Properties

Label 3.7.al_cd_ags
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:  $( 1 - 5 x + 7 x^{2} )( 1 - 6 x + 18 x^{2} - 42 x^{3} + 49 x^{4} )$
Frobenius angles:  $\pm0.0461154155528$, $\pm0.106147807505$, $\pm0.453884584447$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 60 90480 36164880 12804729600 4652481286500 1632390679745280 559793180264991180 191595514633735680000 65707433404317129112560 22541972792430127694502000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 39 306 2215 16467 117936 825381 5765231 40350582 282508239

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.af $\times$ 2.7.ag_s and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{7}$
The base change of $A$ to $\F_{7^{4}}$ is 1.2401.ade 2 $\times$ 1.2401.ax. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{7^{4}}$.
Remainder of endomorphism lattice by field

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_af_g$2$(not in LMFDB)
3.7.b_af_ag$2$(not in LMFDB)
3.7.l_cd_gs$2$(not in LMFDB)
3.7.af_t_aco$3$(not in LMFDB)
3.7.ac_b_am$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.ab_af_g$2$(not in LMFDB)
3.7.b_af_ag$2$(not in LMFDB)
3.7.l_cd_gs$2$(not in LMFDB)
3.7.af_t_aco$3$(not in LMFDB)
3.7.ac_b_am$3$(not in LMFDB)
3.7.ak_bx_aga$6$(not in LMFDB)
3.7.ah_bf_ady$6$(not in LMFDB)
3.7.c_b_m$6$(not in LMFDB)
3.7.f_t_co$6$(not in LMFDB)
3.7.h_bf_dy$6$(not in LMFDB)
3.7.k_bx_ga$6$(not in LMFDB)
3.7.af_d_u$8$(not in LMFDB)
3.7.af_l_au$8$(not in LMFDB)
3.7.f_d_au$8$(not in LMFDB)
3.7.f_l_u$8$(not in LMFDB)
3.7.ae_d_q$24$(not in LMFDB)
3.7.ae_l_aq$24$(not in LMFDB)
3.7.ab_d_e$24$(not in LMFDB)
3.7.ab_l_ae$24$(not in LMFDB)
3.7.b_d_ae$24$(not in LMFDB)
3.7.b_l_e$24$(not in LMFDB)
3.7.e_d_aq$24$(not in LMFDB)
3.7.e_l_q$24$(not in LMFDB)