# Properties

 Label 3.7.ak_ca_agm Base Field $\F_{7}$ Dimension $3$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{7}$ Dimension: $3$ L-polynomial: $( 1 - 4 x + 7 x^{2} )( 1 - 6 x + 21 x^{2} - 42 x^{3} + 49 x^{4} )$ Frobenius angles: $\pm0.185925252552$, $\pm0.227185525829$, $\pm0.403118263531$ Angle rank: $3$ (numerical)

This isogeny class is not simple.

## Newton polygon

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

## 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 $A(\F_{q^r})$ 92 131376 47653424 14599026624 4812245621132 1638894270843648 559965643297751972 191574865005304225536 65673071043379567114256 22532485782908781704677296

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 54 400 2530 17038 118404 825634 5764610 40329472 282389334

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The isogeny class factors as 1.7.ae $\times$ 2.7.ag_v 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 $\F_{7}$.

## 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 3.7.ac_e_a $2$ (not in LMFDB) 3.7.c_e_a $2$ (not in LMFDB) 3.7.k_ca_gm $2$ (not in LMFDB) 3.7.ah_bi_aeb $3$ (not in LMFDB) 3.7.ab_ac_v $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.ac_e_a $2$ (not in LMFDB) 3.7.c_e_a $2$ (not in LMFDB) 3.7.k_ca_gm $2$ (not in LMFDB) 3.7.ah_bi_aeb $3$ (not in LMFDB) 3.7.ab_ac_v $3$ (not in LMFDB) 3.7.al_cg_ahh $6$ (not in LMFDB) 3.7.af_w_acl $6$ (not in LMFDB) 3.7.b_ac_av $6$ (not in LMFDB) 3.7.f_w_cl $6$ (not in LMFDB) 3.7.h_bi_eb $6$ (not in LMFDB) 3.7.l_cg_hh $6$ (not in LMFDB)