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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

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Results (16 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
6.2.ad_e_ac_ac_r_abj	$6$	$\F_{2}$	$2$	$( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - x - x^{2} + 3 x^{3} - x^{4} + 6 x^{5} - 4 x^{6} - 8 x^{7} + 16 x^{8} )$	$6$	$0$	$0$	$22$	2.2.ac_d $\times$ 4.2.ab_ab_d_ab
6.2.ac_a_c_c_f_au	$6$	$\F_{2}$	$2$	$( 1 - x - 2 x^{3} + 4 x^{4} )( 1 - x - x^{2} + 3 x^{3} - x^{4} + 6 x^{5} - 4 x^{6} - 8 x^{7} + 16 x^{8} )$	$5$	$1$	$1$	$22$	2.2.ab_a $\times$ 4.2.ab_ab_d_ab
6.2.ac_b_b_b_i_av	$6$	$\F_{2}$	$2$	$( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x - x^{2} + 3 x^{3} - x^{4} + 6 x^{5} - 4 x^{6} - 8 x^{7} + 16 x^{8} )$	$6$	$0$	$1$	$33$	2.2.ab_b $\times$ 4.2.ab_ab_d_ab
6.2.ac_d_ab_ab_o_ax	$6$	$\F_{2}$	$2$	$( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x - x^{2} + 3 x^{3} - x^{4} + 6 x^{5} - 4 x^{6} - 8 x^{7} + 16 x^{8} )$	$6$	$0$	$1$	$55$	2.2.ab_d $\times$ 4.2.ab_ab_d_ab
6.2.ab_a_ac_c_af_n	$6$	$\F_{2}$	$2$	$( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 + x - x^{2} - 3 x^{3} - x^{4} - 6 x^{5} - 4 x^{6} + 8 x^{7} + 16 x^{8} )$	$6$	$0$	$2$	$22$	2.2.ac_d $\times$ 4.2.b_ab_ad_ab
6.2.a_ac_ae_e_b_e	$6$	$\F_{2}$	$2$	$( 1 - x - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} - 3 x^{3} - x^{4} - 6 x^{5} - 4 x^{6} + 8 x^{7} + 16 x^{8} )$	$5$	$1$	$3$	$22$	2.2.ab_a $\times$ 4.2.b_ab_ad_ab
6.2.a_ac_e_e_ab_e	$6$	$\F_{2}$	$2$	$( 1 + x + 2 x^{3} + 4 x^{4} )( 1 - x - x^{2} + 3 x^{3} - x^{4} + 6 x^{5} - 4 x^{6} - 8 x^{7} + 16 x^{8} )$	$5$	$1$	$3$	$88$	2.2.b_a $\times$ 4.2.ab_ab_d_ab
6.2.a_ab_ad_d_ac_d	$6$	$\F_{2}$	$2$	$( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} - 3 x^{3} - x^{4} - 6 x^{5} - 4 x^{6} + 8 x^{7} + 16 x^{8} )$	$6$	$0$	$3$	$33$	2.2.ab_b $\times$ 4.2.b_ab_ad_ab
6.2.a_ab_d_d_c_d	$6$	$\F_{2}$	$2$	$( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )( 1 - x - x^{2} + 3 x^{3} - x^{4} + 6 x^{5} - 4 x^{6} - 8 x^{7} + 16 x^{8} )$	$6$	$0$	$3$	$99$	2.2.b_b $\times$ 4.2.ab_ab_d_ab
6.2.a_b_ab_b_ai_b	$6$	$\F_{2}$	$2$	$( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} - 3 x^{3} - x^{4} - 6 x^{5} - 4 x^{6} + 8 x^{7} + 16 x^{8} )$	$6$	$0$	$3$	$55$	2.2.ab_d $\times$ 4.2.b_ab_ad_ab
6.2.a_b_b_b_i_b	$6$	$\F_{2}$	$2$	$( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )( 1 - x - x^{2} + 3 x^{3} - x^{4} + 6 x^{5} - 4 x^{6} - 8 x^{7} + 16 x^{8} )$	$6$	$0$	$3$	$121$	2.2.b_d $\times$ 4.2.ab_ab_d_ab
6.2.b_a_c_c_f_n	$6$	$\F_{2}$	$2$	$( 1 + 2 x + 3 x^{2} + 4 x^{3} + 4 x^{4} )( 1 - x - x^{2} + 3 x^{3} - x^{4} + 6 x^{5} - 4 x^{6} - 8 x^{7} + 16 x^{8} )$	$6$	$0$	$4$	$154$	2.2.c_d $\times$ 4.2.ab_ab_d_ab
6.2.c_a_ac_c_af_au	$6$	$\F_{2}$	$2$	$( 1 + x + 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} - 3 x^{3} - x^{4} - 6 x^{5} - 4 x^{6} + 8 x^{7} + 16 x^{8} )$	$5$	$1$	$5$	$88$	2.2.b_a $\times$ 4.2.b_ab_ad_ab
6.2.c_b_ab_b_ai_av	$6$	$\F_{2}$	$2$	$( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} - 3 x^{3} - x^{4} - 6 x^{5} - 4 x^{6} + 8 x^{7} + 16 x^{8} )$	$6$	$0$	$5$	$99$	2.2.b_b $\times$ 4.2.b_ab_ad_ab
6.2.c_d_b_ab_ao_ax	$6$	$\F_{2}$	$2$	$( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} - 3 x^{3} - x^{4} - 6 x^{5} - 4 x^{6} + 8 x^{7} + 16 x^{8} )$	$6$	$0$	$5$	$121$	2.2.b_d $\times$ 4.2.b_ab_ad_ab
6.2.d_e_c_ac_ar_abj	$6$	$\F_{2}$	$2$	$( 1 + 2 x + 3 x^{2} + 4 x^{3} + 4 x^{4} )( 1 + x - x^{2} - 3 x^{3} - x^{4} - 6 x^{5} - 4 x^{6} + 8 x^{7} + 16 x^{8} )$	$6$	$0$	$6$	$154$	2.2.c_d $\times$ 4.2.b_ab_ad_ab

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