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Properties

Label 6.2.a_a_ae_a_a_i
Base field $\F_{2}$
Dimension $6$
$p$-rank $0$
Ordinary no
Supersingular yes
Simple yes
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{2}$
Dimension:  $6$
L-polynomial:  $1 - 4 x^{3} + 8 x^{6} - 32 x^{9} + 64 x^{12}$
Frobenius angles:  $\pm0.0277777777778$, $\pm0.194444444444$, $\pm0.472222222222$, $\pm0.638888888889$, $\pm0.694444444444$, $\pm0.861111111111$
Angle rank:  $0$ (numerical)
Number field:  \(\Q(\zeta_{36})\)
Galois group:  $C_6\times C_2$
Jacobians:  $0$

This isogeny class is simple but not geometrically simple, primitive, not ordinary, and supersingular. It is principally polarizable.

Newton polygon

This isogeny class is supersingular.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $37$ $4033$ $50653$ $16265089$ $1082163457$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $3$ $5$ $-3$ $17$ $33$ $65$ $129$ $257$ $321$ $1025$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{36}}$.

Endomorphism algebra over $\F_{2}$
The endomorphism algebra of this simple isogeny class is \(\Q(\zeta_{36})\).
Endomorphism algebra over $\overline{\F}_{2}$
The base change of $A$ to $\F_{2^{36}}$ is 1.68719476736.bdvoy 6 and its endomorphism algebra is $\mathrm{M}_{6}(B)$, where $B$ is the quaternion algebra over \(\Q\) ramified at $2$ and $\infty$.
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
6.2.a_a_e_a_a_i$2$(not in LMFDB)
6.2.a_a_a_a_a_ai$8$(not in LMFDB)
6.2.a_a_a_a_a_i$8$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
6.2.a_a_e_a_a_i$2$(not in LMFDB)
6.2.a_a_a_a_a_ai$8$(not in LMFDB)
6.2.a_a_a_a_a_i$8$(not in LMFDB)
6.2.am_cu_aku_bea_acku_dwy$9$(not in LMFDB)
6.2.ag_s_abc_m_bw_aei$9$(not in LMFDB)
6.2.a_a_i_a_a_bg$9$(not in LMFDB)
6.2.g_s_bs_ds_gm_jo$9$(not in LMFDB)
6.2.ak_by_agi_pg_abcy_bsy$18$(not in LMFDB)
6.2.ai_bg_adk_hk_ano_uy$18$(not in LMFDB)
6.2.ai_bg_adc_fk_ahk_jw$18$(not in LMFDB)
6.2.ag_s_abs_ds_agm_jo$18$(not in LMFDB)
6.2.ag_s_abk_ci_ads_fo$18$(not in LMFDB)
6.2.ae_i_aq_bg_abw_cm$18$(not in LMFDB)
