# Properties

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

## Invariants

 Base field: $\F_{7^{2}}$ Dimension: $2$ L-polynomial: $( 1 - 11 x + 49 x^{2} )( 1 - 10 x + 49 x^{2} )$ Frobenius angles: $\pm0.212295615010$, $\pm0.246751714429$ Angle rank: $2$ (numerical) Jacobians: 0

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 is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1560 5709600 13930600320 33285255120000 79808634019147800 191583555362580326400 459985853908391853109080 1104427068735782409433920000 2651730618514761281441921927040 6366805714559645619652482262740000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 29 2377 118406 5773873 282533189 13841455102 678222066341 33232912349473 1628413458299174 79792265716736377

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
 The isogeny class factors as 1.49.al $\times$ 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.49.ab_am $2$ (not in LMFDB) 2.49.b_am $2$ (not in LMFDB) 2.49.v_ia $2$ (not in LMFDB) 2.49.am_eo $3$ (not in LMFDB) 2.49.d_abg $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.49.ab_am $2$ (not in LMFDB) 2.49.b_am $2$ (not in LMFDB) 2.49.v_ia $2$ (not in LMFDB) 2.49.am_eo $3$ (not in LMFDB) 2.49.d_abg $3$ (not in LMFDB) 2.49.ax_iu $6$ (not in LMFDB) 2.49.ai_da $6$ (not in LMFDB) 2.49.ad_abg $6$ (not in LMFDB) 2.49.i_da $6$ (not in LMFDB) 2.49.m_eo $6$ (not in LMFDB) 2.49.x_iu $6$ (not in LMFDB)