Abelian Variety Search Results

base field	base char.	dimension	$p$-rank	initial coefficients
slopes	points on variety	points on curve	simple factors
angle rank	# Jacobians	# Hyp. Jacobians	# twists	max twist degree
End. degree	$p$-rank deficit
simple	geom. simple	primitive	princ polarizable	jacobian
Use geometric decomposition in the following inputs
dim 1 factors	dim 2 factors	dim 3 factors	dim 4 factors	dim 5 factors
(distinct)	(distinct)	(distinct)	number field	Galois group

Results (displaying matches 1-50 of )

LMFDB label	dimension	base field	L-polynomial	$p$-rank	isogeny factors
6.2.am_cu_aku_bea_acku_dwy	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{6}$	$ 0$	1.2.ac^6
6.2.al_cj_aio_wq_abtw_cuy	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^4 $\times$ 2.2.ad_f
6.2.al_ck_aiw_xw_abwy_dae	6	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{5}$	$ 1$	1.2.ac^5 $\times$ 1.2.ab
6.2.ak_by_agi_pg_abcy_bsy	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 0$	1.2.ac^4 $\times$ 2.2.ac_c
6.2.ak_bz_ags_qz_abho_cay	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$	$ 4$	1.2.ac^2 $\times$ 2.2.ad_f^2
6.2.ak_bz_agr_qs_abgs_bzk	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^3 $\times$ 3.2.ae_j_ap
6.2.ak_bz_agq_qm_abga_bye	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^4 $\times$ 2.2.ac_d
6.2.ak_ca_agz_ry_abju_ceq	6	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$ 3$	1.2.ac^3 $\times$ 1.2.ab $\times$ 2.2.ad_f
6.2.ak_ca_agy_rs_abjc_cdk	6	$\F_{2}$	$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{5}$	$ 0$	1.2.ac^5 $\times$ 1.2.a
6.2.ak_cb_ahg_sy_abme_ciq	6	$\F_{2}$	$( 1 - x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{4}$	$ 2$	1.2.ac^4 $\times$ 1.2.ab^2
6.2.aj_bm_adt_gk_aig_km	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^3 $\times$ 3.2.ad_c_b
6.2.aj_bn_aec_hw_ama_qy	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^4 $\times$ 2.2.ab_ab
6.2.aj_bo_aem_jp_aqq_yy	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac^2 $\times$ 4.2.af_m_au_bd
6.2.aj_bo_aek_jc_apc_we	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - x - 2 x^{3} + 4 x^{4} )$	$ 1$	1.2.ac^4 $\times$ 2.2.ab_a
6.2.aj_bp_aew_li_avg_bgy	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^2 $\times$ 2.2.ad_f $\times$ 2.2.ac_c
6.2.aj_bp_aev_lb_auk_bfk	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac^2 $\times$ 4.2.af_n_az_bn
6.2.aj_bp_aet_ko_asw_bcq	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^3 $\times$ 3.2.ad_f_ah
6.2.aj_bp_aes_ki_ase_bbk	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^4 $\times$ 2.2.ab_b
6.2.aj_bq_aff_ms_ayp_bmn	6	$\F_{2}$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{3}$	$ 6$	2.2.ad_f^3
6.2.aj_bq_afe_mm_axz_blm	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$	$ 5$	1.2.ac $\times$ 2.2.ad_f $\times$ 3.2.ae_j_ap
6.2.aj_bq_afd_mh_axm_bkq	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 4$	1.2.ac^2 $\times$ 2.2.ad_f $\times$ 2.2.ac_d
6.2.aj_bq_afc_ma_awq_bjc	6	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 1$	1.2.ac^3 $\times$ 1.2.ab $\times$ 2.2.ac_c
6.2.aj_bq_afb_lu_avy_bhw	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^3 $\times$ 3.2.ad_g_aj
6.2.aj_bq_afa_lo_avg_bgq	6	$\F_{2}$	$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{5}$	$ 1$	1.2.ac^5 $\times$ 1.2.b
