Properties

Label 4.5.an_dd_amd_bgi
Base Field $\F_{5}$
Dimension $4$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.200000000000$, $\pm0.400000000000$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 44 312400 285043484 166666649600 100060969290304 61906285437739600 38089735991599372124 23446514423076677222400 14550041109224787799036844 9084194718280899304552960000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 19 143 679 3278 16219 79863 393359 1952873 9754074

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.af_p 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 $\overline{\F}_{5}$
The base change of $A$ to $\F_{5^{10}}$ is 1.9765625.ajgk 2 $\times$ 1.9765625.sg 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5^{10}}$.
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
4.5.af_j_f_abo$2$(not in LMFDB)
4.5.ad_b_af_bo$2$(not in LMFDB)
4.5.d_b_f_bo$2$(not in LMFDB)
4.5.f_j_af_abo$2$(not in LMFDB)
4.5.n_dd_md_bgi$2$(not in LMFDB)
4.5.ab_g_a_p$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.af_j_f_abo$2$(not in LMFDB)
4.5.ad_b_af_bo$2$(not in LMFDB)
4.5.d_b_f_bo$2$(not in LMFDB)
4.5.f_j_af_abo$2$(not in LMFDB)
4.5.n_dd_md_bgi$2$(not in LMFDB)
4.5.ab_g_a_p$3$(not in LMFDB)
4.5.al_cl_ajb_xw$4$(not in LMFDB)
4.5.aj_bx_agt_rs$4$(not in LMFDB)
4.5.ah_bb_acx_gy$4$(not in LMFDB)
4.5.af_v_acd_fk$4$(not in LMFDB)
4.5.ad_h_f_au$4$(not in LMFDB)
4.5.ab_d_af_u$4$(not in LMFDB)
4.5.ab_j_ap_ci$4$(not in LMFDB)
4.5.b_d_f_u$4$(not in LMFDB)
4.5.b_j_p_ci$4$(not in LMFDB)
4.5.d_h_af_au$4$(not in LMFDB)
4.5.f_v_cd_fk$4$(not in LMFDB)
4.5.h_bb_cx_gy$4$(not in LMFDB)
4.5.j_bx_gt_rs$4$(not in LMFDB)
4.5.l_cl_jb_xw$4$(not in LMFDB)
4.5.ai_q_bo_aic$5$(not in LMFDB)
4.5.aj_bu_age_pz$6$(not in LMFDB)
4.5.b_g_a_p$6$(not in LMFDB)
4.5.j_bu_ge_pz$6$(not in LMFDB)
4.5.af_h_p_acs$8$(not in LMFDB)
4.5.af_x_acn_go$8$(not in LMFDB)
4.5.f_h_ap_acs$8$(not in LMFDB)
4.5.f_x_cn_go$8$(not in LMFDB)
4.5.a_aq_a_eg$10$(not in LMFDB)
4.5.i_q_abo_aic$10$(not in LMFDB)
4.5.ah_y_aci_ff$12$(not in LMFDB)
4.5.ad_e_u_acn$12$(not in LMFDB)
4.5.d_e_au_acn$12$(not in LMFDB)
4.5.h_y_ci_ff$12$(not in LMFDB)
4.5.ai_bf_adc_gy$15$(not in LMFDB)
4.5.e_b_au_aci$15$(not in LMFDB)
4.5.e_q_bo_eb$15$(not in LMFDB)
4.5.ai_bk_aeq_ly$20$(not in LMFDB)
4.5.ag_i_be_afa$20$(not in LMFDB)
4.5.ag_bc_adm_iw$20$(not in LMFDB)
