LMFDB - Abelian variety search results

Refine search

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

			Sort order	Select

Results (1-50 of 190 matches)

Next Download displayed columns for results to

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_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.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_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_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.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_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_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.a_ai_a_y	$4$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{4}$	$0$	$4$	$3$	$1$	2.2.a_ae²
4.2.a_ae_a_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$	$0$	$4$	$3$	$5$	1.2.ac $\times$ 1.2.c $\times$ 2.2.a_ae
4.2.a_a_a_ai	$4$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{2}( 1 + 2 x^{2} )^{2}$	$0$	$4$	$3$	$9$	1.2.a² $\times$ 2.2.a_ae
4.2.a_a_a_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )^{2}( 1 + 2 x + 2 x^{2} )^{2}$	$0$	$4$	$3$	$25$	1.2.ac² $\times$ 1.2.c²
4.2.a_e_a_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 + 2 x^{2} )^{2}$	$0$	$4$	$3$	$45$	1.2.ac $\times$ 1.2.a² $\times$ 1.2.c
4.2.a_i_a_y	$4$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )^{4}$	$0$	$4$	$3$	$81$	1.2.a⁴
4.2.c_a_ae_ai	$4$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$	$0$	$4$	$5$	$15$	1.2.a $\times$ 1.2.c $\times$ 2.2.a_ae
4.2.c_e_e_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )^{2}$	$0$	$4$	$5$	$75$	1.2.ac $\times$ 1.2.a $\times$ 1.2.c²
4.2.c_i_m_y	$4$	$\F_{2}$	$2$	$( 1 + 2 x + 2 x^{2} )( 1 + 2 x^{2} )^{3}$	$0$	$4$	$5$	$135$	1.2.a³ $\times$ 1.2.c
4.2.e_e_ai_ay	$4$	$\F_{2}$	$2$	$( 1 - 2 x^{2} )^{2}( 1 + 2 x + 2 x^{2} )^{2}$	$0$	$4$	$7$	$25$	1.2.c² $\times$ 2.2.a_ae
4.2.e_i_i_i	$4$	$\F_{2}$	$2$	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )^{3}$	$0$	$4$	$7$	$125$	1.2.ac $\times$ 1.2.c³
4.2.e_m_y_bo	$4$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )^{2}( 1 + 2 x + 2 x^{2} )^{2}$	$0$	$4$	$7$	$225$	1.2.a² $\times$ 1.2.c²
4.2.g_u_bs_cu	$4$	$\F_{2}$	$2$	$( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )^{3}$	$0$	$4$	$9$	$375$	1.2.a $\times$ 1.2.c³
4.2.i_bg_dc_fg	$4$	$\F_{2}$	$2$	$( 1 + 2 x + 2 x^{2} )^{4}$	$0$	$4$	$11$	$625$	1.2.c⁴
4.3.ai_bg_adk_gw	$4$	$\F_{3}$	$3$	$( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )^{2}$	$4$	$0$	$-4$	$4$	2.3.ae_i²
4.3.ai_bi_ads_hm	$4$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$	$4$	$0$	$-4$	$8$	1.3.ac² $\times$ 2.3.ae_i
4.3.ae_g_ae_c	$4$	$\F_{3}$	$3$	$( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )( 1 - 2 x^{2} + 9 x^{4} )$	$4$	$0$	$0$	$16$	2.3.ae_i $\times$ 2.3.a_ac
4.3.ae_k_au_bi	$4$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$	$4$	$0$	$0$	$24$	1.3.ac $\times$ 1.3.c $\times$ 2.3.ae_i
4.3.ac_ac_c_k	$4$	$\F_{3}$	$3$	$( 1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4} )( 1 - 4 x^{2} + 9 x^{4} )$	$4$	$0$	$2$	$24$	2.3.ac_c $\times$ 2.3.a_ae
4.3.ac_g_ao_ba	$4$	$\F_{3}$	$3$	$( 1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4} )( 1 + 4 x^{2} + 9 x^{4} )$	$4$	$0$	$2$	$56$	2.3.ac_c $\times$ 2.3.a_e
