Properties

Label 3.13.ap_dy_aqx
Base Field $\F_{13}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
L-polynomial:  $( 1 - x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.455715642762$
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
$A(\F_{q^r})$ 637 4213755 10125466624 22758933199275 50961221941086457 112500615380537180160 247131956265713730738709 542811441823314176232085275 1192537920497238107784957242368 2620019459632019140624088299414275

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 149 2096 27893 369659 4828748 62765639 815746757 10604540528 137859744989

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah 2 $\times$ 1.13.ab 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 $\F_{13}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.an_cw_ald$2$(not in LMFDB)
3.13.ab_ak_x$2$(not in LMFDB)
3.13.b_ak_ax$2$(not in LMFDB)
3.13.n_cw_ld$2$(not in LMFDB)
3.13.p_dy_qx$2$(not in LMFDB)
3.13.ag_be_afm$3$(not in LMFDB)
3.13.ad_g_abr$3$(not in LMFDB)
3.13.d_bn_cw$3$(not in LMFDB)
3.13.g_bq_fq$3$(not in LMFDB)
3.13.j_cc_ib$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.an_cw_ald$2$(not in LMFDB)
3.13.ab_ak_x$2$(not in LMFDB)
3.13.b_ak_ax$2$(not in LMFDB)
3.13.n_cw_ld$2$(not in LMFDB)
3.13.p_dy_qx$2$(not in LMFDB)
3.13.ag_be_afm$3$(not in LMFDB)
3.13.ad_g_abr$3$(not in LMFDB)
3.13.d_bn_cw$3$(not in LMFDB)
3.13.g_bq_fq$3$(not in LMFDB)
3.13.j_cc_ib$3$(not in LMFDB)
3.13.ab_bk_ax$4$(not in LMFDB)
3.13.b_bk_x$4$(not in LMFDB)
3.13.an_di_aoj$6$(not in LMFDB)
3.13.al_ck_ajr$6$(not in LMFDB)
3.13.al_cw_alz$6$(not in LMFDB)
3.13.ak_ck_ako$6$(not in LMFDB)
3.13.aj_cc_aib$6$(not in LMFDB)
3.13.ai_bs_ahm$6$(not in LMFDB)
3.13.ai_ce_aik$6$(not in LMFDB)
3.13.ag_bq_afq$6$(not in LMFDB)
3.13.af_bv_afe$6$(not in LMFDB)
3.13.ae_u_aeo$6$(not in LMFDB)
3.13.ae_bg_adq$6$(not in LMFDB)
3.13.ad_bn_acw$6$(not in LMFDB)
3.13.ac_ba_ack$6$(not in LMFDB)
3.13.ab_c_acj$6$(not in LMFDB)
3.13.ab_o_ab$6$(not in LMFDB)
3.13.ab_bj_aw$6$(not in LMFDB)
3.13.b_c_cj$6$(not in LMFDB)
3.13.b_o_b$6$(not in LMFDB)
3.13.b_bj_w$6$(not in LMFDB)
3.13.c_ba_ck$6$(not in LMFDB)
3.13.d_g_br$6$(not in LMFDB)
3.13.e_u_eo$6$(not in LMFDB)
3.13.e_bg_dq$6$(not in LMFDB)
3.13.f_bv_fe$6$(not in LMFDB)
3.13.g_be_fm$6$(not in LMFDB)
3.13.i_bs_hm$6$(not in LMFDB)
3.13.i_ce_ik$6$(not in LMFDB)
3.13.k_ck_ko$6$(not in LMFDB)
3.13.l_ck_jr$6$(not in LMFDB)
3.13.l_cw_lz$6$(not in LMFDB)
3.13.n_di_oj$6$(not in LMFDB)
3.13.ab_aj_w$12$(not in LMFDB)
3.13.ab_m_b$12$(not in LMFDB)
3.13.b_aj_aw$12$(not in LMFDB)
3.13.b_m_ab$12$(not in LMFDB)