LMFDB - Abelian variety search results

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Base field	Base char.	Dimension	$p$-rank	Initial coefficients

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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

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Results (1-50 of 1736 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.ai_bg_adc_fg	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{4}$	$0$	$4$	$-5$	$1$	1.2.ac⁴
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.ac² $\times$ 2.2.ac_c
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.ac³ $\times$ 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.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.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.ac² $\times$ 2.2.a_ae
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_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.ac² $\times$ 2.2.a_ac
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_c²
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.ac³ $\times$ 1.2.c
4.2.ae_k_au_bg	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$0$	$4$	$-1$	$3$	1.2.ac $\times$ 1.2.a $\times$ 2.2.ac_c
4.2.ae_k_aq_y	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x^{2} + 4 x^{4} )$	$0$	$4$	$-1$	$7$	1.2.ac² $\times$ 2.2.a_c
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_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_ay_bo	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x^{2} )^{2}$	$0$	$4$	$-1$	$9$	1.2.ac² $\times$ 1.2.a²
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_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_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_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.ac_ac_e_a	$4$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$0$	$4$	$1$	$1$	2.2.ac_c $\times$ 2.2.a_ae
4.2.ac_ab_c_c	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 3 x^{2} + 4 x^{4} )$	$2$	$2$	$1$	$2$	2.2.ac_c $\times$ 2.2.a_ad
4.2.ac_a_a_e	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 2 x^{2} + 4 x^{4} )$	$0$	$4$	$1$	$3$	2.2.ac_c $\times$ 2.2.a_ac
4.2.ac_a_e_ai	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x^{2} )^{2}$	$0$	$4$	$1$	$3$	1.2.ac $\times$ 1.2.a $\times$ 2.2.a_ae
4.2.ac_b_c_ae	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )$	$2$	$2$	$1$	$6$	1.2.ac $\times$ 1.2.a $\times$ 2.2.a_ad
4.2.ac_b_e_am	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )^{2}( 1 - 2 x^{2} )^{2}$	$2$	$2$	$1$	$4$	1.2.ab² $\times$ 2.2.a_ae
4.2.ac_c_ae_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$0$	$4$	$1$	$5$	1.2.ac $\times$ 1.2.c $\times$ 2.2.ac_c
4.2.ac_c_a_ae	$4$	$\F_{2}$	$2$	$1 - 2 x + 2 x^{2} - 4 x^{4} + 8 x^{6} - 16 x^{7} + 16 x^{8}$	$0$	$4$	$1$	$5$	simple
4.2.ac_c_a_a	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x^{2} + 4 x^{4} )$	$0$	$4$	$1$	$9$	1.2.ac $\times$ 1.2.a $\times$ 2.2.a_ac
4.2.ac_c_e_ai	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x + 2 x^{2} + 4 x^{3} + 4 x^{4} )$	$0$	$4$	$1$	$13$	1.2.ac² $\times$ 2.2.c_c
4.2.ac_d_a_ac	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )^{2}( 1 - 2 x^{2} + 4 x^{4} )$	$2$	$2$	$1$	$12$	1.2.ab² $\times$ 2.2.a_ac
4.2.ac_e_ai_m	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 + 2 x^{2} + 4 x^{4} )$	$0$	$4$	$1$	$7$	2.2.ac_c $\times$ 2.2.a_c
4.2.ac_e_ae_i	$4$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$	$0$	$4$	$1$	$15$	1.2.ac² $\times$ 1.2.a $\times$ 1.2.c
4.2.ac_f_ak_o	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$2$	$2$	$1$	$8$	1.2.ab $\times$ 1.2.b $\times$ 2.2.ac_c
4.2.ac_f_ai_q	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + x + 2 x^{2} )^{2}$	$2$	$2$	$1$	$16$	1.2.ac² $\times$ 1.2.b²
4.2.ac_f_ae_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}$	$2$	$2$	$1$	$20$	1.2.ac $\times$ 1.2.ab² $\times$ 1.2.c
4.2.ac_g_am_q	$4$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$	$0$	$4$	$1$	$9$	1.2.a² $\times$ 2.2.ac_c
4.2.ac_g_ai_q	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 + 2 x^{2} + 4 x^{4} )$	$0$	$4$	$1$	$21$	1.2.ac $\times$ 1.2.a $\times$ 2.2.a_c
4.2.ac_h_ak_u	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 + x + 2 x^{2} )$	$2$	$2$	$1$	$24$	1.2.ac $\times$ 1.2.ab $\times$ 1.2.a $\times$ 1.2.b
4.2.ac_h_ai_s	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )^{2}( 1 + 2 x^{2} + 4 x^{4} )$	$2$	$2$	$1$	$28$	1.2.ab² $\times$ 2.2.a_c
4.2.ac_i_am_y	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )^{3}$	$0$	$4$	$1$	$27$	1.2.ac $\times$ 1.2.a³
4.2.ac_j_am_bc	$4$	$\F_{2}$	$2$	$( 1 - x + 2 x^{2} )^{2}( 1 + 2 x^{2} )^{2}$	$2$	$2$	$1$	$36$	1.2.ab² $\times$ 1.2.a²
4.2.ab_af_c_m	$4$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$2$	$1$	2.2.ab_ab $\times$ 2.2.a_ae
4.2.ab_ad_a_k	$4$	$\F_{2}$	$2$	$( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 2 x^{2} + 4 x^{4} )$	$2$	$2$	$2$	$3$	2.2.ab_ab $\times$ 2.2.a_ac
4.2.ab_ab_ac_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$2$	$5$	1.2.ac $\times$ 1.2.c $\times$ 2.2.ab_ab
4.2.ab_ab_c_ac	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$	$2$	$2$	$2$	$7$	2.2.ac_c $\times$ 2.2.b_ab
4.2.ab_b_ae_g	$4$	$\F_{2}$	$2$	$( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + 2 x^{2} + 4 x^{4} )$	$2$	$2$	$2$	$7$	2.2.ab_ab $\times$ 2.2.a_c
4.2.ab_b_e_ae	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$	$2$	$2$	$2$	$21$	1.2.ac $\times$ 1.2.a $\times$ 2.2.b_ab
4.2.ab_d_ag_e	$4$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$	$2$	$2$	$2$	$9$	1.2.a² $\times$ 2.2.ab_ab
4.2.a_ai_a_y	$4$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{4}$	$0$	$4$	$3$	$1$	2.2.a_ae²
4.2.a_ah_a_u	$4$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{2}( 1 - 3 x^{2} + 4 x^{4} )$	$2$	$2$	$3$	$2$	2.2.a_ae $\times$ 2.2.a_ad

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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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