Properties

Label 5.3.ap_eb_ari_byf_adyv
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $0$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 3 x + 3 x^{2} )^{5}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$
Angle rank:  $0$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is supersingular.

$p$-rank:  $0$
Slopes:  $[1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2]$

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
$A(\F_{q^r})$ 1 16807 17210368 6240321451 1461660310351 296196766695424 60141254017962349 12936633131256641443 2955063255987167847424 703307297416677005110807

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -11 -5 28 127 379 1000 2593 6967 19684 57835

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 5 and its endomorphism algebra is $\mathrm{M}_{5}($\(\Q(\sqrt{-3}) \)$)$
Endomorphism algebra over $\overline{\F}_{3}$
The base change of $A$ to $\F_{3^{6}}$ is 1.729.cc 5 and its endomorphism algebra is $\mathrm{M}_{5}(B)$, where $B$ is the quaternion algebra over \(\Q\) ramified at $3$ and $\infty$.
All geometric endomorphisms are defined over $\F_{3^{6}}$.
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
5.3.aj_bh_acc_j_dd$2$(not in LMFDB)
5.3.ad_ad_s_j_add$2$(not in LMFDB)
5.3.d_ad_as_j_dd$2$(not in LMFDB)
5.3.j_bh_cc_j_add$2$(not in LMFDB)
5.3.p_eb_ri_byf_dyv$2$(not in LMFDB)
5.3.am_cr_ajs_zh_abxw$3$(not in LMFDB)
5.3.aj_bh_acc_j_dd$3$(not in LMFDB)
5.3.aj_bq_aff_mv_ayy$3$(not in LMFDB)
5.3.ag_p_as_j_a$3$(not in LMFDB)
5.3.ag_y_acu_gp_amm$3$(not in LMFDB)
5.3.ad_ad_s_j_add$3$(not in LMFDB)
5.3.ad_g_aj_j_a$3$(not in LMFDB)
5.3.ad_p_abk_dm_agg$3$(not in LMFDB)
5.3.a_ad_a_j_a$3$(not in LMFDB)
5.3.a_g_a_j_a$3$(not in LMFDB)
5.3.a_p_a_dm_a$3$(not in LMFDB)
5.3.d_ad_as_j_dd$3$(not in LMFDB)
5.3.d_g_j_j_a$3$(not in LMFDB)
5.3.d_p_bk_dm_gg$3$(not in LMFDB)
5.3.g_p_s_j_a$3$(not in LMFDB)
5.3.g_y_cu_gp_mm$3$(not in LMFDB)
5.3.j_bh_cc_j_add$3$(not in LMFDB)
5.3.j_bq_ff_mv_yy$3$(not in LMFDB)
5.3.m_cr_js_zh_bxw$3$(not in LMFDB)
5.3.p_eb_ri_byf_dyv$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.aj_bh_acc_j_dd$2$(not in LMFDB)
5.3.ad_ad_s_j_add$2$(not in LMFDB)
5.3.d_ad_as_j_dd$2$(not in LMFDB)
5.3.j_bh_cc_j_add$2$(not in LMFDB)
5.3.p_eb_ri_byf_dyv$2$(not in LMFDB)
5.3.am_cr_ajs_zh_abxw$3$(not in LMFDB)
5.3.aj_bh_acc_j_dd$3$(not in LMFDB)
5.3.aj_bq_aff_mv_ayy$3$(not in LMFDB)
5.3.ag_p_as_j_a$3$(not in LMFDB)
5.3.ag_y_acu_gp_amm$3$(not in LMFDB)
5.3.ad_ad_s_j_add$3$(not in LMFDB)
5.3.ad_g_aj_j_a$3$(not in LMFDB)
5.3.ad_p_abk_dm_agg$3$(not in LMFDB)
5.3.a_ad_a_j_a$3$(not in LMFDB)
5.3.a_g_a_j_a$3$(not in LMFDB)
5.3.a_p_a_dm_a$3$(not in LMFDB)
5.3.d_ad_as_j_dd$3$(not in LMFDB)
5.3.d_g_j_j_a$3$(not in LMFDB)
5.3.d_p_bk_dm_gg$3$(not in LMFDB)
5.3.g_p_s_j_a$3$(not in LMFDB)
5.3.g_y_cu_gp_mm$3$(not in LMFDB)
5.3.j_bh_cc_j_add$3$(not in LMFDB)
5.3.j_bq_ff_mv_yy$3$(not in LMFDB)
5.3.m_cr_js_zh_bxw$3$(not in LMFDB)
5.3.p_eb_ri_byf_dyv$3$(not in LMFDB)
5.3.aj_bn_aee_ir_app$4$(not in LMFDB)
