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

Sort order

Select

Results (1-50 of 279175 matches)

  There are too many results (279175) to download.

Label	Dimension	Base field	Base char.	L-polynomial	$p$-rank	$p$-rank deficit	points on curve	points on variety	Isogeny factors
1.3.ad	$1$	$\F_{3}$	$3$	$1 - 3 x + 3 x^{2}$	$0$	$1$	$1$	$1$	simple
1.3.ac	$1$	$\F_{3}$	$3$	$1 - 2 x + 3 x^{2}$	$1$	$0$	$2$	$2$	simple
1.3.ab	$1$	$\F_{3}$	$3$	$1 - x + 3 x^{2}$	$1$	$0$	$3$	$3$	simple
1.3.a	$1$	$\F_{3}$	$3$	$1 + 3 x^{2}$	$0$	$1$	$4$	$4$	simple
1.3.b	$1$	$\F_{3}$	$3$	$1 + x + 3 x^{2}$	$1$	$0$	$5$	$5$	simple
1.3.c	$1$	$\F_{3}$	$3$	$1 + 2 x + 3 x^{2}$	$1$	$0$	$6$	$6$	simple
1.3.d	$1$	$\F_{3}$	$3$	$1 + 3 x + 3 x^{2}$	$0$	$1$	$7$	$7$	simple
2.3.ag_p	$2$	$\F_{3}$	$3$	$( 1 - 3 x + 3 x^{2} )^{2}$	$0$	$2$	$-2$	$1$	1.3.ad^2
2.3.af_m	$2$	$\F_{3}$	$3$	$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )$	$1$	$1$	$-1$	$2$	1.3.ad $\times$ 1.3.ac
2.3.ae_i	$2$	$\F_{3}$	$3$	$1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4}$	$2$	$0$	$0$	$2$	simple
2.3.ae_j	$2$	$\F_{3}$	$3$	$( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} )$	$1$	$1$	$0$	$3$	1.3.ad $\times$ 1.3.ab
2.3.ae_k	$2$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )^{2}$	$2$	$0$	$0$	$4$	1.3.ac^2
2.3.ad_f	$2$	$\F_{3}$	$3$	$1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4}$	$2$	$0$	$1$	$3$	simple
2.3.ad_g	$2$	$\F_{3}$	$3$	$( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )$	$0$	$2$	$1$	$4$	1.3.ad $\times$ 1.3.a
2.3.ad_h	$2$	$\F_{3}$	$3$	$1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4}$	$2$	$0$	$1$	$5$	simple
2.3.ad_i	$2$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )( 1 - x + 3 x^{2} )$	$2$	$0$	$1$	$6$	1.3.ac $\times$ 1.3.ab
2.3.ac_b	$2$	$\F_{3}$	$3$	$1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4}$	$2$	$0$	$2$	$3$	simple
2.3.ac_c	$2$	$\F_{3}$	$3$	$1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4}$	$2$	$0$	$2$	$4$	simple
2.3.ac_d	$2$	$\F_{3}$	$3$	$( 1 - 3 x + 3 x^{2} )( 1 + x + 3 x^{2} )$	$1$	$1$	$2$	$5$	1.3.ad $\times$ 1.3.b
2.3.ac_e	$2$	$\F_{3}$	$3$	$1 - 2 x + 4 x^{2} - 6 x^{3} + 9 x^{4}$	$2$	$0$	$2$	$6$	simple
2.3.ac_f	$2$	$\F_{3}$	$3$	$1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4}$	$2$	$0$	$2$	$7$	simple
2.3.ac_g	$2$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )( 1 + 3 x^{2} )$	$1$	$1$	$2$	$8$	1.3.ac $\times$ 1.3.a
2.3.ac_h	$2$	$\F_{3}$	$3$	$( 1 - x + 3 x^{2} )^{2}$	$2$	$0$	$2$	$9$	1.3.ab^2
