Properties

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

Learn more about

Invariants

Base field:  $\F_{7^{2}}$
Dimension:  $2$
L-polynomial:  $1 - 21 x + 198 x^{2} - 1029 x^{3} + 2401 x^{4}$
Frobenius angles:  $\pm0.0658419374597$, $\pm0.325440921041$
Angle rank:  $2$ (numerical)
Number field:  4.0.1983580.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1550 5657500 13855964600 33230344600000 79783719103742750 191576956129185280000 459985682426761289771150 1104427828823344830741600000 2651731011712694383487262270200 6366805813860283284355398718937500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 29 2357 117776 5764353 282444989 13840978322 678221813501 33232935220993 1628413699759904 79792266961225877

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.1983580.1.
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_hq$2$(not in LMFDB)