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Label | Dimension | Base field | L-polynomial | $p$-rank | Isogeny factors |
---|---|---|---|---|---|
5.2.ag_u_abx_dr_aft | $5$ | $\F_{2}$ | $( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ac_d $\times$ 3.2.ae_j_ap |
5.2.af_l_aq_y_abl | $5$ | $\F_{2}$ | $( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ac_d $\times$ 3.2.ad_c_b |
5.2.af_n_aba_bt_acq | $5$ | $\F_{2}$ | $( 1 - x - 2 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $4$ | 2.2.ab_a $\times$ 3.2.ae_j_ap |
5.2.af_o_abe_cc_adf | $5$ | $\F_{2}$ | $( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ab_b $\times$ 3.2.ae_j_ap |
5.2.af_q_abm_cu_aej | $5$ | $\F_{2}$ | $( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ab_d $\times$ 3.2.ae_j_ap |
5.2.af_u_aby_eb_agf | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{5}$ | $5$ | 1.2.ab 5 |
5.2.ae_f_ad_n_abg | $5$ | $\F_{2}$ | $( 1 - x - 2 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $4$ | 2.2.ab_a $\times$ 3.2.ad_c_b |
5.2.ae_g_ag_p_abf | $5$ | $\F_{2}$ | $( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ab_b $\times$ 3.2.ad_c_b |
5.2.ae_i_am_t_abd | $5$ | $\F_{2}$ | $( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ab_d $\times$ 3.2.ad_c_b |
5.2.ae_j_ar_bc_abp | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ac_d $\times$ 2.2.ab_ab |
5.2.ad_e_ah_p_ay | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$ | $4$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.ab_a |
5.2.ad_f_aj_r_abb | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.ab_b |
5.2.ad_f_ae_ab_e | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $4$ | 2.2.b_a $\times$ 3.2.ae_j_ap |
5.2.ad_g_ai_i_al | $5$ | $\F_{2}$ | $( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.b_b $\times$ 3.2.ae_j_ap |
5.2.ad_h_an_v_abh | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.ab_d |
5.2.ad_i_aq_ba_abp | $5$ | $\F_{2}$ | $( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.b_d $\times$ 3.2.ae_j_ap |
5.2.ad_i_ak_n_al | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{3}( 1 - x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab 3 $\times$ 2.2.a_ab |
5.2.ad_m_aw_bx_acl | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + 2 x^{2} )^{4}$ | $5$ | 1.2.ab 4 $\times$ 1.2.b |
5.2.ac_ab_f_d_aq | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $4$ | 2.2.b_a $\times$ 3.2.ad_c_b |
5.2.ac_a_c_f_ap | $5$ | $\F_{2}$ | $( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.b_b $\times$ 3.2.ad_c_b |
5.2.ac_c_ae_j_an | $5$ | $\F_{2}$ | $( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.b_d $\times$ 3.2.ad_c_b |
5.2.ac_d_aj_o_ap | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ac_d $\times$ 2.2.ab_ab |
5.2.ac_d_b_ag_p | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ac_d $\times$ 2.2.b_ab |
5.2.ac_e_af_d_af | $5$ | $\F_{2}$ | $( 1 + 2 x + 3 x^{2} + 4 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.c_d $\times$ 3.2.ae_j_ap |
5.2.ab_ab_a_e_af | $5$ | $\F_{2}$ | $( 1 + 2 x + 3 x^{2} + 4 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.c_d $\times$ 3.2.ad_c_b |
5.2.ab_a_ah_j_a | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$ | $4$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.ab_a |
5.2.ab_a_b_b_ai | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x + 2 x^{3} + 4 x^{4} )$ | $4$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.b_a |
5.2.ab_a_d_ab_a | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $4$ | 1.2.ab $\times$ 2.2.ab_a $\times$ 2.2.b_ab |
5.2.ab_b_ah_j_af | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.ab_b |
5.2.ab_b_ab_d_al | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.b_b |
5.2.ab_b_d_ab_f | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_b $\times$ 2.2.b_ab |
5.2.ab_d_ah_j_ap | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.ab_d |
5.2.ab_d_af_h_ar | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.b_d |
5.2.ab_d_d_ab_p | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_d $\times$ 2.2.b_ab |
5.2.ab_e_ac_j_af | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 - x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab 2 $\times$ 1.2.b $\times$ 2.2.a_ab |
5.2.ab_i_ag_bd_ar | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{3}$ | $5$ | 1.2.ab 3 $\times$ 1.2.b 2 |
5.2.a_b_ab_a_aj | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + 2 x + 3 x^{2} + 4 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.c_d |
5.2.a_b_b_a_j | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ac_d $\times$ 2.2.b_ab |
5.2.b_ab_a_e_f | $5$ | $\F_{2}$ | $( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 + 3 x + 2 x^{2} - x^{3} + 4 x^{4} + 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ac_d $\times$ 3.2.d_c_ab |
5.2.b_a_ad_ab_a | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x + 2 x^{3} + 4 x^{4} )$ | $4$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.b_a |
5.2.b_a_ab_b_i | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $4$ | 1.2.b $\times$ 2.2.ab_a $\times$ 2.2.b_ab |
5.2.b_a_h_j_a | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )( 1 + x + 2 x^{3} + 4 x^{4} )$ | $4$ | 1.2.ab $\times$ 2.2.b_ab $\times$ 2.2.b_a |
5.2.b_b_ad_ab_af | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.b_b |
5.2.b_b_b_d_l | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_b $\times$ 2.2.b_ab |
5.2.b_b_h_j_f | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.b_ab $\times$ 2.2.b_b |
5.2.b_d_ad_ab_ap | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.b_d |
5.2.b_d_f_h_r | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_d $\times$ 2.2.b_ab |
5.2.b_d_h_j_p | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )( 1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.b_ab $\times$ 2.2.b_d |
5.2.b_e_c_j_f | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )^{2}( 1 - x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 1.2.b 2 $\times$ 2.2.a_ab |
5.2.b_i_g_bd_r | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{2}( 1 + x + 2 x^{2} )^{3}$ | $5$ | 1.2.ab 2 $\times$ 1.2.b 3 |