Properties

Label 2.49.aw_ik
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:  $( 1 - 12 x + 49 x^{2} )( 1 - 10 x + 49 x^{2} )$
Frobenius angles:  $\pm0.172237328522$, $\pm0.246751714429$
Angle rank:  $2$ (numerical)
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1520 5654400 13901070320 33276098764800 79807921836143600 191584669587359126400 459986696959355624971760 1104427435757914105705267200 2651730724182108519258040237040 6366805727324421151255906048560000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 28 2354 118156 5772286 282530668 13841535602 678223309372 33232923393406 1628413523188924 79792265876711474

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The isogeny class factors as 1.49.am $\times$ 1.49.ak 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.ac_aw$2$(not in LMFDB)
2.49.c_aw$2$(not in LMFDB)
2.49.w_ik$2$(not in LMFDB)