Properties

Label 2.49.av_hx
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:  $1 - 21 x + 205 x^{2} - 1029 x^{3} + 2401 x^{4}$
Frobenius angles:  $\pm0.158364966887$, $\pm0.286633143828$
Angle rank:  $2$ (numerical)
Number field:  4.0.100893.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1557 5693949 13908196773 33269020875477 79801781945790672 191582374013198141229 459986472437217205966461 1104427698486458883151204773 2651730908989166605230759786141 6366805790360631556320761406787584

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 29 2371 118217 5771059 282508934 13841369755 678222978329 33232931299075 1628413636677941 79792266666715486

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.100893.1.
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_hx$2$(not in LMFDB)