Abelian variety search results

Base field	Base char.	Dimension	$p$-rank	Initial coefficients
Simple	Geom. simple	Primitive	Princ. polarizable	Jacobian
Slopes	Points on variety	Points on curve	Simple factors
Angle rank	# Jacobians	# Hyp. Jacobians	# twists	Max twist degree
End. degree	$p$-rank deficit	(Geom.) Sq.free
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

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Label	Dimension	Base field	Base char.	L-polynomial	$p$-rank	$p$-rank deficit	points on curve	points on variety	Isogeny factors
4.2.ai_bg_adc_fg	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{4}$	$0$	$4$	$-5$	$1$	1.2.ac^4
4.2.ah_z_acg_ds	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$2$	$2$	$-4$	$1$	1.2.ac^2 $\times$ 2.2.ad_f
4.2.ah_ba_ack_ea	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$1$	$3$	$-4$	$2$	1.2.ac^3 $\times$ 1.2.ab
4.2.ag_s_abk_ce	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$0$	$4$	$-3$	$1$	1.2.ac^2 $\times$ 2.2.ac_c
4.2.ag_t_abq_cr	$4$	$\F_{2}$	$2$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$	$4$	$0$	$-3$	$1$	2.2.ad_f^2
4.2.ag_t_abp_co	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$	$3$	$1$	$-3$	$1$	1.2.ac $\times$ 3.2.ae_j_ap
4.2.ag_t_abo_cm	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$2$	$2$	$-3$	$2$	1.2.ac^2 $\times$ 2.2.ac_d
4.2.ag_u_abt_cw	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$3$	$1$	$-3$	$2$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.ad_f
4.2.ag_u_abs_cu	$4$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$0$	$4$	$-3$	$3$	1.2.ac^3 $\times$ 1.2.a
4.2.ag_v_abw_dc	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{2}$	$2$	$2$	$-3$	$4$	1.2.ac^2 $\times$ 1.2.ab^2
4.2.af_k_aj_g	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$	$3$	$1$	$-2$	$1$	1.2.ac $\times$ 3.2.ad_c_b
4.2.af_l_ao_q	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$-2$	$1$	1.2.ac^2 $\times$ 2.2.ab_ab
4.2.af_m_au_bd	$4$	$\F_{2}$	$2$	$1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8}$	$4$	$0$	$-2$	$1$	simple
4.2.af_m_as_y	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x - 2 x^{3} + 4 x^{4} )$	$1$	$3$	$-2$	$2$	1.2.ac^2 $\times$ 2.2.ab_a
4.2.af_n_aba_bq	$4$	$\F_{2}$	$2$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$2$	$2$	$-2$	$1$	2.2.ad_f $\times$ 2.2.ac_c
4.2.af_n_az_bn	$4$	$\F_{2}$	$2$	$1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8}$	$4$	$0$	$-2$	$1$	simple
4.2.af_n_ax_bi	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$	$3$	$1$	$-2$	$2$	1.2.ac $\times$ 3.2.ad_f_ah
4.2.af_n_aw_bg	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$-2$	$3$	1.2.ac^2 $\times$ 2.2.ab_b
4.2.af_o_abd_bv	$4$	$\F_{2}$	$2$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$4$	$0$	$-2$	$2$	2.2.ad_f $\times$ 2.2.ac_d
4.2.af_o_abc_bs	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$1$	$3$	$-2$	$2$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.ac_c
4.2.af_o_abb_bq	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$	$3$	$1$	$-2$	$3$	1.2.ac $\times$ 3.2.ad_g_aj
4.2.af_o_aba_bo	$4$	$\F_{2}$	$2$	$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$1$	$3$	$-2$	$4$	1.2.ac^3 $\times$ 1.2.b
4.2.af_p_abg_bz	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$	$4$	$0$	$-2$	$2$	1.2.ab $\times$ 3.2.ae_j_ap
