Properties

Label 3.7.al_ci_ahr
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:  $( 1 - 5 x + 7 x^{2} )( 1 - 3 x + 7 x^{2} )^{2}$
Frobenius angles:  $\pm0.106147807505$, $\pm0.308124534521$, $\pm0.308124534521$
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
$A(\F_{q^r})$ 75 117975 46785600 14572861875 4736816720625 1615529973657600 557228911685436975 191688283559051296875 65764170805896642859200 22547164189151946740199375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 49 396 2525 16767 116716 821601 5768021 40385412 282573289

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.af $\times$ 1.7.ad 2 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.af_m_az$2$(not in LMFDB)
3.7.ab_a_bf$2$(not in LMFDB)
3.7.b_a_abf$2$(not in LMFDB)
3.7.f_m_z$2$(not in LMFDB)
3.7.l_ci_hr$2$(not in LMFDB)
3.7.af_y_acj$3$(not in LMFDB)
3.7.ac_ag_bg$3$(not in LMFDB)
3.7.ac_g_i$3$(not in LMFDB)
3.7.e_m_bs$3$(not in LMFDB)
3.7.h_v_by$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.af_m_az$2$(not in LMFDB)
3.7.ab_a_bf$2$(not in LMFDB)
3.7.b_a_abf$2$(not in LMFDB)
3.7.f_m_z$2$(not in LMFDB)
3.7.l_ci_hr$2$(not in LMFDB)
3.7.af_y_acj$3$(not in LMFDB)
3.7.ac_ag_bg$3$(not in LMFDB)
3.7.ac_g_i$3$(not in LMFDB)
3.7.e_m_bs$3$(not in LMFDB)
3.7.h_v_by$3$(not in LMFDB)
3.7.af_c_z$4$(not in LMFDB)
3.7.f_c_az$4$(not in LMFDB)
3.7.ak_cc_agu$6$(not in LMFDB)
3.7.ai_y_aca$6$(not in LMFDB)
3.7.ah_v_aby$6$(not in LMFDB)
3.7.ah_bk_aed$6$(not in LMFDB)
3.7.ae_m_abs$6$(not in LMFDB)
3.7.ae_m_au$6$(not in LMFDB)
3.7.ac_g_abo$6$(not in LMFDB)
3.7.ab_ad_bi$6$(not in LMFDB)
3.7.ab_m_af$6$(not in LMFDB)
3.7.b_ad_abi$6$(not in LMFDB)
3.7.b_m_f$6$(not in LMFDB)
3.7.c_ag_abg$6$(not in LMFDB)
3.7.c_g_ai$6$(not in LMFDB)
3.7.c_g_bo$6$(not in LMFDB)
3.7.e_m_u$6$(not in LMFDB)
3.7.f_y_cj$6$(not in LMFDB)
3.7.h_bk_ed$6$(not in LMFDB)
3.7.i_y_ca$6$(not in LMFDB)
3.7.k_cc_gu$6$(not in LMFDB)
3.7.ae_c_u$12$(not in LMFDB)
3.7.ab_c_f$12$(not in LMFDB)
3.7.b_c_af$12$(not in LMFDB)
3.7.e_c_au$12$(not in LMFDB)