6.2.ae_i_ai_a_q_abg$18$(not in LMFDB)
6.2.ae_i_ai_m_abg_cm$18$(not in LMFDB)
6.2.ac_c_ae_a_i_ai$18$(not in LMFDB)
6.2.ac_c_ae_m_aq_q$18$(not in LMFDB)
6.2.ac_c_e_ae_a_q$18$(not in LMFDB)
6.2.a_a_ai_a_a_bg$18$(not in LMFDB)
6.2.a_a_a_a_a_a$18$(not in LMFDB)
6.2.a_a_a_m_a_a$18$(not in LMFDB)
6.2.c_c_ae_ae_a_q$18$(not in LMFDB)
6.2.c_c_e_a_ai_ai$18$(not in LMFDB)
6.2.c_c_e_m_q_q$18$(not in LMFDB)
6.2.e_i_i_a_aq_abg$18$(not in LMFDB)
6.2.e_i_i_m_bg_cm$18$(not in LMFDB)
6.2.e_i_q_bg_bw_cm$18$(not in LMFDB)
6.2.g_s_bc_m_abw_aei$18$(not in LMFDB)
6.2.g_s_bk_ci_ds_fo$18$(not in LMFDB)
6.2.i_bg_dc_fk_hk_jw$18$(not in LMFDB)
6.2.i_bg_dk_hk_no_uy$18$(not in LMFDB)
6.2.k_by_gi_pg_bcy_bsy$18$(not in LMFDB)
6.2.m_cu_ku_bea_cku_dwy$18$(not in LMFDB)
6.2.ac_c_a_a_i_aq$45$(not in LMFDB)
6.2.e_i_m_m_i_i$45$(not in LMFDB)
6.2.c_c_a_ae_ai_ai$63$(not in LMFDB)
6.2.ak_ca_agy_rs_abjc_cdk$72$(not in LMFDB)
6.2.ai_bc_abw_m_ey_alc$72$(not in LMFDB)
6.2.ai_be_acm_cy_abg_aq$72$(not in LMFDB)
6.2.ai_bi_adw_iu_aqi_zg$72$(not in LMFDB)
6.2.ai_bi_ads_hw_ano_ui$72$(not in LMFDB)
6.2.ai_bk_aei_ki_ats_beu$72$(not in LMFDB)
6.2.ag_o_am_am_bw_adc$72$(not in LMFDB)
6.2.ag_q_ay_y_ay_bg$72$(not in LMFDB)
6.2.ag_q_au_ae_cm_aey$72$(not in LMFDB)
6.2.ag_s_abg_bk_ay_q$72$(not in LMFDB)
6.2.ag_u_aca_ei_ahs_ls$72$(not in LMFDB)
6.2.ag_u_abw_ds_agm_jw$72$(not in LMFDB)
6.2.ag_u_abs_cy_aei_ge$72$(not in LMFDB)
6.2.ag_w_aci_fc_ajg_oe$72$(not in LMFDB)
6.2.ag_w_ace_em_ahs_ls$72$(not in LMFDB)
6.2.ag_y_acq_ga_alc_rg$72$(not in LMFDB)
6.2.ae_a_y_abk_abg_ey$72$(not in LMFDB)
6.2.ae_c_q_abc_aq_dc$72$(not in LMFDB)
6.2.ae_e_a_a_q_abw$72$(not in LMFDB)
6.2.ae_e_i_au_a_bg$72$(not in LMFDB)
6.2.ae_e_i_aq_aq_cm$72$(not in LMFDB)
6.2.ae_g_ai_q_aq_i$72$(not in LMFDB)
6.2.ae_g_ae_ae_y_abw$72$(not in LMFDB)
6.2.ae_g_a_am_q_aq$72$(not in LMFDB)
6.2.ae_g_a_ae_aq_bw$72$(not in LMFDB)
6.2.ae_i_am_q_aq_q$72$(not in LMFDB)
6.2.ae_i_ai_ae_bg_acm$72$(not in LMFDB)
6.2.ae_i_ai_i_aq_bg$72$(not in LMFDB)
6.2.ae_k_ay_bw_adc_eq$72$(not in LMFDB)
6.2.ae_k_au_bk_ace_dc$72$(not in LMFDB)
6.2.ae_k_aq_u_aq_q$72$(not in LMFDB)