2.3.ab_ac	$2$	$\F_{3}$	$3$	$1 - x - 2 x^{2} - 3 x^{3} + 9 x^{4}$	$2$	$0$	$3$	$4$	simple
2.3.ab_ab	$2$	$\F_{3}$	$3$	$1 - x - x^{2} - 3 x^{3} + 9 x^{4}$	$2$	$0$	$3$	$5$	simple
2.3.ab_a	$2$	$\F_{3}$	$3$	$( 1 - 3 x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )$	$1$	$1$	$3$	$6$	1.3.ad $\times$ 1.3.c
2.3.ab_b	$2$	$\F_{3}$	$3$	$1 - x + x^{2} - 3 x^{3} + 9 x^{4}$	$2$	$0$	$3$	$7$	simple
2.3.ab_c	$2$	$\F_{3}$	$3$	$1 - x + 2 x^{2} - 3 x^{3} + 9 x^{4}$	$2$	$0$	$3$	$8$	simple
2.3.ab_d	$2$	$\F_{3}$	$3$	$1 - x + 3 x^{2} - 3 x^{3} + 9 x^{4}$	$1$	$1$	$3$	$9$	simple
2.3.ab_e	$2$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )( 1 + x + 3 x^{2} )$	$2$	$0$	$3$	$10$	1.3.ac $\times$ 1.3.b
2.3.ab_f	$2$	$\F_{3}$	$3$	$1 - x + 5 x^{2} - 3 x^{3} + 9 x^{4}$	$2$	$0$	$3$	$11$	simple
2.3.ab_g	$2$	$\F_{3}$	$3$	$( 1 - x + 3 x^{2} )( 1 + 3 x^{2} )$	$1$	$1$	$3$	$12$	1.3.ab $\times$ 1.3.a
2.3.a_ag	$2$	$\F_{3}$	$3$	$( 1 - 3 x^{2} )^{2}$	$0$	$2$	$4$	$4$	simple
2.3.a_af	$2$	$\F_{3}$	$3$	$1 - 5 x^{2} + 9 x^{4}$	$2$	$0$	$4$	$5$	simple
2.3.a_ae	$2$	$\F_{3}$	$3$	$1 - 4 x^{2} + 9 x^{4}$	$2$	$0$	$4$	$6$	simple
2.3.a_ad	$2$	$\F_{3}$	$3$	$( 1 - 3 x + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$	$0$	$2$	$4$	$7$	1.3.ad $\times$ 1.3.d
2.3.a_ac	$2$	$\F_{3}$	$3$	$1 - 2 x^{2} + 9 x^{4}$	$2$	$0$	$4$	$8$	simple
2.3.a_ab	$2$	$\F_{3}$	$3$	$1 - x^{2} + 9 x^{4}$	$2$	$0$	$4$	$9$	simple
2.3.a_a	$2$	$\F_{3}$	$3$	$1 + 9 x^{4}$	$0$	$2$	$4$	$10$	simple
2.3.a_b	$2$	$\F_{3}$	$3$	$1 + x^{2} + 9 x^{4}$	$2$	$0$	$4$	$11$	simple
2.3.a_c	$2$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )$	$2$	$0$	$4$	$12$	1.3.ac $\times$ 1.3.c
2.3.a_d	$2$	$\F_{3}$	$3$	$1 + 3 x^{2} + 9 x^{4}$	$0$	$2$	$4$	$13$	simple
2.3.a_e	$2$	$\F_{3}$	$3$	$1 + 4 x^{2} + 9 x^{4}$	$2$	$0$	$4$	$14$	simple
2.3.a_f	$2$	$\F_{3}$	$3$	$( 1 - x + 3 x^{2} )( 1 + x + 3 x^{2} )$	$2$	$0$	$4$	$15$	1.3.ab $\times$ 1.3.b
2.3.a_g	$2$	$\F_{3}$	$3$	$( 1 + 3 x^{2} )^{2}$	$0$	$2$	$4$	$16$	1.3.a^2
2.3.b_ac	$2$	$\F_{3}$	$3$	$1 + x - 2 x^{2} + 3 x^{3} + 9 x^{4}$	$2$	$0$	$5$	$12$	simple
2.3.b_ab	$2$	$\F_{3}$	$3$	$1 + x - x^{2} + 3 x^{3} + 9 x^{4}$	$2$	$0$	$5$	$13$	simple
2.3.b_a	$2$	$\F_{3}$	$3$	$( 1 - 2 x + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$	$1$	$1$	$5$	$14$	1.3.ac $\times$ 1.3.d
2.3.b_b	$2$	$\F_{3}$	$3$	$1 + x + x^{2} + 3 x^{3} + 9 x^{4}$	$2$	$0$	$5$	$15$	simple
2.3.b_c	$2$	$\F_{3}$	$3$	$1 + x + 2 x^{2} + 3 x^{3} + 9 x^{4}$	$2$	$0$	$5$	$16$	simple

  There are too many results (279175) to download.