Properties

Label 2.49.av_hs
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:  $1 - 21 x + 200 x^{2} - 1029 x^{3} + 2401 x^{4}$
Frobenius angles:  $\pm0.0956797089624$, $\pm0.316591506724$
Angle rank:  $2$ (numerical)
Number field:  4.0.40293.1
Galois group:  $D_{4}$
Jacobians:  16

This isogeny class is simple and geometrically 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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1552 5667904 13870882048 33241508796672 79789176320595472 191578886515963285504 459986235155575799230096 1104427997328665986302256128 2651731081945235071066430622976 6366805844665530819892086118878784

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 29 2361 117902 5766289 282464309 13841117790 678222628469 33232940291425 1628413742889326 79792267347293961

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.40293.1.
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.v_hs$2$(not in LMFDB)