6.2.ae_k_aq_bc_abw_dc$72$(not in LMFDB)
6.2.ae_k_am_e_y_abw$72$(not in LMFDB)
6.2.ae_m_abg_cm_aei_gu$72$(not in LMFDB)
6.2.ae_m_abc_ce_ads_fo$72$(not in LMFDB)
6.2.ae_m_ay_bs_acm_ds$72$(not in LMFDB)
6.2.ae_m_ay_bw_adc_ey$72$(not in LMFDB)
6.2.ae_o_abk_cy_afg_ia$72$(not in LMFDB)
6.2.ae_o_abg_cq_aei_gu$72$(not in LMFDB)
6.2.ae_q_abo_do_age_jw$72$(not in LMFDB)
6.2.ac_ag_m_m_aq_aq$72$(not in LMFDB)
6.2.ac_ae_i_i_ai_aq$72$(not in LMFDB)
6.2.ac_ae_m_ae_aq_bg$72$(not in LMFDB)
6.2.ac_ac_e_e_a_aq$72$(not in LMFDB)
6.2.ac_ac_e_i_ai_ai$72$(not in LMFDB)
6.2.ac_ac_i_ae_ai_q$72$(not in LMFDB)
6.2.ac_ac_m_am_aq_bw$72$(not in LMFDB)
6.2.ac_a_a_a_i_aq$72$(not in LMFDB)
6.2.ac_a_a_i_ai_a$72$(not in LMFDB)
6.2.ac_a_e_ae_a_a$72$(not in LMFDB)
6.2.ac_a_e_a_ai_q$72$(not in LMFDB)
6.2.ac_a_i_ai_ai_bg$72$(not in LMFDB)
6.2.ac_c_ae_ae_q_aq$72$(not in LMFDB)
6.2.ac_c_ae_i_ai_i$72$(not in LMFDB)
6.2.ac_c_a_ae_i_aq$72$(not in LMFDB)
6.2.ac_c_a_e_ai_q$72$(not in LMFDB)
6.2.ac_e_am_q_ay_bw$72$(not in LMFDB)
6.2.ac_e_ai_i_ai_q$72$(not in LMFDB)
6.2.ac_e_ai_q_ay_bg$72$(not in LMFDB)
6.2.ac_e_ae_ae_q_abg$72$(not in LMFDB)
6.2.ac_e_ae_a_i_aq$72$(not in LMFDB)
6.2.ac_e_ae_i_ai_q$72$(not in LMFDB)
6.2.ac_e_ae_m_aq_bg$72$(not in LMFDB)
6.2.ac_e_a_a_i_a$72$(not in LMFDB)
6.2.ac_g_am_u_abg_bw$72$(not in LMFDB)
6.2.ac_g_am_y_abo_ce$72$(not in LMFDB)
6.2.ac_g_ai_m_ai_q$72$(not in LMFDB)
6.2.ac_g_ai_u_ay_bw$72$(not in LMFDB)
6.2.ac_g_ae_e_q_aq$72$(not in LMFDB)
6.2.ac_i_aq_bg_ace_dc$72$(not in LMFDB)
6.2.ac_i_am_bc_abg_cm$72$(not in LMFDB)
6.2.ac_i_am_bg_abo_dc$72$(not in LMFDB)
6.2.ac_k_au_bs_adc_ei$72$(not in LMFDB)
6.2.ac_k_aq_bs_ace_ei$72$(not in LMFDB)
6.2.ac_m_au_ci_adc_ge$72$(not in LMFDB)
6.2.a_am_a_ci_a_age$72$(not in LMFDB)
6.2.a_ak_a_bs_a_aei$72$(not in LMFDB)
6.2.a_ai_a_bc_a_acm$72$(not in LMFDB)
6.2.a_ai_a_bg_a_adc$72$(not in LMFDB)
6.2.a_ag_a_m_a_aq$72$(not in LMFDB)
6.2.a_ag_a_u_a_abw$72$(not in LMFDB)
6.2.a_ag_a_y_a_ace$72$(not in LMFDB)
6.2.a_ae_a_ae_a_bg$72$(not in LMFDB)
6.2.a_ae_a_a_a_q$72$(not in LMFDB)
6.2.a_ae_a_i_a_aq$72$(not in LMFDB)
