{2}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{7^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 12 x + 49 x^{2} )( 1 - 9 x + 49 x^{2} )$
Frobenius angles:  $\pm0.172237328522$, $\pm0.277748883973$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 the Jacobians of 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1558 5699164 13915663384 33274455030720 79804125241799398 191582843392417555456 459986328472585187815798 1104427523945993268222017280 2651730825137491182999203339224 6366805766422581908047864110941404

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 29 2373 118280 5772001 282517229 13841403666 678222766061 33232926047041 1628413585185080 79792266366710853

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The isogeny class factors as 1.49.am $\times$ 1.49.aj 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 $\F_{7^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.49.ad_ak$2$(not in LMFDB)
2.49.d_ak$2$(not in LMFDB)
2.49.v_hy$2$(not in LMFDB)