Properties

Label 3.7.am_cp_aip
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:  $( 1 - 5 x + 7 x^{2} )( 1 - 7 x + 25 x^{2} - 49 x^{3} + 49 x^{4} )$
Frobenius angles:  $\pm0.106147807505$, $\pm0.162349854003$, $\pm0.351370772325$
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
$A(\F_{q^r})$ 57 97071 42224004 14146059759 4762715284272 1632875028862896 560363983937994531 191950117471752464175 65753434806167474684532 22540842492703355938081536

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 40 359 2452 16861 117973 826220 5775892 40378823 282494075

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.af $\times$ 2.7.ah_z 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.ac_ad_bb$2$(not in LMFDB)
3.7.c_ad_abb$2$(not in LMFDB)
3.7.m_cp_ip$2$(not in LMFDB)
3.7.ag_z_acv$3$(not in LMFDB)
3.7.ad_e_c$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.ac_ad_bb$2$(not in LMFDB)
3.7.c_ad_abb$2$(not in LMFDB)
3.7.m_cp_ip$2$(not in LMFDB)
3.7.ag_z_acv$3$(not in LMFDB)
3.7.ad_e_c$3$(not in LMFDB)
3.7.al_ci_ahq$6$(not in LMFDB)
3.7.ai_bn_aet$6$(not in LMFDB)
3.7.d_e_ac$6$(not in LMFDB)
3.7.g_z_cv$6$(not in LMFDB)
3.7.i_bn_et$6$(not in LMFDB)
3.7.l_ci_hq$6$(not in LMFDB)