Properties

Label 4.5.am_cu_akp_bcc
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.147583617650$, $\pm0.200000000000$, $\pm0.265942140215$, $\pm0.400000000000$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 66 421740 336444768 175781232000 99467228373216 60704070058494720 37575140666632160658 23314520028921029568000 14532517594099089483772896 9086545273779316874774707200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 26 165 714 3259 15911 78800 391154 1950519 9756601

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae $\times$ 1.5.ad $\times$ 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 $\times$ 1.9765625.ell. 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.ag_s_abj_cs$2$(not in LMFDB)
4.5.ae_i_f_abe$2$(not in LMFDB)
4.5.ac_c_af_be$2$(not in LMFDB)
4.5.c_c_f_be$2$(not in LMFDB)
4.5.e_i_af_abe$2$(not in LMFDB)
4.5.g_s_bj_cs$2$(not in LMFDB)
4.5.m_cu_kp_bcc$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ag_s_abj_cs$2$(not in LMFDB)
4.5.ae_i_f_abe$2$(not in LMFDB)
4.5.ac_c_af_be$2$(not in LMFDB)
4.5.c_c_f_be$2$(not in LMFDB)
4.5.e_i_af_abe$2$(not in LMFDB)
4.5.g_s_bj_cs$2$(not in LMFDB)
4.5.m_cu_kp_bcc$2$(not in LMFDB)
4.5.ak_ce_ahx_uu$4$(not in LMFDB)
4.5.ag_y_acn_ge$4$(not in LMFDB)
4.5.ae_o_az_ci$4$(not in LMFDB)
4.5.a_g_af_bo$4$(not in LMFDB)
4.5.a_g_f_bo$4$(not in LMFDB)
4.5.e_o_z_ci$4$(not in LMFDB)
4.5.g_y_cn_ge$4$(not in LMFDB)
4.5.k_ce_hx_uu$4$(not in LMFDB)
4.5.ah_m_bj_ago$5$(not in LMFDB)
4.5.ac_c_af_be$5$(not in LMFDB)
4.5.ab_am_f_cs$10$(not in LMFDB)
4.5.b_am_af_cs$10$(not in LMFDB)
4.5.h_m_abj_ago$10$(not in LMFDB)
4.5.ah_bb_acs_ge$15$(not in LMFDB)
4.5.ah_bg_aeb_kk$20$(not in LMFDB)
4.5.af_g_z_aeg$20$(not in LMFDB)
4.5.af_ba_acx_ic$20$(not in LMFDB)
4.5.ab_ag_f_k$20$(not in LMFDB)
4.5.ab_i_ap_be$20$(not in LMFDB)
4.5.ab_o_ap_dm$20$(not in LMFDB)
4.5.b_ag_af_k$20$(not in LMFDB)
4.5.b_i_p_be$20$(not in LMFDB)
4.5.b_o_p_dm$20$(not in LMFDB)
4.5.f_g_az_aeg$20$(not in LMFDB)
4.5.f_ba_cx_ic$20$(not in LMFDB)
4.5.h_bg_eb_kk$20$(not in LMFDB)
4.5.ab_d_ak_bo$30$(not in LMFDB)
4.5.b_d_k_bo$30$(not in LMFDB)
4.5.h_bb_cs_ge$30$(not in LMFDB)
4.5.ah_w_abj_by$40$(not in LMFDB)
4.5.af_q_az_by$40$(not in LMFDB)
4.5.ab_ac_af_by$40$(not in LMFDB)
4.5.ab_e_af_by$40$(not in LMFDB)
4.5.b_ac_f_by$40$(not in LMFDB)
4.5.b_e_f_by$40$(not in LMFDB)
4.5.f_q_z_by$40$(not in LMFDB)
4.5.h_w_bj_by$40$(not in LMFDB)
4.5.ah_r_a_aci$60$(not in LMFDB)
4.5.af_l_a_abe$60$(not in LMFDB)
4.5.af_v_aby_fa$60$(not in LMFDB)
4.5.ab_ah_a_ci$60$(not in LMFDB)
4.5.ab_ab_a_be$60$(not in LMFDB)
4.5.ab_j_ak_cs$60$(not in LMFDB)
4.5.b_ah_a_ci$60$(not in LMFDB)
4.5.b_ab_a_be$60$(not in LMFDB)
4.5.b_j_k_cs$60$(not in LMFDB)
4.5.f_l_a_abe$60$(not in LMFDB)
4.5.f_v_by_fa$60$(not in LMFDB)
4.5.h_r_a_aci$60$(not in LMFDB)