6.2.a_ae_a_m_a_abg$72$(not in LMFDB)
6.2.a_ae_a_q_a_abg$72$(not in LMFDB)
6.2.a_ac_ae_ae_i_q$72$(not in LMFDB)
6.2.a_ac_a_ae_a_q$72$(not in LMFDB)
6.2.a_ac_a_a_a_i$72$(not in LMFDB)
6.2.a_ac_a_e_a_aq$72$(not in LMFDB)
6.2.a_ac_a_i_a_ai$72$(not in LMFDB)
6.2.a_ac_a_m_a_aq$72$(not in LMFDB)
6.2.a_ac_e_ae_ai_q$72$(not in LMFDB)
6.2.a_a_ae_a_a_q$72$(not in LMFDB)
6.2.a_a_a_ae_a_a$72$(not in LMFDB)
6.2.a_a_a_a_a_aq$72$(not in LMFDB)
6.2.a_a_a_a_a_q$72$(not in LMFDB)
6.2.a_a_a_i_a_a$72$(not in LMFDB)
6.2.a_a_e_a_a_q$72$(not in LMFDB)
6.2.a_c_ae_e_ai_q$72$(not in LMFDB)
6.2.a_c_a_ae_a_aq$72$(not in LMFDB)
6.2.a_c_a_a_a_ai$72$(not in LMFDB)
6.2.a_c_a_e_a_q$72$(not in LMFDB)
6.2.a_c_a_i_a_i$72$(not in LMFDB)
6.2.a_c_a_m_a_q$72$(not in LMFDB)
6.2.a_c_e_e_i_q$72$(not in LMFDB)
6.2.a_e_ae_i_aq_q$72$(not in LMFDB)
6.2.a_e_a_ae_a_abg$72$(not in LMFDB)
6.2.a_e_a_a_a_aq$72$(not in LMFDB)
6.2.a_e_a_i_a_q$72$(not in LMFDB)
6.2.a_e_a_m_a_bg$72$(not in LMFDB)
6.2.a_e_a_q_a_bg$72$(not in LMFDB)
6.2.a_e_e_i_q_q$72$(not in LMFDB)
6.2.a_g_ae_m_ay_q$72$(not in LMFDB)
6.2.a_g_a_m_a_q$72$(not in LMFDB)
6.2.a_g_a_u_a_bw$72$(not in LMFDB)
6.2.a_g_a_y_a_ce$72$(not in LMFDB)
6.2.a_g_e_m_y_q$72$(not in LMFDB)
6.2.a_i_a_bc_a_cm$72$(not in LMFDB)
6.2.a_i_a_bg_a_dc$72$(not in LMFDB)
6.2.a_k_a_bs_a_ei$72$(not in LMFDB)
6.2.a_m_a_ci_a_ge$72$(not in LMFDB)
6.2.c_ag_am_m_q_aq$72$(not in LMFDB)
6.2.c_ae_am_ae_q_bg$72$(not in LMFDB)
6.2.c_ae_ai_i_i_aq$72$(not in LMFDB)
6.2.c_ac_am_am_q_bw$72$(not in LMFDB)
6.2.c_ac_ai_ae_i_q$72$(not in LMFDB)
6.2.c_ac_ae_e_a_aq$72$(not in LMFDB)
6.2.c_ac_ae_i_i_ai$72$(not in LMFDB)
6.2.c_a_ai_ai_i_bg$72$(not in LMFDB)
6.2.c_a_ae_ae_a_a$72$(not in LMFDB)
6.2.c_a_ae_a_i_q$72$(not in LMFDB)
6.2.c_a_a_a_ai_aq$72$(not in LMFDB)
6.2.c_a_a_i_i_a$72$(not in LMFDB)
6.2.c_c_a_ae_ai_aq$72$(not in LMFDB)
6.2.c_c_a_e_i_q$72$(not in LMFDB)
6.2.c_c_e_ae_aq_aq$72$(not in LMFDB)
6.2.c_c_e_i_i_i$72$(not in LMFDB)
6.2.c_e_a_a_ai_a$72$(not in LMFDB)
6.2.c_e_e_ae_aq_abg$72$(not in LMFDB)
6.2.c_e_e_a_ai_aq$72$(not in LMFDB)
6.2.c_e_e_i_i_q$72$(not in LMFDB)