4.3.a_ai_a_bi	$4$	$\F_{3}$	$3$	$( 1 - 4 x^{2} + 9 x^{4} )^{2}$	$4$	$0$	$4$	$36$	2.3.a_ae²
4.3.a_a_a_ar	$4$	$\F_{3}$	$3$	$1 - 17 x^{4} + 81 x^{8}$	$4$	$0$	$4$	$65$	simple
4.3.a_a_a_ao	$4$	$\F_{3}$	$3$	$( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )( 1 + 4 x + 8 x^{2} + 12 x^{3} + 9 x^{4} )$	$4$	$0$	$4$	$68$	2.3.ae_i $\times$ 2.3.e_i
4.3.a_a_a_c	$4$	$\F_{3}$	$3$	$( 1 - 4 x^{2} + 9 x^{4} )( 1 + 4 x^{2} + 9 x^{4} )$	$4$	$0$	$4$	$84$	2.3.a_ae $\times$ 2.3.a_e
4.3.a_a_a_h	$4$	$\F_{3}$	$3$	$1 + 7 x^{4} + 81 x^{8}$	$4$	$0$	$4$	$89$	simple
4.3.a_c_ai_c	$4$	$\F_{3}$	$3$	$( 1 + 2 x + 3 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$	$4$	$0$	$4$	$72$	1.3.c² $\times$ 2.3.ae_i
4.3.a_c_i_c	$4$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )^{2}( 1 + 4 x + 8 x^{2} + 12 x^{3} + 9 x^{4} )$	$4$	$0$	$4$	$136$	1.3.ac² $\times$ 2.3.e_i
4.3.a_i_a_bi	$4$	$\F_{3}$	$3$	$( 1 + 4 x^{2} + 9 x^{4} )^{2}$	$4$	$0$	$4$	$196$	2.3.a_e²
4.3.c_ac_ac_k	$4$	$\F_{3}$	$3$	$( 1 - 4 x^{2} + 9 x^{4} )( 1 + 2 x + 2 x^{2} + 6 x^{3} + 9 x^{4} )$	$4$	$0$	$6$	$120$	2.3.a_ae $\times$ 2.3.c_c
4.3.c_g_o_ba	$4$	$\F_{3}$	$3$	$( 1 + 4 x^{2} + 9 x^{4} )( 1 + 2 x + 2 x^{2} + 6 x^{3} + 9 x^{4} )$	$4$	$0$	$6$	$280$	2.3.a_e $\times$ 2.3.c_c
4.3.e_g_e_c	$4$	$\F_{3}$	$3$	$( 1 - 2 x^{2} + 9 x^{4} )( 1 + 4 x + 8 x^{2} + 12 x^{3} + 9 x^{4} )$	$4$	$0$	$8$	$272$	2.3.a_ac $\times$ 2.3.e_i
4.3.e_k_u_bi	$4$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )( 1 + 4 x + 8 x^{2} + 12 x^{3} + 9 x^{4} )$	$4$	$0$	$8$	$408$	1.3.ac $\times$ 1.3.c $\times$ 2.3.e_i
4.3.i_bg_dk_gw	$4$	$\F_{3}$	$3$	$( 1 + 4 x + 8 x^{2} + 12 x^{3} + 9 x^{4} )^{2}$	$4$	$0$	$12$	$1156$	2.3.e_i²
4.3.i_bi_ds_hm	$4$	$\F_{3}$	$3$	$( 1 + 2 x + 3 x^{2} )^{2}( 1 + 4 x + 8 x^{2} + 12 x^{3} + 9 x^{4} )$	$4$	$0$	$12$	$1224$	1.3.c² $\times$ 2.3.e_i
4.4.af_n_au_bg	$4$	$\F_{2^{2}}$	$2$	$( 1 - 5 x + 13 x^{2} - 20 x^{3} + 16 x^{4} )( 1 + 16 x^{4} )$	$2$	$2$	$0$	$85$	2.4.af_n $\times$ 2.4.a_a
4.4.ae_j_aq_bg	$4$	$\F_{2^{2}}$	$2$	$( 1 - 4 x + 9 x^{2} - 16 x^{3} + 16 x^{4} )( 1 + 16 x^{4} )$	$2$	$2$	$1$	$102$	2.4.ae_j $\times$ 2.4.a_a
4.4.ae_l_aq_bg	$4$	$\F_{2^{2}}$	$2$	$( 1 - 3 x + 4 x^{2} )( 1 - x + 4 x^{2} )( 1 + 16 x^{4} )$	$2$	$2$	$1$	$136$	1.4.ad $\times$ 1.4.ab $\times$ 2.4.a_a
4.4.ad_g_am_bg	$4$	$\F_{2^{2}}$	$2$	$( 1 - 3 x + 6 x^{2} - 12 x^{3} + 16 x^{4} )( 1 + 16 x^{4} )$	$1$	$3$	$2$	$136$	2.4.ad_g $\times$ 2.4.a_a
4.4.ad_j_am_bg	$4$	$\F_{2^{2}}$	$2$	$( 1 - 3 x + 9 x^{2} - 12 x^{3} + 16 x^{4} )( 1 + 16 x^{4} )$	$2$	$2$	$2$	$187$	2.4.ad_j $\times$ 2.4.a_a
4.4.ac_b_ai_bg	$4$	$\F_{2^{2}}$	$2$	$( 1 - 2 x + x^{2} - 8 x^{3} + 16 x^{4} )( 1 + 16 x^{4} )$	$2$	$2$	$3$	$136$	2.4.ac_b $\times$ 2.4.a_a
4.4.ac_d_ai_bg	$4$	$\F_{2^{2}}$	$2$	$( 1 - 2 x + 3 x^{2} - 8 x^{3} + 16 x^{4} )( 1 + 16 x^{4} )$	$2$	$2$	$3$	$170$	2.4.ac_d $\times$ 2.4.a_a
4.4.ac_f_ai_bg	$4$	$\F_{2^{2}}$	$2$	$( 1 - 3 x + 4 x^{2} )( 1 + x + 4 x^{2} )( 1 + 16 x^{4} )$	$2$	$2$	$3$	$204$	1.4.ad $\times$ 1.4.b $\times$ 2.4.a_a

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 190 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.

Learn more

Refine search Advanced search options

Results (1-50 of 190 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.

Refine search