↑

Learn more

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
Newton elevation # Jacobians # Hyp. Jacobians # twists Max twist degree
Angle rank Angle corank End. degree $p$-corank (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 164937 matches)

Next   displayed columns for results
Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
6.2.am_cu_aku_bea_acku_dwy $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{6}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ 1.2.ac 6
6.2.al_cj_aio_wq_abtw_cuy $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2^2$ 1.2.ac 4 $\times$ 2.2.ad_f
6.2.al_ck_aiw_xw_abwy_dae $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{5}$ $1$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.2.ac 5 $\times$ 1.2.ab
6.2.ak_by_agi_pg_abcy_bsy $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\zeta_{12})\) $C_2$, $C_2^2$ 1.2.ac 4 $\times$ 2.2.ac_c
6.2.ak_bz_ags_qz_abho_cay $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ $4$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2^2$ 1.2.ac 2 $\times$ 2.2.ad_f 2
6.2.ak_bz_agr_qs_abgs_bzk $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ $3$ \(\Q(\sqrt{-1}) \), \(\Q(\zeta_{7})\) $C_2$, $C_6$ 1.2.ac 3 $\times$ 3.2.ae_j_ap
6.2.ak_bz_agq_qm_abga_bye $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), 4.0.1088.2 $C_2$, $D_{4}$ 1.2.ac 4 $\times$ 2.2.ac_d
6.2.ak_ca_agz_ry_abju_ceq $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2$, $C_2^2$ 1.2.ac 3 $\times$ 1.2.ab $\times$ 2.2.ad_f
6.2.ak_ca_agy_rs_abjc_cdk $6$ $\F_{2}$ $( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{5}$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.2.ac 5 $\times$ 1.2.a
6.2.ak_cb_ahg_sy_abme_ciq $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{4}$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.2.ac 4 $\times$ 1.2.ab 2
6.2.aj_bm_adt_gk_aig_km $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ $3$ \(\Q(\sqrt{-1}) \), \(\Q(\zeta_{7})\) $C_2$, $C_6$ 1.2.ac 3 $\times$ 3.2.ad_c_b
6.2.aj_bn_aec_hw_ama_qy $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2$, $C_2^2$ 1.2.ac 4 $\times$ 2.2.ab_ab
6.2.aj_bo_aem_jp_aqq_yy $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$ $4$ \(\Q(\sqrt{-1}) \), 8.0.13140625.1 $C_2$, $C_2^2:C_4$ 1.2.ac 2 $\times$ 4.2.af_m_au_bd
6.2.aj_bo_aek_jc_apc_we $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - x - 2 x^{3} + 4 x^{4} )$ $1$ \(\Q(\sqrt{-1}) \), 4.0.2312.1 $C_2$, $D_{4}$ 1.2.ac 4 $\times$ 2.2.ab_a
6.2.aj_bp_aew_li_avg_bgy $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{12})\) $C_2$, $C_2^2$, $C_2^2$ 1.2.ac 2 $\times$ 2.2.ad_f $\times$ 2.2.ac_c
6.2.aj_bp_aev_lb_auk_bfk $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$ $4$ \(\Q(\sqrt{-1}) \), \(\Q(\zeta_{15})\) $C_2$, $C_4\times C_2$ 1.2.ac 2 $\times$ 4.2.af_n_az_bn
6.2.aj_bp_aet_ko_asw_bcq $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$ $3$ \(\Q(\sqrt{-1}) \), 6.0.679024.1 $C_2$, $S_4\times C_2$ 1.2.ac 3 $\times$ 3.2.ad_f_ah
6.2.aj_bp_aes_ki_ase_bbk $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), 4.0.2873.1 $C_2$, $D_{4}$ 1.2.ac 4 $\times$ 2.2.ab_b
6.2.aj_bq_aff_ms_ayp_bmn $6$ $\F_{2}$ $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{3}$ $6$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ 2.2.ad_f 3
6.2.aj_bq_afe_mm_axz_blm $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ $5$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{7})\) $C_2$, $C_2^2$, $C_6$ 1.2.ac $\times$ 2.2.ad_f $\times$ 3.2.ae_j_ap
6.2.aj_bq_afd_mh_axm_bkq $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ $4$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.1088.2 $C_2$, $C_2^2$, $D_{4}$ 1.2.ac 2 $\times$ 2.2.ad_f $\times$ 2.2.ac_d
6.2.aj_bq_afc_ma_awq_bjc $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ $1$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\zeta_{12})\) $C_2$, $C_2$, $C_2^2$ 1.2.ac 3 $\times$ 1.2.ab $\times$ 2.2.ac_c
6.2.aj_bq_afb_lu_avy_bhw $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$ $3$ \(\Q(\sqrt{-1}) \), 6.0.465831.1 $C_2$, $A_4\times C_2$ 1.2.ac 3 $\times$ 3.2.ad_g_aj
6.2.aj_bq_afa_lo_avg_bgq $6$ $\F_{2}$ $( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{5}$ $1$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.2.ac 5 $\times$ 1.2.b
6.2.aj_br_afl_nl_abaf_bpe $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ $5$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2$, $C_2^2$ 1.2.ac $\times$ 1.2.ab $\times$ 2.2.ad_f 2