6.2.aj_br_afl_nl_abaf_bpe	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$	$ 5$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.ad_f^2
6.2.aj_br_afk_nf_azo_boa	6	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$	$ 4$	1.2.ac^2 $\times$ 1.2.ab $\times$ 3.2.ae_j_ap
6.2.aj_br_afk_ng_azs_boi	6	$\F_{2}$	$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^3 $\times$ 1.2.a $\times$ 2.2.ad_f
6.2.aj_br_afj_na_aza_bnc	6	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 3$	1.2.ac^3 $\times$ 1.2.ab $\times$ 2.2.ac_d
6.2.aj_br_afi_mu_ayi_blw	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^4 $\times$ 2.2.ab_d
6.2.aj_bs_afr_of_abby_bsa	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$ 4$	1.2.ac^2 $\times$ 1.2.ab^2 $\times$ 2.2.ad_f
6.2.aj_bs_afq_oa_abbk_brc	6	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$	$ 1$	1.2.ac^4 $\times$ 1.2.ab $\times$ 1.2.a
6.2.aj_bt_afx_pa_abdu_bvc	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x + 2 x^{2} )^{3}$	$ 3$	1.2.ac^3 $\times$ 1.2.ab^3
6.2.ai_bc_abx_t_ec_ajo	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac^2 $\times$ 4.2.ae_e_h_av
6.2.ai_bc_abw_m_ey_alc	6	$\F_{2}$	$( 1 - 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{4}$	$ 0$	1.2.ac^4 $\times$ 2.2.a_ae
6.2.ai_bd_acg_cf_i_adc	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac^2 $\times$ 4.2.ae_f_c_al
6.2.ai_bd_ace_bs_bw_afw	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - 3 x^{2} + 4 x^{4} )$	$ 2$	1.2.ac^4 $\times$ 2.2.a_ad
6.2.ai_be_acs_en_agf_ik	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 5$	1.2.ac $\times$ 2.2.ad_f $\times$ 3.2.ad_c_b
6.2.ai_be_acq_dy_aei_ey	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 6 x^{2} - 4 x^{3} + 2 x^{4} - 8 x^{5} + 24 x^{6} - 32 x^{7} + 16 x^{8} )$	$ 0$	1.2.ac^2 $\times$ 4.2.ae_g_ae_c
6.2.ai_be_acn_de_aby_q	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^3 $\times$ 3.2.ac_a_d
6.2.ai_be_acm_cy_abg_aq	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - 2 x^{2} + 4 x^{4} )$	$ 0$	1.2.ac^4 $\times$ 2.2.a_ac
6.2.ai_bf_ada_fr_aiy_my	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$ 4$	1.2.ac^2 $\times$ 2.2.ad_f $\times$ 2.2.ab_ab
6.2.ai_bf_acx_ex_ago_iq	6	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 4$	1.2.ac^2 $\times$ 1.2.ab $\times$ 3.2.ad_c_b
6.2.ai_bf_acw_eq_afs_hc	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$	$ 2$	1.2.ac^3 $\times$ 3.2.ac_b_a
6.2.ai_bf_acv_ek_afa_fw	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^3 $\times$ 3.2.ac_b_b
6.2.ai_bf_acu_ee_aei_eq	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{4}( 1 - x^{2} + 4 x^{4} )$	$ 2$	1.2.ac^4 $\times$ 2.2.a_ab
6.2.ai_bg_adk_hk_ano_uy	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )^{2}$	$ 0$	1.2.ac^2 $\times$ 2.2.ac_c^2
6.2.ai_bg_adj_hb_amh_sn	6	$\F_{2}$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$	$ 6$	2.2.ad_f $\times$ 4.2.af_m_au_bd
6.2.ai_bg_adh_gq_ale_qq	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$	$ 3$	1.2.ac^2 $\times$ 2.2.ad_f $\times$ 2.2.ab_a
6.2.ai_bg_adg_gj_aki_pc	6	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac^2 $\times$ 4.2.ae_i_am_r
6.2.ai_bg_adf_gc_ajm_no	6	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$ 3$	1.2.ac^3 $\times$ 1.2.ab $\times$ 2.2.ab_ab

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