# Properties

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

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## Invariants

 Base field: $\F_{7^{2}}$ Dimension: $2$ L-polynomial: $( 1 - 7 x )^{2}( 1 - 11 x + 49 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.212295615010$ 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 $A(\F_{q^r})$ 1404 5481216 13794266304 33229872000000 79792089206639004 191580099210202300416 459985468327682400887004 1104427067459638133952000000 2651730588152789271029629850304 6366805674073169973346283287862016

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 25 2281 117250 5764273 282474625 13841205406 678221497825 33232912311073 1628413439654050 79792265209337881

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
 The isogeny class factors as 1.49.ao $\times$ 1.49.al 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.al : $$\Q(\sqrt{-3})$$.
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.ad_ace $2$ (not in LMFDB) 2.49.d_ace $2$ (not in LMFDB) 2.49.z_js $2$ (not in LMFDB) 2.49.aq_ew $3$ (not in LMFDB) 2.49.ab_adg $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.49.ad_ace $2$ (not in LMFDB) 2.49.d_ace $2$ (not in LMFDB) 2.49.z_js $2$ (not in LMFDB) 2.49.aq_ew $3$ (not in LMFDB) 2.49.ab_adg $3$ (not in LMFDB) 2.49.al_du $4$ (not in LMFDB) 2.49.l_du $4$ (not in LMFDB) 2.49.abb_ku $6$ (not in LMFDB) 2.49.am_cs $6$ (not in LMFDB) 2.49.b_adg $6$ (not in LMFDB) 2.49.m_cs $6$ (not in LMFDB) 2.49.q_ew $6$ (not in LMFDB) 2.49.bb_ku $6$ (not in LMFDB) 2.49.an_du $12$ (not in LMFDB) 2.49.ac_du $12$ (not in LMFDB) 2.49.c_du $12$ (not in LMFDB) 2.49.n_du $12$ (not in LMFDB)