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Label | Dimension | Base field | L-polynomial | $p$-rank | Isogeny factors |
---|---|---|---|---|---|
5.2.ah_ba_acq_fg_aih | $5$ | $\F_{2}$ | $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ad_f $\times$ 3.2.ae_j_ap |
5.2.ag_q_aba_bh_abr | $5$ | $\F_{2}$ | $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ad_f $\times$ 3.2.ad_c_b |
5.2.ag_w_acf_ej_agx | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 1.2.ab 2 $\times$ 3.2.ae_j_ap |
5.2.ag_x_acj_eu_ahp | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab 3 $\times$ 2.2.ad_f |
5.2.af_n_az_bn_acd | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ad_f $\times$ 2.2.ab_ab |
5.2.af_n_aw_bc_abj | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 1.2.ab 2 $\times$ 3.2.ad_c_b |
5.2.ae_h_af_ag_t | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ad_f $\times$ 2.2.a_ad |
5.2.ae_i_al_n_ar | $5$ | $\F_{2}$ | $( 1 - x^{2} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.a_ab $\times$ 3.2.ae_j_ap |
5.2.ae_k_at_bf_abv | $5$ | $\F_{2}$ | $( 1 + x^{2} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.a_b $\times$ 3.2.ae_j_ap |
5.2.ae_l_av_bg_abv | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{3}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab 3 $\times$ 2.2.ab_ab |
5.2.ae_m_abb_bx_acz | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 1.2.ab $\times$ 1.2.b $\times$ 3.2.ae_j_ap |
5.2.ae_n_abd_cc_adf | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab 2 $\times$ 1.2.b $\times$ 2.2.ad_f |
5.2.ad_b_e_g_az | $5$ | $\F_{2}$ | $( 1 - x^{2} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.a_ab $\times$ 3.2.ad_c_b |
5.2.ad_d_af_n_av | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )^{2}$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab 2 |
5.2.ad_d_ac_k_ax | $5$ | $\F_{2}$ | $( 1 + x^{2} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.a_b $\times$ 3.2.ad_c_b |
5.2.ad_f_al_t_az | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ad_f $\times$ 2.2.ab_ab |
5.2.ad_f_ai_o_av | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 1.2.ab $\times$ 1.2.b $\times$ 3.2.ad_c_b |
5.2.ad_f_ab_al_z | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ad_f $\times$ 2.2.b_ab |
5.2.ad_g_ae_af_p | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{3}( 1 - 3 x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab 3 $\times$ 2.2.a_ad |
5.2.ad_k_aq_bf_abl | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{3}( 1 + x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab 3 $\times$ 2.2.a_b |
5.2.ac_ab_d_c_ah | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 3 x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.a_ad |
5.2.ac_b_ab_a_f | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x^{2} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ad_f $\times$ 2.2.a_ad |
5.2.ac_b_ab_g_an | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.a_ab |
5.2.ac_d_af_k_at | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.ab_ab $\times$ 2.2.a_b |
5.2.ac_f_aj_o_az | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab 2 $\times$ 1.2.b $\times$ 2.2.ab_ab |
5.2.ac_f_b_ag_z | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )^{3}( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab 3 $\times$ 2.2.b_ab |
5.2.ac_g_an_v_abj | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 1.2.b 2 $\times$ 3.2.ae_j_ap |
5.2.ac_h_an_y_abl | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 1.2.b 2 $\times$ 2.2.ad_f |
5.2.ab_ae_g_f_ar | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )^{2}$ | $5$ | 1.2.ab $\times$ 2.2.a_ad 2 |
5.2.ab_ac_e_d_al | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )( 1 - x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.a_ad $\times$ 2.2.a_ab |
5.2.ab_ab_ah_j_f | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )^{2}$ | $5$ | 1.2.b $\times$ 2.2.ab_ab 2 |
5.2.ab_ab_d_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.ab $\times$ 2.2.ab_ab $\times$ 2.2.b_ab |
5.2.ab_a_c_b_af | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )( 1 + x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.a_ad $\times$ 2.2.a_b |
5.2.ab_b_ag_i_ad | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )^{2}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 1.2.b 2 $\times$ 3.2.ad_c_b |
5.2.ab_b_b_ad_h | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ad_f $\times$ 2.2.b_ab |
5.2.ab_c_ac_ac_b | $5$ | $\F_{2}$ | $( 1 + 3 x + 5 x^{2} + 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ | $5$ | 2.2.d_f $\times$ 3.2.ae_j_ap |
5.2.ab_c_a_ab_b | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 - 3 x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab 2 $\times$ 1.2.b $\times$ 2.2.a_ad |
5.2.ab_f_ad_l_af | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + 3 x^{2} + 5 x^{4} + 12 x^{6} + 16 x^{8} )$ | $5$ | 1.2.ab $\times$ 4.2.a_d_a_f |
5.2.ab_g_ae_t_al | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 + x^{2} + 4 x^{4} )$ | $5$ | 1.2.ab 2 $\times$ 1.2.b $\times$ 2.2.a_b |
5.2.a_ad_af_e_p | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 3 x^{2} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.a_ad |
5.2.a_ad_f_e_ap | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.a_ad $\times$ 2.2.b_ab |
5.2.a_ac_ac_d_f | $5$ | $\F_{2}$ | $( 1 + 3 x + 5 x^{2} + 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.d_f $\times$ 3.2.ad_c_b |
5.2.a_ac_c_d_af | $5$ | $\F_{2}$ | $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 + 3 x + 2 x^{2} - x^{3} + 4 x^{4} + 12 x^{5} + 8 x^{6} )$ | $5$ | 2.2.ad_f $\times$ 3.2.d_c_ab |
5.2.a_ab_af_e_f | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - x^{2} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.a_ab |
5.2.a_ab_f_e_af | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.a_ab $\times$ 2.2.b_ab |
5.2.a_b_af_e_af | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 + x^{2} + 4 x^{4} )$ | $5$ | 1.2.b $\times$ 2.2.ab_ab $\times$ 2.2.a_b |
5.2.a_b_f_e_f | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x^{2} + 4 x^{4} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 2.2.a_b $\times$ 2.2.b_ab |
5.2.a_d_af_e_ap | $5$ | $\F_{2}$ | $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab $\times$ 1.2.b 2 $\times$ 2.2.ab_ab |
5.2.a_d_f_e_p | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ | $5$ | 1.2.ab 2 $\times$ 1.2.b $\times$ 2.2.b_ab |
5.2.a_f_af_k_at | $5$ | $\F_{2}$ | $( 1 + x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ | $5$ | 1.2.b 3 $\times$ 2.2.ad_f |