6.2.aj_br_afk_nf_azo_boa $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ $4$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\zeta_{7})\) $C_2$, $C_2$, $C_6$ 1.2.ac 2 $\times$ 1.2.ab $\times$ 3.2.ae_j_ap
6.2.aj_br_afk_ng_azs_boi $6$ $\F_{2}$ $( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2$, $C_2^2$ 1.2.ac 3 $\times$ 1.2.a $\times$ 2.2.ad_f
6.2.aj_br_afj_na_aza_bnc $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), 4.0.1088.2 $C_2$, $C_2$, $D_{4}$ 1.2.ac 3 $\times$ 1.2.ab $\times$ 2.2.ac_d
6.2.aj_br_afi_mu_ayi_blw $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), 4.0.1025.1 $C_2$, $D_{4}$ 1.2.ac 4 $\times$ 2.2.ab_d
6.2.aj_bs_afr_of_abby_bsa $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ $4$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2$, $C_2^2$ 1.2.ac 2 $\times$ 1.2.ab 2 $\times$ 2.2.ad_f
6.2.aj_bs_afq_oa_abbk_brc $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$ $1$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$, $C_2$ 1.2.ac 4 $\times$ 1.2.ab $\times$ 1.2.a
6.2.aj_bt_afx_pa_abdu_bvc $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{3}( 1 - x + 2 x^{2} )^{3}$ $3$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.2.ac 3 $\times$ 1.2.ab 3
6.2.ai_bc_abx_t_ec_ajo $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8} )$ $4$ \(\Q(\sqrt{-1}) \), \(\Q(\zeta_{15})\) $C_2$, $C_4\times C_2$ 1.2.ac 2 $\times$ 4.2.ae_e_h_av
6.2.ai_bc_abw_m_ey_alc $6$ $\F_{2}$ $( 1 - 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{4}$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}) \) $C_2$, $C_2$ 1.2.ac 4 $\times$ 2.2.a_ae
6.2.ai_bd_acg_cf_i_adc $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$ $4$ \(\Q(\sqrt{-1}) \), 8.0.22581504.2 $C_2$, $D_4\times C_2$ 1.2.ac 2 $\times$ 4.2.ae_f_c_al
6.2.ai_bd_ace_bs_bw_afw $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - 3 x^{2} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(i, \sqrt{7})\) $C_2$, $C_2^2$ 1.2.ac 4 $\times$ 2.2.a_ad
6.2.ai_be_acs_en_agf_ik $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ $5$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{7})\) $C_2$, $C_2^2$, $C_6$ 1.2.ac $\times$ 2.2.ad_f $\times$ 3.2.ad_c_b
6.2.ai_be_acq_dy_aei_ey $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 6 x^{2} - 4 x^{3} + 2 x^{4} - 8 x^{5} + 24 x^{6} - 32 x^{7} + 16 x^{8} )$ $0$ \(\Q(\sqrt{-1}) \), 8.0.18939904.2 $C_2$, $D_4\times C_2$ 1.2.ac 2 $\times$ 4.2.ae_g_ae_c
6.2.ai_be_acn_de_aby_q $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$ $3$ \(\Q(\sqrt{-1}) \), 6.0.1539727.2 $C_2$, $D_{6}$ 1.2.ac 3 $\times$ 3.2.ac_a_d
6.2.ai_be_acm_cy_abg_aq $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - 2 x^{2} + 4 x^{4} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2$, $C_2^2$ 1.2.ac 4 $\times$ 2.2.a_ac
6.2.ai_bf_ada_fr_aiy_my $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ $4$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2$, $C_2^2$, $C_2^2$ 1.2.ac 2 $\times$ 2.2.ad_f $\times$ 2.2.ab_ab
6.2.ai_bf_acx_ex_ago_iq $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ $4$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\zeta_{7})\) $C_2$, $C_2$, $C_6$ 1.2.ac 2 $\times$ 1.2.ab $\times$ 3.2.ad_c_b
6.2.ai_bf_acw_eq_afs_hc $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$ $2$ \(\Q(\sqrt{-1}) \), 6.0.2580992.1 $C_2$, $D_{6}$ 1.2.ac 3 $\times$ 3.2.ac_b_a
6.2.ai_bf_acv_ek_afa_fw $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$ $3$ \(\Q(\sqrt{-1}) \), 6.0.2369943.1 $C_2$, $S_4\times C_2$ 1.2.ac 3 $\times$ 3.2.ac_b_b
6.2.ai_bf_acu_ee_aei_eq $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{4}( 1 - x^{2} + 4 x^{4} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2^2$ 1.2.ac 4 $\times$ 2.2.a_ab
6.2.ai_bg_adk_hk_ano_uy $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )^{2}$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\zeta_{12})\) $C_2$, $C_2^2$ 1.2.ac 2 $\times$ 2.2.ac_c 2
6.2.ai_bg_adj_hb_amh_sn $6$ $\F_{2}$ $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$ $6$ \(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.13140625.1 $C_2^2$, $C_2^2:C_4$ 2.2.ad_f $\times$ 4.2.af_m_au_bd
6.2.ai_bg_adh_gq_ale_qq $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.2312.1 $C_2$, $C_2^2$, $D_{4}$ 1.2.ac 2 $\times$ 2.2.ad_f $\times$ 2.2.ab_a
6.2.ai_bg_adg_gj_aki_pc $6$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8} )$ $4$ \(\Q(\sqrt{-1}) \), 8.0.18939904.2 $C_2$, $D_4\times C_2$ 1.2.ac 2 $\times$ 4.2.ae_i_am_r
6.2.ai_bg_adf_gc_ajm_no $6$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2$, $C_2$, $C_2^2$ 1.2.ac 3 $\times$ 1.2.ab $\times$ 2.2.ab_ab
Next   displayed columns for results