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
5.2.ak_by_age_nw_awu	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{5}$	$ 0$	1.2.ac^5
5.2.aj_bp_aes_kc_aqi	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^3 $\times$ 2.2.ad_f
5.2.aj_bq_aey_ku_aro	5	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$	$ 1$	1.2.ac^4 $\times$ 1.2.ab
5.2.ai_bg_adg_gi_ajw	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 0$	1.2.ac^3 $\times$ 2.2.ac_c
5.2.ai_bh_ado_hj_alu	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$	$ 4$	1.2.ac $\times$ 2.2.ad_f^2
5.2.ai_bh_adn_he_alk	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^2 $\times$ 3.2.ae_j_ap
5.2.ai_bh_adm_ha_alc	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^3 $\times$ 2.2.ac_d
5.2.ai_bi_adt_hw_amq	5	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$ 3$	1.2.ac^2 $\times$ 1.2.ab $\times$ 2.2.ad_f
5.2.ai_bi_ads_hs_ami	5	$\F_{2}$	$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$	$ 0$	1.2.ac^4 $\times$ 1.2.a
5.2.ai_bj_ady_ik_ano	5	$\F_{2}$	$( 1 - x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$	$ 2$	1.2.ac^3 $\times$ 1.2.ab^2
5.2.ah_w_abn_bs_abw	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^2 $\times$ 3.2.ad_c_b
5.2.ah_x_abu_co_adk	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^3 $\times$ 2.2.ab_ab
5.2.ah_y_acc_dp_afi	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac $\times$ 4.2.af_m_au_bd
5.2.ah_y_aca_dg_aeq	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x - 2 x^{3} + 4 x^{4} )$	$ 1$	1.2.ac^3 $\times$ 2.2.ab_a
5.2.ah_z_ack_eq_ahg	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ac_c
5.2.ah_z_acj_el_agw	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac $\times$ 4.2.af_n_az_bn
5.2.ah_z_ach_ec_age	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^2 $\times$ 3.2.ad_f_ah
5.2.ah_z_acg_dy_afw	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^3 $\times$ 2.2.ab_b
5.2.ah_ba_acq_fg_aih	5	$\F_{2}$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$	$ 5$	2.2.ad_f $\times$ 3.2.ae_j_ap
5.2.ah_ba_acp_fd_aic	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 4$	1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ac_d
5.2.ah_ba_aco_ey_ahs	5	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 1$	1.2.ac^2 $\times$ 1.2.ab $\times$ 2.2.ac_c
5.2.ah_ba_acn_eu_ahk	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^2 $\times$ 3.2.ad_g_aj
5.2.ah_ba_acm_eq_ahc	5	$\F_{2}$	$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$	$ 1$	1.2.ac^4 $\times$ 1.2.b
5.2.ah_bb_acv_ft_ajd	5	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$	$ 5$	1.2.ab $\times$ 2.2.ad_f^2
5.2.ah_bb_acu_fp_aiw	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$	$ 4$	1.2.ac $\times$ 1.2.ab $\times$ 3.2.ae_j_ap
5.2.ah_bb_acu_fq_aiy	5	$\F_{2}$	$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^2 $\times$ 1.2.a $\times$ 2.2.ad_f
5.2.ah_bb_act_fm_aiq	5	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$ 3$	1.2.ac^2 $\times$ 1.2.ab $\times$ 2.2.ac_d
5.2.ah_bb_acs_fi_aii	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$	$ 2$	1.2.ac^3 $\times$ 2.2.ab_d
5.2.ah_bc_acz_gd_aju	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$ 4$	1.2.ac $\times$ 1.2.ab^2 $\times$ 2.2.ad_f
5.2.ah_bc_acy_ga_ajo	5	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$ 1$	1.2.ac^3 $\times$ 1.2.ab $\times$ 1.2.a
5.2.ah_bd_add_go_akm	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{3}$	$ 3$	1.2.ac^2 $\times$ 1.2.ab^3
5.2.ag_o_aj_abb_cs	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac $\times$ 4.2.ae_e_h_av
5.2.ag_o_ai_abg_dc	5	$\F_{2}$	$( 1 - 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$	$ 0$	1.2.ac^3 $\times$ 2.2.a_ae
5.2.ag_p_aq_af_be	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac $\times$ 4.2.ae_f_c_al
5.2.ag_p_ao_ao_bw	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x^{2} + 4 x^{4} )$	$ 2$	1.2.ac^3 $\times$ 2.2.a_ad
5.2.ag_q_aba_bh_abr	5	$\F_{2}$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 5$	2.2.ad_f $\times$ 3.2.ad_c_b
5.2.ag_q_ay_w_au	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 6 x^{2} - 4 x^{3} + 2 x^{4} - 8 x^{5} + 24 x^{6} - 32 x^{7} + 16 x^{8} )$	$ 0$	1.2.ac $\times$ 4.2.ae_g_ae_c
5.2.ag_q_av_i_i	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^2 $\times$ 3.2.ac_a_d
5.2.ag_q_au_e_q	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x^{2} + 4 x^{4} )$	$ 0$	1.2.ac^3 $\times$ 2.2.a_ac
5.2.ag_r_abg_bx_acs	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$ 4$	1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ab_ab
5.2.ag_r_abd_bj_abq	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$	$ 4$	1.2.ac $\times$ 1.2.ab $\times$ 3.2.ad_c_b
5.2.ag_r_abc_be_abg	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$	$ 2$	1.2.ac^2 $\times$ 3.2.ac_b_a
5.2.ag_r_abb_ba_ay	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^2 $\times$ 3.2.ac_b_b
5.2.ag_r_aba_w_aq	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x^{2} + 4 x^{4} )$	$ 2$	1.2.ac^3 $\times$ 2.2.a_ab
5.2.ag_s_abo_cy_aeq	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )^{2}$	$ 0$	1.2.ac $\times$ 2.2.ac_c^2
5.2.ag_s_abl_ck_ado	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$	$ 3$	1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ab_a
5.2.ag_s_abk_cf_ade	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8} )$	$ 4$	1.2.ac $\times$ 4.2.ae_i_am_r
5.2.ag_s_abj_ca_acu	5	$\F_{2}$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$ 3$	1.2.ac^2 $\times$ 1.2.ab $\times$ 2.2.ab_ab
5.2.ag_s_abi_bw_acm	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$	$ 0$	1.2.ac^2 $\times$ 3.2.ac_c_ac
5.2.ag_s_abh_bs_ace	5	$\F_{2}$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$	$ 3$	1.2.ac^2 $\times$ 3.2.ac_c_ab

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