Properties

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

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $( 1 - 5 x + 7 x^{2} )( 1 - 6 x + 21 x^{2} - 42 x^{3} + 49 x^{4} )$
Frobenius angles:  $\pm0.106147807505$, $\pm0.185925252552$, $\pm0.403118263531$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 69 106743 42416784 13914697251 4752671352999 1638894270843648 561165128410352073 191851115047590091275 65714030199587768598576 22536879029879021279109183

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 45 360 2413 16827 118404 827397 5772917 40354632 282444405

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.af $\times$ 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.
TwistExtension DegreeCommon base change
3.7.ab_ac_v$2$(not in LMFDB)
3.7.b_ac_av$2$(not in LMFDB)
3.7.l_cg_hh$2$(not in LMFDB)
3.7.af_w_acl$3$(not in LMFDB)
3.7.ac_e_a$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.ab_ac_v$2$(not in LMFDB)
3.7.b_ac_av$2$(not in LMFDB)
3.7.l_cg_hh$2$(not in LMFDB)
3.7.af_w_acl$3$(not in LMFDB)
3.7.ac_e_a$3$(not in LMFDB)
3.7.ak_ca_agm$6$(not in LMFDB)
3.7.ah_bi_aeb$6$(not in LMFDB)
3.7.c_e_a$6$(not in LMFDB)
3.7.f_w_cl$6$(not in LMFDB)
3.7.h_bi_eb$6$(not in LMFDB)
3.7.k_ca_gm$6$(not in LMFDB)