5.3.ad_d_a_j_abb$4$(not in LMFDB)
5.3.ad_j_as_bt_add$4$(not in LMFDB)
5.3.d_d_a_j_bb$4$(not in LMFDB)
5.3.d_j_s_bt_dd$4$(not in LMFDB)
5.3.j_bn_ee_ir_pp$4$(not in LMFDB)
5.3.a_a_a_a_bb$5$(not in LMFDB)
5.3.ad_d_a_aj_bb$8$(not in LMFDB)
5.3.d_d_a_aj_abb$8$(not in LMFDB)
5.3.ag_p_abb_cl_aff$9$(not in LMFDB)
5.3.ag_p_aj_abt_ff$9$(not in LMFDB)
5.3.ad_g_as_bk_acc$9$(not in LMFDB)
5.3.ad_g_a_as_cc$9$(not in LMFDB)
5.3.a_ad_aj_j_bb$9$(not in LMFDB)
5.3.a_ad_j_j_abb$9$(not in LMFDB)
5.3.a_g_aj_j_acc$9$(not in LMFDB)
5.3.a_g_j_j_cc$9$(not in LMFDB)
5.3.d_g_a_as_acc$9$(not in LMFDB)
5.3.d_g_s_bk_cc$9$(not in LMFDB)
5.3.g_p_j_abt_aff$9$(not in LMFDB)
5.3.g_p_bb_cl_ff$9$(not in LMFDB)
5.3.ag_s_abk_cc_add$10$(not in LMFDB)
5.3.a_a_a_a_abb$10$(not in LMFDB)
5.3.g_s_bk_cc_dd$10$(not in LMFDB)
5.3.aj_be_abb_adv_mm$12$(not in LMFDB)
5.3.ag_m_a_abt_ee$12$(not in LMFDB)
5.3.ag_v_acc_en_aii$12$(not in LMFDB)
5.3.ad_aj_bk_s_agg$12$(not in LMFDB)
5.3.ad_ag_bb_j_aee$12$(not in LMFDB)
5.3.ad_a_j_aj_a$12$(not in LMFDB)
5.3.ad_d_a_as_cc$12$(not in LMFDB)
5.3.ad_m_abb_cl_aee$12$(not in LMFDB)
5.3.a_aj_a_s_a$12$(not in LMFDB)
5.3.a_ag_a_j_a$12$(not in LMFDB)
5.3.a_a_a_aj_a$12$(not in LMFDB)
5.3.a_d_a_as_a$12$(not in LMFDB)
5.3.a_d_a_j_a$12$(not in LMFDB)
5.3.a_j_a_bt_a$12$(not in LMFDB)
5.3.a_m_a_cl_a$12$(not in LMFDB)
5.3.d_aj_abk_s_gg$12$(not in LMFDB)
5.3.d_ag_abb_j_ee$12$(not in LMFDB)
5.3.d_a_aj_aj_a$12$(not in LMFDB)
5.3.d_d_a_as_acc$12$(not in LMFDB)
5.3.d_m_bb_cl_ee$12$(not in LMFDB)
5.3.g_m_a_abt_aee$12$(not in LMFDB)
5.3.g_v_cc_en_ii$12$(not in LMFDB)
5.3.j_be_bb_adv_amm$12$(not in LMFDB)
5.3.ag_s_abk_cc_add$15$(not in LMFDB)
5.3.ad_a_j_a_abb$15$(not in LMFDB)
5.3.ad_j_as_bb_acc$15$(not in LMFDB)
5.3.a_a_a_a_abb$15$(not in LMFDB)
5.3.a_a_a_a_a$15$(not in LMFDB)
5.3.d_a_aj_a_bb$15$(not in LMFDB)
5.3.d_j_s_bb_cc$15$(not in LMFDB)
5.3.g_s_bk_cc_dd$15$(not in LMFDB)
5.3.aj_bk_add_en_agg$24$(not in LMFDB)
5.3.ag_s_abk_cl_aee$24$(not in LMFDB)
5.3.ad_ad_s_a_acc$24$(not in LMFDB)
5.3.ad_a_j_j_acc$24$(not in LMFDB)
5.3.ad_d_a_s_acc$24$(not in LMFDB)
5.3.ad_g_aj_bb_acc$24$(not in LMFDB)
5.3.ad_j_as_bk_acc$24$(not in LMFDB)
5.3.a_ad_a_a_a$24$(not in LMFDB)
5.3.a_a_a_j_a$24$(not in LMFDB)
5.3.a_d_a_aj_a$24$(not in LMFDB)
5.3.a_d_a_s_a$24$(not in LMFDB)
5.3.a_g_a_bb_a$24$(not in LMFDB)
5.3.a_j_a_bk_a$24$(not in LMFDB)
5.3.d_ad_as_a_cc$24$(not in LMFDB)
5.3.d_a_aj_j_cc$24$(not in LMFDB)
5.3.d_d_a_s_cc$24$(not in LMFDB)
5.3.d_g_j_bb_cc$24$(not in LMFDB)
5.3.d_j_s_bk_cc$24$(not in LMFDB)
5.3.g_s_bk_cl_ee$24$(not in LMFDB)
5.3.j_bk_dd_en_gg$24$(not in LMFDB)
5.3.a_ag_aj_j_cc$36$(not in LMFDB)
5.3.a_ag_j_j_acc$36$(not in LMFDB)
5.3.a_d_aj_j_abb$36$(not in LMFDB)
5.3.a_d_j_j_bb$36$(not in LMFDB)
5.3.ad_d_a_a_a$48$(not in LMFDB)
5.3.a_d_a_a_a$48$(not in LMFDB)
5.3.d_d_a_a_a$48$(not in LMFDB)
5.3.ad_g_aj_s_abb$60$(not in LMFDB)
5.3.a_g_a_s_a$60$(not in LMFDB)
5.3.d_g_j_s_bb$60$(not in LMFDB)
5.3.a_a_aj_j_a$72$(not in LMFDB)
5.3.a_a_j_j_a$72$(not in LMFDB)