6.2.c_e_e_m_q_bg$72$(not in LMFDB)
6.2.c_e_i_i_i_q$72$(not in LMFDB)
6.2.c_e_i_q_y_bg$72$(not in LMFDB)
6.2.c_e_m_q_y_bw$72$(not in LMFDB)
6.2.c_g_e_e_aq_aq$72$(not in LMFDB)
6.2.c_g_i_m_i_q$72$(not in LMFDB)
6.2.c_g_i_u_y_bw$72$(not in LMFDB)
6.2.c_g_m_u_bg_bw$72$(not in LMFDB)
6.2.c_g_m_y_bo_ce$72$(not in LMFDB)
6.2.c_i_m_bc_bg_cm$72$(not in LMFDB)
6.2.c_i_m_bg_bo_dc$72$(not in LMFDB)
6.2.c_i_q_bg_ce_dc$72$(not in LMFDB)
6.2.c_k_q_bs_ce_ei$72$(not in LMFDB)
6.2.c_k_u_bs_dc_ei$72$(not in LMFDB)
6.2.c_m_u_ci_dc_ge$72$(not in LMFDB)
6.2.e_a_ay_abk_bg_ey$72$(not in LMFDB)
6.2.e_c_aq_abc_q_dc$72$(not in LMFDB)
6.2.e_e_ai_au_a_bg$72$(not in LMFDB)
6.2.e_e_ai_aq_q_cm$72$(not in LMFDB)
6.2.e_e_a_a_aq_abw$72$(not in LMFDB)
6.2.e_g_a_am_aq_aq$72$(not in LMFDB)
6.2.e_g_a_ae_q_bw$72$(not in LMFDB)
6.2.e_g_e_ae_ay_abw$72$(not in LMFDB)
6.2.e_g_i_q_q_i$72$(not in LMFDB)
6.2.e_i_i_ae_abg_acm$72$(not in LMFDB)
6.2.e_i_i_i_q_bg$72$(not in LMFDB)
6.2.e_i_m_q_q_q$72$(not in LMFDB)
6.2.e_k_m_e_ay_abw$72$(not in LMFDB)
6.2.e_k_q_u_q_q$72$(not in LMFDB)
6.2.e_k_q_bc_bw_dc$72$(not in LMFDB)
6.2.e_k_u_bk_ce_dc$72$(not in LMFDB)
6.2.e_k_y_bw_dc_eq$72$(not in LMFDB)
6.2.e_m_y_bs_cm_ds$72$(not in LMFDB)
6.2.e_m_y_bw_dc_ey$72$(not in LMFDB)
6.2.e_m_bc_ce_ds_fo$72$(not in LMFDB)
6.2.e_m_bg_cm_ei_gu$72$(not in LMFDB)
6.2.e_o_bg_cq_ei_gu$72$(not in LMFDB)
6.2.e_o_bk_cy_fg_ia$72$(not in LMFDB)
6.2.e_q_bo_do_ge_jw$72$(not in LMFDB)
6.2.g_o_m_am_abw_adc$72$(not in LMFDB)
6.2.g_q_u_ae_acm_aey$72$(not in LMFDB)
6.2.g_q_y_y_y_bg$72$(not in LMFDB)
6.2.g_s_bg_bk_y_q$72$(not in LMFDB)
6.2.g_u_bs_cy_ei_ge$72$(not in LMFDB)
6.2.g_u_bw_ds_gm_jw$72$(not in LMFDB)
6.2.g_u_ca_ei_hs_ls$72$(not in LMFDB)
6.2.g_w_ce_em_hs_ls$72$(not in LMFDB)
6.2.g_w_ci_fc_jg_oe$72$(not in LMFDB)
6.2.g_y_cq_ga_lc_rg$72$(not in LMFDB)
6.2.i_bc_bw_m_aey_alc$72$(not in LMFDB)
6.2.i_be_cm_cy_bg_aq$72$(not in LMFDB)
6.2.i_bi_ds_hw_no_ui$72$(not in LMFDB)
6.2.i_bi_dw_iu_qi_zg$72$(not in LMFDB)
6.2.i_bk_ei_ki_ts_beu$72$(not in LMFDB)
6.2.k_ca_gy_rs_bjc_cdk$72$(not in LMFDB)
6.2.ag_s_abg_bg_ai_aq$90$(not in LMFDB)
