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Results (1-50 of 1023894 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
3.2.ae_j_ap $3$ $\F_{2}$ $1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6}$ $3$ \(\Q(\zeta_{7})\) $C_6$ simple
3.2.ae_k_ar $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2^2$ 1.2.ab $\times$ 2.2.ad_f
3.2.ad_c_b $3$ $\F_{2}$ $1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6}$ $3$ \(\Q(\zeta_{7})\) $C_6$ simple
3.2.ad_f_ah $3$ $\F_{2}$ $1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6}$ $3$ 6.0.679024.1 $S_4\times C_2$ simple
3.2.ad_g_aj $3$ $\F_{2}$ $1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6}$ $3$ 6.0.465831.1 $A_4\times C_2$ simple
3.2.ad_h_al $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), 4.0.1088.2 $C_2$, $D_{4}$ 1.2.ab $\times$ 2.2.ac_d
3.2.ad_j_an $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )^{3}$ $3$ \(\Q(\sqrt{-7}) \) $C_2$ 1.2.ab 3
3.2.ac_a_d $3$ $\F_{2}$ $1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6}$ $3$ 6.0.1539727.2 $D_{6}$ simple
3.2.ac_b_b $3$ $\F_{2}$ $1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6}$ $3$ 6.0.2369943.1 $S_4\times C_2$ simple
3.2.ac_c_ad $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2$, $C_2^2$ 1.2.ab $\times$ 2.2.ab_ab
3.2.ac_c_ab $3$ $\F_{2}$ $1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6}$ $3$ 6.0.2464727.1 $S_4\times C_2$ simple
3.2.ac_d_af $3$ $\F_{2}$ $1 - 2 x + 3 x^{2} - 5 x^{3} + 6 x^{4} - 8 x^{5} + 8 x^{6}$ $3$ 6.0.3194271.1 $S_4\times C_2$ simple
3.2.ac_d_ad $3$ $\F_{2}$ $1 - 2 x + 3 x^{2} - 3 x^{3} + 6 x^{4} - 8 x^{5} + 8 x^{6}$ $3$ 6.0.2256319.1 $A_4\times C_2$ simple
3.2.ac_e_ah $3$ $\F_{2}$ $( 1 + x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2^2$ 1.2.b $\times$ 2.2.ad_f
3.2.ac_e_af $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), 4.0.2873.1 $C_2$, $D_{4}$ 1.2.ab $\times$ 2.2.ab_b
3.2.ac_f_ah $3$ $\F_{2}$ $1 - 2 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 8 x^{5} + 8 x^{6}$ $3$ 6.0.400967.1 $A_4\times C_2$ simple
3.2.ac_g_ah $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), 4.0.1025.1 $C_2$, $D_{4}$ 1.2.ab $\times$ 2.2.ab_d
3.2.ab_ab_d $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\) $C_2$, $C_2^2$ 1.2.ab $\times$ 2.2.a_ad
3.2.ab_ab_f $3$ $\F_{2}$ $1 - x - x^{2} + 5 x^{3} - 2 x^{4} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.1142512.1 $S_4\times C_2$ simple
3.2.ab_a_ab $3$ $\F_{2}$ $1 - x - x^{3} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.6902343.1 $S_4\times C_2$ simple
3.2.ab_a_b $3$ $\F_{2}$ $1 - x + x^{3} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.14173175.1 $S_4\times C_2$ simple
3.2.ab_a_d $3$ $\F_{2}$ $1 - x + 3 x^{3} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.4039951.1 $A_4\times C_2$ simple
3.2.ab_b_ad $3$ $\F_{2}$ $1 - x + x^{2} - 3 x^{3} + 2 x^{4} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.503792.1 $S_4\times C_2$ simple
3.2.ab_b_ab $3$ $\F_{2}$ $1 - x + x^{2} - x^{3} + 2 x^{4} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.14950512.2 $S_4\times C_2$ simple
3.2.ab_b_b $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2$, $C_2^2$ 1.2.ab $\times$ 2.2.a_ab
