Properties

Label 3.7.am_co_aik
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:  $( 1 - 2 x + 7 x^{2} )( 1 - 5 x + 7 x^{2} )^{2}$
Frobenius angles:  $\pm0.106147807505$, $\pm0.106147807505$, $\pm0.376624142786$
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
$A(\F_{q^r})$ 54 91260 39680928 13583138400 4693974261174 1629844913249280 560764481120763498 192025133181414000000 65760380398145050952544 22542614089580303490786300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 38 338 2354 16616 117752 826808 5778146 40383086 282516278

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The isogeny class factors as 1.7.af 2 $\times$ 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:
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.ai_ba_ack$2$(not in LMFDB)
3.7.ac_ae_w$2$(not in LMFDB)
3.7.c_ae_aw$2$(not in LMFDB)
3.7.i_ba_ck$2$(not in LMFDB)
3.7.m_co_ik$2$(not in LMFDB)
3.7.ag_y_acw$3$(not in LMFDB)
3.7.ad_d_ac$3$(not in LMFDB)
3.7.a_s_ac$3$(not in LMFDB)
3.7.d_p_bi$3$(not in LMFDB)
3.7.g_v_ca$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.ai_ba_ack$2$(not in LMFDB)
3.7.ac_ae_w$2$(not in LMFDB)
3.7.c_ae_aw$2$(not in LMFDB)
3.7.i_ba_ck$2$(not in LMFDB)
3.7.m_co_ik$2$(not in LMFDB)
3.7.ag_y_acw$3$(not in LMFDB)
3.7.ad_d_ac$3$(not in LMFDB)
3.7.a_s_ac$3$(not in LMFDB)
3.7.d_p_bi$3$(not in LMFDB)
3.7.g_v_ca$3$(not in LMFDB)
3.7.ac_s_aw$4$(not in LMFDB)
3.7.c_s_w$4$(not in LMFDB)
3.7.al_ch_ahm$6$(not in LMFDB)
3.7.ak_cb_agq$6$(not in LMFDB)
3.7.ai_bm_aes$6$(not in LMFDB)
3.7.ah_x_acg$6$(not in LMFDB)
3.7.ah_bj_aec$6$(not in LMFDB)
3.7.ag_v_aca$6$(not in LMFDB)
3.7.af_x_ack$6$(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_f_e$6$(not in LMFDB)
3.7.ac_i_abm$6$(not in LMFDB)
3.7.ac_u_aba$6$(not in LMFDB)
3.7.ab_ab_ba$6$(not in LMFDB)
3.7.ab_l_aw$6$(not in LMFDB)
3.7.a_s_c$6$(not in LMFDB)
3.7.b_ab_aba$6$(not in LMFDB)
3.7.b_l_w$6$(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_d_c$6$(not in LMFDB)
3.7.e_o_bu$6$(not in LMFDB)
3.7.e_ba_cg$6$(not in LMFDB)
3.7.f_x_ck$6$(not in LMFDB)
3.7.g_y_cw$6$(not in LMFDB)
3.7.h_x_cg$6$(not in LMFDB)
3.7.h_bj_ec$6$(not in LMFDB)
3.7.i_bm_es$6$(not in LMFDB)
3.7.k_cb_gq$6$(not in LMFDB)
3.7.l_ch_hm$6$(not in LMFDB)
3.7.ac_ag_ba$12$(not in LMFDB)
3.7.ac_j_ae$12$(not in LMFDB)
3.7.c_ag_aba$12$(not in LMFDB)
3.7.c_j_e$12$(not in LMFDB)