LMFDB - Abelian variety search results

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Results (1-50 of 182 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
5.2.ak_by_age_nw_awu	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{5}$	$0$	$5$	$-7$	$1$	1.2.ac⁵
5.2.aj_bq_aey_ku_aro	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$	$1$	$4$	$-6$	$2$	1.2.ac⁴ $\times$ 1.2.ab
5.2.ai_bi_ads_hs_ami	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$	$0$	$5$	$-5$	$3$	1.2.ac⁴ $\times$ 1.2.a
5.2.ah_y_acc_dp_afi	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$	$4$	$1$	$-4$	$1$	1.2.ac $\times$ 4.2.af_m_au_bd
5.2.ah_ba_acm_eq_ahc	$5$	$\F_{2}$	$2$	$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$	$1$	$4$	$-4$	$4$	1.2.ac⁴ $\times$ 1.2.b
5.2.ah_bc_acy_ga_ajo	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$1$	$4$	$-4$	$6$	1.2.ac³ $\times$ 1.2.ab $\times$ 1.2.a
5.2.ag_o_ai_abg_dc	$5$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$	$0$	$5$	$-3$	$1$	1.2.ac³ $\times$ 2.2.a_ae
5.2.ag_s_abg_bo_abw	$5$	$\F_{2}$	$2$	$( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$	$0$	$5$	$-3$	$5$	1.2.ac⁴ $\times$ 1.2.c
5.2.ag_w_ace_ei_agu	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$	$0$	$5$	$-3$	$9$	1.2.ac³ $\times$ 1.2.a²
5.2.af_k_ae_ay_ce	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x^{2} )^{2}$	$1$	$4$	$-2$	$2$	1.2.ac² $\times$ 1.2.ab $\times$ 2.2.a_ae
5.2.af_o_abe_cb_adc	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$	$4$	$1$	$-2$	$3$	1.2.a $\times$ 4.2.af_m_au_bd
5.2.af_o_ay_bg_abo	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$1$	$4$	$-2$	$10$	1.2.ac³ $\times$ 1.2.ab $\times$ 1.2.c
5.2.af_q_abk_cq_aea	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$1$	$4$	$-2$	$12$	1.2.ac³ $\times$ 1.2.a $\times$ 1.2.b
5.2.af_s_abs_dk_afg	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x^{2} )^{2}$	$1$	$4$	$-2$	$18$	1.2.ac² $\times$ 1.2.ab $\times$ 1.2.a²
5.2.ae_g_a_aq_bg	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x^{2} )^{2}$	$0$	$5$	$-1$	$3$	1.2.ac² $\times$ 1.2.a $\times$ 2.2.a_ae
5.2.ae_k_aq_y_abg	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$0$	$5$	$-1$	$15$	1.2.ac³ $\times$ 1.2.a $\times$ 1.2.c
5.2.ae_n_abc_cd_ade	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )^{2}$	$4$	$1$	$-1$	$25$	1.2.ac $\times$ 2.2.ab_d²
5.2.ae_o_abg_cm_ads	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x^{2} )^{3}$	$0$	$5$	$-1$	$27$	1.2.ac² $\times$ 1.2.a³
5.2.ad_c_e_ai_i	$5$	$\F_{2}$	$2$	$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x^{2} )^{2}$	$1$	$4$	$0$	$4$	1.2.ac² $\times$ 1.2.b $\times$ 2.2.a_ae
5.2.ad_e_ag_n_aw	$5$	$\F_{2}$	$2$	$( 1 + 2 x + 2 x^{2} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$	$4$	$1$	$0$	$5$	1.2.c $\times$ 4.2.af_m_au_bd
5.2.ad_e_a_am_y	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x^{2} )^{2}$	$1$	$4$	$0$	$6$	1.2.ac $\times$ 1.2.ab $\times$ 1.2.a $\times$ 2.2.a_ae
5.2.ad_g_ai_q_ay	$5$	$\F_{2}$	$2$	$( 1 + x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$	$1$	$4$	$0$	$20$	1.2.ac³ $\times$ 1.2.b $\times$ 1.2.c
5.2.ad_i_am_u_ay	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$	$1$	$4$	$0$	$30$	1.2.ac² $\times$ 1.2.ab $\times$ 1.2.a $\times$ 1.2.c
5.2.ad_k_au_bo_ace	$5$	$\F_{2}$	$2$	$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x^{2} )^{2}$	$1$	$4$	$0$	$36$	1.2.ac² $\times$ 1.2.a² $\times$ 1.2.b
5.2.ad_m_ay_ca_acu	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )^{3}$	$1$	$4$	$0$	$54$	1.2.ac $\times$ 1.2.ab $\times$ 1.2.a³
5.2.ac_ag_q_i_abw	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 2 x^{2} )^{4}$	$0$	$5$	$1$	$1$	1.2.ac $\times$ 2.2.a_ae²
