Properties

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

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 11 x^{2} - 28 x^{3} + 49 x^{4} )$
Frobenius angles:  $\pm0.106147807505$, $\pm0.158901191781$, $\pm0.538942184569$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 87 105183 36569232 13454693811 4856713533717 1648938266696448 559622658311689227 191739316707149863275 65755815233310693563184 22542145617400040024253783

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 45 308 2333 17189 119124 825131 5769557 40380284 282510405

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.af $\times$ 2.7.ae_l 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_b$2$(not in LMFDB)
3.7.b_ac_ab$2$(not in LMFDB)
3.7.j_bm_eh$2$(not in LMFDB)
3.7.ad_o_abt$3$(not in LMFDB)
3.7.a_c_am$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.ab_ac_b$2$(not in LMFDB)
3.7.b_ac_ab$2$(not in LMFDB)
3.7.j_bm_eh$2$(not in LMFDB)
3.7.ad_o_abt$3$(not in LMFDB)
3.7.a_c_am$3$(not in LMFDB)
3.7.ai_bi_adw$6$(not in LMFDB)
3.7.af_w_acp$6$(not in LMFDB)
3.7.a_c_m$6$(not in LMFDB)
3.7.d_o_bt$6$(not in LMFDB)
3.7.f_w_cp$6$(not in LMFDB)
3.7.i_bi_dw$6$(not in LMFDB)