LMFDB - Abelian variety search results

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Results (1-50 of 2498 matches)

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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.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.ac² $\times$ 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.ac³ $\times$ 1.2.ab
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_f²
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.ac² $\times$ 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_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.ac² $\times$ 1.2.ab²
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.ac² $\times$ 2.2.ab_ab
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.ac² $\times$ 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_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.ac² $\times$ 2.2.ab_b
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_aba_bo	$4$	$\F_{2}$	$2$	$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$1$	$3$	$-2$	$4$	1.2.ac³ $\times$ 1.2.b
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_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.ac² $\times$ 2.2.ab_d
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.ac² $\times$ 1.2.ab $\times$ 1.2.a
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.ac² $\times$ 2.2.a_ad
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.ac² $\times$ 2.2.a_ab
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_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_am_q	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + x^{2} + 4 x^{4} )$	$2$	$2$	$-1$	$6$	1.2.ac² $\times$ 2.2.a_b
4.2.ae_k_at_be	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$3$	$1$	$-1$	$4$	1.2.ac $\times$ 1.2.b $\times$ 2.2.ad_f
4.2.ae_l_aw_bi	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$2$	$2$	$-1$	$4$	1.2.ab² $\times$ 2.2.ac_c
4.2.ae_l_aw_bk	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$	$2$	$2$	$-1$	$6$	1.2.ac $\times$ 1.2.a $\times$ 2.2.ac_d
4.2.ae_l_au_bg	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$	$2$	$2$	$-1$	$8$	1.2.ac² $\times$ 1.2.ab $\times$ 1.2.b
4.2.ae_m_az_bo	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$3$	$1$	$-1$	$6$	1.2.ab $\times$ 1.2.a $\times$ 2.2.ad_f
4.2.ae_n_aba_bs	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}$	$2$	$2$	$-1$	$12$	1.2.ac $\times$ 1.2.ab² $\times$ 1.2.a
4.2.ad_b_g_am	$4$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$1$	2.2.ad_f $\times$ 2.2.a_ae
4.2.ad_c_g_aq	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$	$1$	$3$	$0$	$2$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.a_ae
4.2.ad_d_ag_o	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$1$	2.2.ac_c $\times$ 2.2.ab_ab
4.2.ad_d_a_ac	$4$	$\F_{2}$	$2$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x^{2} + 4 x^{4} )$	$2$	$2$	$0$	$3$	2.2.ad_f $\times$ 2.2.a_ac
4.2.ad_d_g_aq	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$7$	1.2.ac² $\times$ 2.2.b_ab
4.2.ad_e_ai_q	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$	$1$	$3$	$0$	$2$	2.2.ac_c $\times$ 2.2.ab_a
4.2.ad_e_ad_d	$4$	$\F_{2}$	$2$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x^{2} + 4 x^{4} )$	$4$	$0$	$0$	$4$	2.2.ad_f $\times$ 2.2.a_ab
4.2.ad_e_a_ae	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 2 x^{2} + 4 x^{4} )$	$1$	$3$	$0$	$6$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.a_ac
4.2.ad_e_c_ai	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + x + 2 x^{3} + 4 x^{4} )$	$1$	$3$	$0$	$8$	1.2.ac² $\times$ 2.2.b_a
4.2.ad_f_ak_s	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$3$	2.2.ac_c $\times$ 2.2.ab_b
4.2.ad_f_ai_m	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$3$	1.2.ac $\times$ 1.2.a $\times$ 2.2.ab_ab
4.2.ad_f_ag_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$5$	1.2.ac $\times$ 1.2.c $\times$ 2.2.ad_f
4.2.ad_f_ad_c	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$	$3$	$1$	$0$	$8$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.a_ab
4.2.ad_f_ac_a	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$9$	1.2.ac² $\times$ 2.2.b_b
4.2.ad_g_am_u	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$1$	$3$	$0$	$4$	1.2.ac $\times$ 1.2.b $\times$ 2.2.ac_c
4.2.ad_g_ak_q	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - x - 2 x^{3} + 4 x^{4} )$	$1$	$3$	$0$	$6$	1.2.ac $\times$ 1.2.a $\times$ 2.2.ab_a
4.2.ad_g_ag_i	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$	$1$	$3$	$0$	$10$	1.2.ac² $\times$ 1.2.ab $\times$ 1.2.c
4.2.ad_h_ao_w	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$5$	2.2.ac_c $\times$ 2.2.ab_d
4.2.ad_h_am_s	$4$	$\F_{2}$	$2$	$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 + 2 x^{2} + 4 x^{4} )$	$2$	$2$	$0$	$7$	2.2.ad_f $\times$ 2.2.a_c
4.2.ad_h_am_u	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$9$	1.2.ac $\times$ 1.2.a $\times$ 2.2.ab_b
4.2.ad_h_ak_q	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )$	$2$	$2$	$0$	$11$	1.2.ac² $\times$ 2.2.b_d
4.2.ad_h_aj_o	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + x^{2} + 4 x^{4} )$	$3$	$1$	$0$	$12$	1.2.ac $\times$ 1.2.ab $\times$ 2.2.a_b
4.2.ad_i_aq_y	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$1$	$3$	$0$	$6$	1.2.ab $\times$ 1.2.a $\times$ 2.2.ac_c

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Elliptic curves over $\Q$
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Results (1-50 of 2498 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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