3.2.ab_c_af $3$ $\F_{2}$ $1 - x + 2 x^{2} - 5 x^{3} + 4 x^{4} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.1342367.1 $A_4\times C_2$ simple
3.2.ab_c_ad $3$ $\F_{2}$ $1 - x + 2 x^{2} - 3 x^{3} + 4 x^{4} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.8140239.1 $S_4\times C_2$ simple
3.2.ab_c_ab $3$ $\F_{2}$ $1 - x + 2 x^{2} - x^{3} + 4 x^{4} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.6803047.1 $S_4\times C_2$ simple
3.2.ab_d_af $3$ $\F_{2}$ $( 1 + x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), 4.0.1088.2 $C_2$, $D_{4}$ 1.2.b $\times$ 2.2.ac_d
3.2.ab_d_ad $3$ $\F_{2}$ $1 - x + 3 x^{2} - 3 x^{3} + 6 x^{4} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.3307504.1 $S_4\times C_2$ simple
3.2.ab_d_ab $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 + x^{2} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{3}, \sqrt{-5})\) $C_2$, $C_2^2$ 1.2.ab $\times$ 2.2.a_b
3.2.ab_e_ad $3$ $\F_{2}$ $1 - x + 4 x^{2} - 3 x^{3} + 8 x^{4} - 4 x^{5} + 8 x^{6}$ $3$ 6.0.573839.1 $A_4\times C_2$ simple
3.2.ab_f_ad $3$ $\F_{2}$ $( 1 + x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.2.ab 2 $\times$ 1.2.b
3.2.a_ab_ab $3$ $\F_{2}$ $1 - x^{2} - x^{3} - 2 x^{4} + 8 x^{6}$ $3$ 6.0.12663175.1 $S_4\times C_2$ simple
3.2.a_ab_b $3$ $\F_{2}$ $1 - x^{2} + x^{3} - 2 x^{4} + 8 x^{6}$ $3$ 6.0.12663175.1 $S_4\times C_2$ simple
3.2.a_a_af $3$ $\F_{2}$ $( 1 + x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2$, $C_2^2$ 1.2.b $\times$ 2.2.ab_ab
3.2.a_a_ad $3$ $\F_{2}$ $1 - 3 x^{3} + 8 x^{6}$ $3$ 6.0.8869743.1 $D_{6}$ simple
3.2.a_a_ab $3$ $\F_{2}$ $1 - x^{3} + 8 x^{6}$ $3$ 6.0.21717639.1 $D_{6}$ simple
3.2.a_a_b $3$ $\F_{2}$ $1 + x^{3} + 8 x^{6}$ $3$ 6.0.21717639.1 $D_{6}$ simple
3.2.a_a_d $3$ $\F_{2}$ $1 + 3 x^{3} + 8 x^{6}$ $3$ 6.0.8869743.1 $D_{6}$ simple
3.2.a_a_f $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 + x - x^{2} + 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2$, $C_2^2$ 1.2.ab $\times$ 2.2.b_ab
3.2.a_b_ad $3$ $\F_{2}$ $1 + x^{2} - 3 x^{3} + 2 x^{4} + 8 x^{6}$ $3$ 6.0.4161087.1 $S_4\times C_2$ simple
3.2.a_b_ab $3$ $\F_{2}$ $1 + x^{2} - x^{3} + 2 x^{4} + 8 x^{6}$ $3$ 6.0.15884759.1 $S_4\times C_2$ simple
3.2.a_b_b $3$ $\F_{2}$ $1 + x^{2} + x^{3} + 2 x^{4} + 8 x^{6}$ $3$ 6.0.15884759.1 $S_4\times C_2$ simple
3.2.a_b_d $3$ $\F_{2}$ $1 + x^{2} + 3 x^{3} + 2 x^{4} + 8 x^{6}$ $3$ 6.0.4161087.1 $S_4\times C_2$ simple
3.2.a_c_ad $3$ $\F_{2}$ $( 1 + x + 2 x^{2} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), 4.0.2873.1 $C_2$, $D_{4}$ 1.2.b $\times$ 2.2.ab_b
3.2.a_c_ab $3$ $\F_{2}$ $1 + 2 x^{2} - x^{3} + 4 x^{4} + 8 x^{6}$ $3$ 6.0.6660007.1 $S_4\times C_2$ simple
3.2.a_c_b $3$ $\F_{2}$ $1 + 2 x^{2} + x^{3} + 4 x^{4} + 8 x^{6}$ $3$ 6.0.6660007.1 $S_4\times C_2$ simple
3.2.a_c_d $3$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 + x + x^{2} + 2 x^{3} + 4 x^{4} )$ $3$ \(\Q(\sqrt{-7}) \), 4.0.2873.1 $C_2$, $D_{4}$ 1.2.ab $\times$ 2.2.b_b
3.2.a_d_ab $3$ $\F_{2}$ $1 + 3 x^{2} - x^{3} + 6 x^{4} + 8 x^{6}$ $3$ 6.0.1305639.1 $A_4\times C_2$ simple
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