Properties

Label 4.5.am_cq_ajk_yg
Base Field $\F_{5}$
Dimension $4$
Ordinary No
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

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

This isogeny class is not simple.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 48 288000 228796848 150994944000 102624949503408 63336001057056000 38055879314533355568 23397172002403909632000 14584065785848469246657328 9102096763908314775156000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 18 114 618 3354 16578 79794 392538 1957434 9773298

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 3 $\times$ 1.5.a 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 $\F_{5^{2}}$ is 1.25.ag 3 $\times$ 1.25.k. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5^{2}}$.

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.ae_e_e_ak$2$(not in LMFDB)
4.5.e_e_ae_ak$2$(not in LMFDB)
4.5.m_cq_jk_yg$2$(not in LMFDB)
4.5.a_f_ae_a$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ae_e_e_ak$2$(not in LMFDB)
4.5.e_e_ae_ak$2$(not in LMFDB)
4.5.m_cq_jk_yg$2$(not in LMFDB)
4.5.a_f_ae_a$3$(not in LMFDB)
4.5.ak_ca_aha_sc$4$(not in LMFDB)
4.5.ai_bo_afg_nm$4$(not in LMFDB)
4.5.ag_u_acg_fu$4$(not in LMFDB)
4.5.ag_bg_adu_kk$4$(not in LMFDB)
4.5.ae_q_abs_eg$4$(not in LMFDB)
4.5.ac_e_c_ak$4$(not in LMFDB)
4.5.ac_q_aw_eg$4$(not in LMFDB)
4.5.a_i_aq_be$4$(not in LMFDB)
4.5.a_i_q_be$4$(not in LMFDB)
4.5.c_e_ac_ak$4$(not in LMFDB)
4.5.c_q_w_eg$4$(not in LMFDB)
4.5.e_q_bs_eg$4$(not in LMFDB)
4.5.g_u_cg_fu$4$(not in LMFDB)
4.5.g_bg_du_kk$4$(not in LMFDB)
4.5.i_bo_fg_nm$4$(not in LMFDB)
4.5.k_ca_ha_sc$4$(not in LMFDB)
4.5.ai_bl_aeu_mi$6$(not in LMFDB)
4.5.a_f_e_a$6$(not in LMFDB)
4.5.i_bl_eu_mi$6$(not in LMFDB)
4.5.ae_c_m_abe$8$(not in LMFDB)
4.5.ae_s_aca_fa$8$(not in LMFDB)
4.5.ac_c_g_abe$8$(not in LMFDB)
4.5.ac_s_aba_fa$8$(not in LMFDB)
4.5.c_c_ag_abe$8$(not in LMFDB)
4.5.c_s_ba_fa$8$(not in LMFDB)
4.5.e_c_am_abe$8$(not in LMFDB)
4.5.e_s_ca_fa$8$(not in LMFDB)
4.5.ag_r_abu_eq$12$(not in LMFDB)
4.5.ag_bd_ado_jg$12$(not in LMFDB)
4.5.ae_n_abm_dc$12$(not in LMFDB)
4.5.ac_b_o_abo$12$(not in LMFDB)
4.5.ac_n_abc_dc$12$(not in LMFDB)
4.5.a_f_aw_a$12$(not in LMFDB)
4.5.a_f_w_a$12$(not in LMFDB)
4.5.c_b_ao_abo$12$(not in LMFDB)
4.5.c_n_bc_dc$12$(not in LMFDB)
4.5.e_n_bm_dc$12$(not in LMFDB)
4.5.g_r_bu_eq$12$(not in LMFDB)
4.5.g_bd_do_jg$12$(not in LMFDB)