5.2.ac_ad_k_d_aba	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 5 x^{2} + 13 x^{4} - 20 x^{6} + 16 x^{8} )$	$4$	$1$	$1$	$5$	1.2.ac $\times$ 4.2.a_af_a_n
5.2.ac_ac_i_a_aq	$5$	$\F_{2}$	$2$	$( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x^{2} )^{2}$	$0$	$5$	$1$	$5$	1.2.ac² $\times$ 1.2.c $\times$ 2.2.a_ae
5.2.ac_ab_g_d_as	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 3 x^{2} + 9 x^{4} - 12 x^{6} + 16 x^{8} )$	$4$	$1$	$1$	$11$	1.2.ac $\times$ 4.2.a_ad_a_j
5.2.ac_c_a_ai_q	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - 2 x^{2} )^{2}( 1 + 2 x^{2} )^{2}$	$0$	$5$	$1$	$9$	1.2.ac $\times$ 1.2.a² $\times$ 2.2.a_ae
5.2.ac_c_a_i_aq	$5$	$\F_{2}$	$2$	$( 1 + 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$	$0$	$5$	$1$	$25$	1.2.ac³ $\times$ 1.2.c²
5.2.ac_e_aj_n_as	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} - 5 x^{3} - x^{4} - 10 x^{5} + 8 x^{6} + 16 x^{8} )$	$4$	$1$	$1$	$11$	1.2.ac $\times$ 4.2.a_c_af_ab
5.2.ac_e_b_ah_w	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} + 5 x^{3} - x^{4} + 10 x^{5} + 8 x^{6} + 16 x^{8} )$	$4$	$1$	$1$	$41$	1.2.ac $\times$ 4.2.a_c_f_ab
5.2.ac_f_ag_p_as	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 3 x^{2} + 9 x^{4} + 12 x^{6} + 16 x^{8} )$	$4$	$1$	$1$	$41$	1.2.ac $\times$ 4.2.a_d_a_j
5.2.ac_g_ai_q_aq	$5$	$\F_{2}$	$2$	$( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x^{2} )^{2}$	$0$	$5$	$1$	$45$	1.2.ac² $\times$ 1.2.a² $\times$ 1.2.c
5.2.ac_h_ak_x_aba	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )$	$4$	$1$	$1$	$55$	1.2.ac $\times$ 2.2.ab_d $\times$ 2.2.b_d
5.2.ac_j_ao_bj_abo	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )^{2}$	$4$	$1$	$1$	$75$	1.2.a $\times$ 2.2.ab_d²
5.2.ac_k_aq_bo_abw	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )^{4}$	$0$	$5$	$1$	$81$	1.2.ac $\times$ 1.2.a⁴
5.2.ab_ag_i_i_ay	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 2 x^{2} )^{4}$	$1$	$4$	$2$	$2$	1.2.ab $\times$ 2.2.a_ae²
5.2.ab_ac_e_a_ai	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$	$1$	$4$	$2$	$10$	1.2.ac $\times$ 1.2.ab $\times$ 1.2.c $\times$ 2.2.a_ae
5.2.ab_a_a_ae_i	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$	$1$	$4$	$2$	$12$	1.2.ac $\times$ 1.2.a $\times$ 1.2.b $\times$ 2.2.a_ae
5.2.ab_c_a_ai_i	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 2 x^{2} )^{2}( 1 + 2 x^{2} )^{2}$	$1$	$4$	$2$	$18$	1.2.ab $\times$ 1.2.a² $\times$ 2.2.a_ae
5.2.ab_c_a_i_ai	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x + 2 x^{2} )^{2}$	$1$	$4$	$2$	$50$	1.2.ac² $\times$ 1.2.ab $\times$ 1.2.c²
5.2.ab_e_ae_m_ai	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$	$1$	$4$	$2$	$60$	1.2.ac² $\times$ 1.2.a $\times$ 1.2.b $\times$ 1.2.c
5.2.ab_g_ae_q_ai	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 + 2 x^{2} )^{2}$	$1$	$4$	$2$	$90$	1.2.ac $\times$ 1.2.ab $\times$ 1.2.a² $\times$ 1.2.c
5.2.ab_i_ai_bc_ay	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 + 2 x^{2} )^{3}$	$1$	$4$	$2$	$108$	1.2.ac $\times$ 1.2.a³ $\times$ 1.2.b
5.2.ab_k_ai_bo_ay	$5$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )^{4}$	$1$	$4$	$2$	$162$	1.2.ab $\times$ 1.2.a⁴
5.2.a_ag_a_i_a	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 - 2 x^{2} )^{4}$	$0$	$5$	$3$	$3$	1.2.a $\times$ 2.2.a_ae²
5.2.a_ad_a_d_a	$5$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 - 5 x^{2} + 13 x^{4} - 20 x^{6} + 16 x^{8} )$	$4$	$1$	$3$	$15$	1.2.a $\times$ 4.2.a_af_a_n
5.2.a_ac_a_a_a	$5$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$	$0$	$5$	$3$	$15$	1.2.ac $\times$ 1.2.a $\times$ 1.2.c $\times$ 2.2.a_ae

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Elliptic curves over $\Q$
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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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