Properties

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

Learn more about

Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )( 1 - 2 x + 7 x^{2} )$
Frobenius angles:  $\pm0.106147807505$, $\pm0.227185525829$, $\pm0.376624142786$
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
$A(\F_{q^r})$ 72 112320 44579808 14251161600 4752812767032 1629844913249280 559565852387925672 191748632567132160000 65719392352139385778464 22538219724640995377745600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 47 378 2471 16827 117752 825045 5769839 40357926 282461207

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.af $\times$ 1.7.ae $\times$ 1.7.ac 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 $\F_{7^{6}}$ is 1.117649.asc $\times$ 1.117649.la 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{7^{6}}$.
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.ah_x_acg$2$(not in LMFDB)
3.7.ad_d_ac$2$(not in LMFDB)
3.7.ab_ab_ba$2$(not in LMFDB)
3.7.b_ab_aba$2$(not in LMFDB)
3.7.d_d_c$2$(not in LMFDB)
3.7.h_x_cg$2$(not in LMFDB)
3.7.l_ch_hm$2$(not in LMFDB)
3.7.ai_bm_aes$3$(not in LMFDB)
3.7.af_x_ack$3$(not in LMFDB)
3.7.ac_ae_w$3$(not in LMFDB)
3.7.ac_f_e$3$(not in LMFDB)
3.7.ac_u_aba$3$(not in LMFDB)
3.7.b_l_w$3$(not in LMFDB)
3.7.e_o_bu$3$(not in LMFDB)
3.7.h_x_cg$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.ah_x_acg$2$(not in LMFDB)
3.7.ad_d_ac$2$(not in LMFDB)
3.7.ab_ab_ba$2$(not in LMFDB)
3.7.b_ab_aba$2$(not in LMFDB)
3.7.d_d_c$2$(not in LMFDB)
3.7.h_x_cg$2$(not in LMFDB)
3.7.l_ch_hm$2$(not in LMFDB)
3.7.ai_bm_aes$3$(not in LMFDB)
3.7.af_x_ack$3$(not in LMFDB)
3.7.ac_ae_w$3$(not in LMFDB)
3.7.ac_f_e$3$(not in LMFDB)
3.7.ac_u_aba$3$(not in LMFDB)
3.7.b_l_w$3$(not in LMFDB)
3.7.e_o_bu$3$(not in LMFDB)
3.7.h_x_cg$3$(not in LMFDB)
3.7.am_co_aik$6$(not in LMFDB)
3.7.ak_cb_agq$6$(not in LMFDB)
3.7.ai_ba_ack$6$(not in LMFDB)
3.7.ah_bj_aec$6$(not in LMFDB)
3.7.ag_v_aca$6$(not in LMFDB)
3.7.ag_y_acw$6$(not in LMFDB)
3.7.ae_o_abu$6$(not in LMFDB)
3.7.ae_ba_acg$6$(not in LMFDB)
3.7.ad_p_abi$6$(not in LMFDB)
3.7.ac_i_abm$6$(not in LMFDB)
3.7.ab_l_aw$6$(not in LMFDB)
3.7.a_s_ac$6$(not in LMFDB)
3.7.a_s_c$6$(not in LMFDB)
3.7.c_ae_aw$6$(not in LMFDB)
3.7.c_f_ae$6$(not in LMFDB)
3.7.c_i_bm$6$(not in LMFDB)
3.7.c_u_ba$6$(not in LMFDB)
3.7.d_p_bi$6$(not in LMFDB)
3.7.e_ba_cg$6$(not in LMFDB)
3.7.f_x_ck$6$(not in LMFDB)
3.7.g_v_ca$6$(not in LMFDB)
3.7.g_y_cw$6$(not in LMFDB)
3.7.h_bj_ec$6$(not in LMFDB)
3.7.i_ba_ck$6$(not in LMFDB)
3.7.i_bm_es$6$(not in LMFDB)
3.7.k_cb_gq$6$(not in LMFDB)
3.7.m_co_ik$6$(not in LMFDB)
3.7.ac_ag_ba$12$(not in LMFDB)
3.7.ac_j_ae$12$(not in LMFDB)
3.7.ac_s_aw$12$(not in LMFDB)
3.7.c_ag_aba$12$(not in LMFDB)
3.7.c_j_e$12$(not in LMFDB)
3.7.c_s_w$12$(not in LMFDB)