Properties

Label 2.49.av_ht
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:  $1 - 21 x + 201 x^{2} - 1029 x^{3} + 2401 x^{4}$
Frobenius angles:  $\pm0.108632527214$, $\pm0.311694440288$
Angle rank:  $2$ (numerical)
Number field:  4.0.2493565.2
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1553 5673109 13878342569 33247056735685 79791816004162448 191579736650474524261 459986412220037518481273 1104428017685352103172224965 2651731084546200842487893261489 6366805846410565115353479776456704

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 29 2363 117965 5767251 282473654 13841179211 678222889541 33232940903971 1628413744486565 79792267369163678

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.2493565.2.
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_ht$2$(not in LMFDB)