4.5.ae_e_u_adm$20$(not in LMFDB)
4.5.ae_y_aci_hi$20$(not in LMFDB)
4.5.ac_ai_k_be$20$(not in LMFDB)
4.5.ac_m_abe_cs$20$(not in LMFDB)
4.5.a_ae_a_ak$20$(not in LMFDB)
4.5.a_e_a_ak$20$(not in LMFDB)
4.5.a_q_a_eg$20$(not in LMFDB)
4.5.c_ai_ak_be$20$(not in LMFDB)
4.5.c_m_be_cs$20$(not in LMFDB)
4.5.e_e_au_adm$20$(not in LMFDB)
4.5.e_y_ci_hi$20$(not in LMFDB)
4.5.g_i_abe_afa$20$(not in LMFDB)
4.5.g_bc_dm_iw$20$(not in LMFDB)
4.5.i_bk_eq_ly$20$(not in LMFDB)
4.5.ae_b_u_aci$30$(not in LMFDB)
4.5.ae_q_abo_eb$30$(not in LMFDB)
4.5.a_ab_a_u$30$(not in LMFDB)
4.5.i_bf_dc_gy$30$(not in LMFDB)
4.5.ai_ba_abo_by$40$(not in LMFDB)
4.5.ag_s_abe_by$40$(not in LMFDB)
4.5.ae_o_au_by$40$(not in LMFDB)
4.5.ac_c_ak_by$40$(not in LMFDB)
4.5.a_as_a_fa$40$(not in LMFDB)
4.5.a_ai_a_by$40$(not in LMFDB)
4.5.a_ag_a_by$40$(not in LMFDB)
4.5.a_ac_a_abe$40$(not in LMFDB)
4.5.a_c_a_abe$40$(not in LMFDB)
4.5.a_g_a_by$40$(not in LMFDB)
4.5.a_i_a_by$40$(not in LMFDB)
4.5.a_s_a_fa$40$(not in LMFDB)
4.5.c_c_k_by$40$(not in LMFDB)
4.5.e_o_u_by$40$(not in LMFDB)
4.5.g_s_be_by$40$(not in LMFDB)
4.5.i_ba_bo_by$40$(not in LMFDB)
4.5.ai_v_a_adc$60$(not in LMFDB)
4.5.ag_n_a_abo$60$(not in LMFDB)
4.5.ag_x_aci_fk$60$(not in LMFDB)
4.5.ae_g_a_af$60$(not in LMFDB)
4.5.ae_j_a_au$60$(not in LMFDB)
4.5.ae_t_abo_eq$60$(not in LMFDB)
4.5.ae_v_aci_ge$60$(not in LMFDB)
4.5.ac_al_k_ci$60$(not in LMFDB)
4.5.ac_ag_a_cd$60$(not in LMFDB)
4.5.ac_ad_a_bo$60$(not in LMFDB)
4.5.ac_e_au_bt$60$(not in LMFDB)
4.5.ac_h_au_ci$60$(not in LMFDB)
4.5.ac_j_abe_bo$60$(not in LMFDB)
4.5.a_al_a_dc$60$(not in LMFDB)
4.5.a_b_a_u$60$(not in LMFDB)
4.5.a_l_a_dc$60$(not in LMFDB)
4.5.c_al_ak_ci$60$(not in LMFDB)
4.5.c_ag_a_cd$60$(not in LMFDB)
4.5.c_ad_a_bo$60$(not in LMFDB)
4.5.c_e_u_bt$60$(not in LMFDB)
4.5.c_h_u_ci$60$(not in LMFDB)
4.5.c_j_be_bo$60$(not in LMFDB)
4.5.e_g_a_af$60$(not in LMFDB)
4.5.e_j_a_au$60$(not in LMFDB)
4.5.e_t_bo_eq$60$(not in LMFDB)
4.5.e_v_ci_ge$60$(not in LMFDB)
4.5.g_n_a_abo$60$(not in LMFDB)
4.5.g_x_ci_fk$60$(not in LMFDB)
4.5.i_v_a_adc$60$(not in LMFDB)
4.5.ae_l_au_by$120$(not in LMFDB)
4.5.ac_ab_ak_by$120$(not in LMFDB)
4.5.a_an_a_dm$120$(not in LMFDB)
4.5.a_ad_a_k$120$(not in LMFDB)
4.5.a_d_a_k$120$(not in LMFDB)
4.5.a_n_a_dm$120$(not in LMFDB)
4.5.c_ab_k_by$120$(not in LMFDB)
4.5.e_l_u_by$120$(not in LMFDB)