6.2.ae_i_am_m_ai_i$90$(not in LMFDB)
6.2.ac_c_a_a_ai_q$90$(not in LMFDB)
6.2.a_a_ae_ae_i_i$90$(not in LMFDB)
6.2.a_a_e_ae_ai_i$90$(not in LMFDB)
6.2.c_c_a_a_ai_aq$90$(not in LMFDB)
6.2.c_c_a_a_i_q$90$(not in LMFDB)
6.2.g_s_bg_bg_i_aq$90$(not in LMFDB)
6.2.ac_c_a_ae_i_ai$126$(not in LMFDB)
6.2.ae_i_ai_e_a_a$144$(not in LMFDB)
6.2.ac_c_ae_e_a_a$144$(not in LMFDB)
6.2.ac_e_ae_e_a_a$144$(not in LMFDB)
6.2.a_ae_a_e_a_a$144$(not in LMFDB)
6.2.a_ac_a_e_a_a$144$(not in LMFDB)
6.2.a_a_a_e_a_a$144$(not in LMFDB)
6.2.a_c_a_e_a_a$144$(not in LMFDB)
6.2.a_e_a_e_a_a$144$(not in LMFDB)
6.2.c_c_e_e_a_a$144$(not in LMFDB)
6.2.c_e_e_e_a_a$144$(not in LMFDB)
6.2.e_i_i_e_a_a$144$(not in LMFDB)
6.2.ae_g_a_ai_a_q$360$(not in LMFDB)
6.2.ae_k_aq_q_ai_a$360$(not in LMFDB)
6.2.ae_k_aq_y_abg_bw$360$(not in LMFDB)
6.2.ac_ac_i_ai_ai_bg$360$(not in LMFDB)
6.2.ac_a_a_e_a_ai$360$(not in LMFDB)
6.2.ac_a_e_ae_ai_y$360$(not in LMFDB)
6.2.ac_c_a_a_a_a$360$(not in LMFDB)
6.2.ac_e_ai_m_aq_y$360$(not in LMFDB)
6.2.ac_e_ae_e_ai_i$360$(not in LMFDB)
6.2.ac_g_ai_i_ai_a$360$(not in LMFDB)
6.2.ac_g_ai_q_aq_bg$360$(not in LMFDB)
6.2.a_ag_a_q_a_abg$360$(not in LMFDB)
6.2.a_ae_a_m_a_ay$360$(not in LMFDB)
6.2.a_ac_a_a_a_a$360$(not in LMFDB)
6.2.a_ac_a_i_a_aq$360$(not in LMFDB)
6.2.a_a_a_e_a_ai$360$(not in LMFDB)
6.2.a_a_a_e_a_i$360$(not in LMFDB)
6.2.a_c_a_a_ai_a$360$(not in LMFDB)
6.2.a_c_a_a_a_a$360$(not in LMFDB)
6.2.a_c_a_a_i_a$360$(not in LMFDB)
6.2.a_c_a_i_a_q$360$(not in LMFDB)
6.2.a_e_a_m_a_y$360$(not in LMFDB)
6.2.a_g_a_q_a_bg$360$(not in LMFDB)
6.2.c_ac_ai_ai_i_bg$360$(not in LMFDB)
6.2.c_a_ae_ae_i_y$360$(not in LMFDB)
6.2.c_a_a_e_a_ai$360$(not in LMFDB)
6.2.c_c_a_a_a_a$360$(not in LMFDB)
6.2.c_e_e_e_i_i$360$(not in LMFDB)
6.2.c_e_i_m_q_y$360$(not in LMFDB)
6.2.c_g_i_i_i_a$360$(not in LMFDB)
6.2.c_g_i_q_q_bg$360$(not in LMFDB)
6.2.e_g_a_ai_a_q$360$(not in LMFDB)
6.2.e_k_q_q_i_a$360$(not in LMFDB)
6.2.e_k_q_y_bg_bw$360$(not in LMFDB)
6.2.a_ac_a_e_a_ai$504$(not in LMFDB)
6.2.a_c_a_e_a_i$504$(not in LMFDB)

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