# Properties

 Label 2.49.ax_iq Base Field $\F_{7^{2}}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{7^{2}}$ Dimension: $2$ L-polynomial: $( 1 - 7 x )^{2}( 1 - 9 x + 49 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.277748883973$ Angle rank: $1$ (numerical) Jacobians: 0

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $1$ Slopes: $[0, 1/2, 1/2, 1]$

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1476 5573376 13830291216 33231254400000 79786022925180996 191576347731494240256 459984319459923999365316 1104426997383375729446400000 2651730714327564184694300053776 6366805750336303584917901627446016

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 27 2321 117558 5764513 282453147 13840934366 678219803883 33232910202433 1628413517137302 79792266165108881

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
 The isogeny class factors as 1.49.ao $\times$ 1.49.aj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.49.ao : the quaternion algebra over $$\Q$$ ramified at $7$ and $\infty$. 1.49.aj : $$\Q(\sqrt{-115})$$.
All geometric endomorphisms are defined over $\F_{7^{2}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.49.af_abc $2$ (not in LMFDB) 2.49.f_abc $2$ (not in LMFDB) 2.49.x_iq $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.49.af_abc $2$ (not in LMFDB) 2.49.f_abc $2$ (not in LMFDB) 2.49.x_iq $2$ (not in LMFDB) 2.49.aj_du $4$ (not in LMFDB) 2.49.j_du $4$ (not in LMFDB)