4.2.af_p_abg_ca	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$2$	$2$	$-2$	$3$	1.2.ac $\times$ 1.2.a $\times$ 2.2.ad_f
4.2.af_p_abf_by	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$3$	$1$	$-2$	$4$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.ac_d
4.2.af_p_abe_bw	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$-2$	$5$	1.2.ac^2 $\times$ 2.2.ab_d
4.2.af_q_abj_cf	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$4$	$0$	$-2$	$4$	1.2.ab^2 $\times$ 2.2.ad_f
4.2.af_q_abi_ce	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$	$1$	$3$	$-2$	$6$	1.2.ac^2 $\times$ 1.2.ab $\times$ 1.2.a
4.2.af_r_abl_ck	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )^{3}$	$3$	$1$	$-2$	$8$	1.2.ac $\times$ 1.2.ab^3
4.2.ae_e_h_av	$4$	$\F_{2}$	$2$	$1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8}$	$4$	$0$	$-1$	$1$	simple
4.2.ae_e_i_ay	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x^{2} )^{2}$	$0$	$4$	$-1$	$1$	1.2.ac^2 $\times$ 2.2.a_ae
4.2.ae_f_c_al	$4$	$\F_{2}$	$2$	$1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8}$	$4$	$0$	$-1$	$1$	simple
4.2.ae_f_e_aq	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x^{2} + 4 x^{4} )$	$2$	$2$	$-1$	$2$	1.2.ac^2 $\times$ 2.2.a_ad
4.2.ae_g_ae_c	$4$	$\F_{2}$	$2$	$1 - 4 x + 6 x^{2} - 4 x^{3} + 2 x^{4} - 8 x^{5} + 24 x^{6} - 32 x^{7} + 16 x^{8}$	$0$	$4$	$-1$	$1$	simple
4.2.ae_g_ab_ag	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$	$3$	$1$	$-1$	$2$	1.2.ac $\times$ 3.2.ac_a_d
4.2.ae_g_a_ai	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x^{2} + 4 x^{4} )$	$0$	$4$	$-1$	$3$	1.2.ac^2 $\times$ 2.2.a_ac
4.2.ae_h_ak_p	$4$	$\F_{2}$	$2$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$4$	$0$	$-1$	$1$	2.2.ad_f $\times$ 2.2.ab_ab
4.2.ae_h_ah_h	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$	$4$	$0$	$-1$	$2$	1.2.ab $\times$ 3.2.ad_c_b
4.2.ae_h_ag_e	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$	$2$	$2$	$-1$	$2$	1.2.ac $\times$ 3.2.ac_b_a
4.2.ae_h_af_c	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$	$3$	$1$	$-1$	$3$	1.2.ac $\times$ 3.2.ac_b_b
4.2.ae_h_ae_a	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x^{2} + 4 x^{4} )$	$2$	$2$	$-1$	$4$	1.2.ac^2 $\times$ 2.2.a_ab
4.2.ae_i_aq_bc	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )^{2}$	$0$	$4$	$-1$	$1$	2.2.ac_c^2
4.2.ae_i_an_u	$4$	$\F_{2}$	$2$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$	$3$	$1$	$-1$	$2$	2.2.ad_f $\times$ 2.2.ab_a
4.2.ae_i_am_r	$4$	$\F_{2}$	$2$	$1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8}$	$4$	$0$	$-1$	$2$	simple
4.2.ae_i_al_o	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$3$	$1$	$-1$	$2$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.ab_ab
4.2.ae_i_ak_m	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$	$0$	$4$	$-1$	$3$	1.2.ac $\times$ 3.2.ac_c_ac
4.2.ae_i_aj_k	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$	$3$	$1$	$-1$	$4$	1.2.ac $\times$ 3.2.ac_c_ab
4.2.ae_i_ai_i	$4$	$\F_{2}$	$2$	$( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$0$	$4$	$-1$	$5$	1.2.ac^3 $\times$ 1.2.c
4.2.ae_j_as_be	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$2$	$2$	$-1$	$2$	2.2.ac_c $\times$ 2.2.ac_d
4.2.ae_j_ar_bb	$4$	$\F_{2}$	$2$	$1 - 4 x + 9 x^{2} - 17 x^{3} + 27 x^{4} - 34 x^{5} + 36 x^{6} - 32 x^{7} + 16 x^{8}$	$4$	$0$	$-1$	$2$	simple

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