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Results (1-50 of 30644 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
1.4.ac $1$ $\F_{2^{2}}$ $1 - 2 x + 4 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.4.a $1$ $\F_{2^{2}}$ $1 + 4 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.4.c $1$ $\F_{2^{2}}$ $1 + 2 x + 4 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.9.ad $1$ $\F_{3^{2}}$ $1 - 3 x + 9 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.9.a $1$ $\F_{3^{2}}$ $1 + 9 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.9.d $1$ $\F_{3^{2}}$ $1 + 3 x + 9 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.16.ae $1$ $\F_{2^{4}}$ $1 - 4 x + 16 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.16.a $1$ $\F_{2^{4}}$ $1 + 16 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.16.e $1$ $\F_{2^{4}}$ $1 + 4 x + 16 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.64.ai $1$ $\F_{2^{6}}$ $1 - 8 x + 64 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.64.a $1$ $\F_{2^{6}}$ $1 + 64 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.64.i $1$ $\F_{2^{6}}$ $1 + 8 x + 64 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.81.aj $1$ $\F_{3^{4}}$ $1 - 9 x + 81 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.81.a $1$ $\F_{3^{4}}$ $1 + 81 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.81.j $1$ $\F_{3^{4}}$ $1 + 9 x + 81 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.121.al $1$ $\F_{11^{2}}$ $1 - 11 x + 121 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.121.a $1$ $\F_{11^{2}}$ $1 + 121 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.121.l $1$ $\F_{11^{2}}$ $1 + 11 x + 121 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.256.aq $1$ $\F_{2^{8}}$ $1 - 16 x + 256 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.256.a $1$ $\F_{2^{8}}$ $1 + 256 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.256.q $1$ $\F_{2^{8}}$ $1 + 16 x + 256 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.729.abb $1$ $\F_{3^{6}}$ $1 - 27 x + 729 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.729.a $1$ $\F_{3^{6}}$ $1 + 729 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.729.bb $1$ $\F_{3^{6}}$ $1 + 27 x + 729 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.1024.abg $1$ $\F_{2^{10}}$ $1 - 32 x + 1024 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.1024.a $1$ $\F_{2^{10}}$ $1 + 1024 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.1024.bg $1$ $\F_{2^{10}}$ $1 + 32 x + 1024 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
2.2.ad_f $2$ $\F_{2}$ $1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ simple
2.2.ab_ab $2$ $\F_{2}$ $1 - x - x^{2} - 2 x^{3} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2^2$ simple
2.2.a_ad $2$ $\F_{2}$ $1 - 3 x^{2} + 4 x^{4}$ $2$ \(\Q(i, \sqrt{7})\) $C_2^2$ simple
2.2.a_b $2$ $\F_{2}$ $1 + x^{2} + 4 x^{4}$ $2$ \(\Q(\sqrt{3}, \sqrt{-5})\) $C_2^2$ simple
2.2.b_ab $2$ $\F_{2}$ $1 + x - x^{2} + 2 x^{3} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2^2$ simple
2.2.d_f $2$ $\F_{2}$ $1 + 3 x + 5 x^{2} + 6 x^{3} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ simple
2.3.ab_ac $2$ $\F_{3}$ $1 - x - 2 x^{2} - 3 x^{3} + 9 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-11})\) $C_2^2$ simple
2.3.a_ag $2$ $\F_{3}$ $( 1 - 3 x^{2} )^{2}$ $0$ \(\Q(\sqrt{3}) \) $C_2$ simple
2.3.a_af $2$ $\F_{3}$ $1 - 5 x^{2} + 9 x^{4}$ $2$ \(\Q(i, \sqrt{11})\) $C_2^2$ simple
2.3.a_ac $2$ $\F_{3}$ $1 - 2 x^{2} + 9 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.3.a_g $2$ $\F_{3}$ $( 1 + 3 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ 1.3.a 2
2.3.b_ac $2$ $\F_{3}$ $1 + x - 2 x^{2} + 3 x^{3} + 9 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-11})\) $C_2^2$ simple
2.4.ai_y $2$ $\F_{2^{2}}$ $( 1 - 2 x )^{4}$ $0$ \(\Q\) Trivial 1.4.ae 2
2.4.af_o $2$ $\F_{2^{2}}$ $( 1 - 3 x + 4 x^{2} )( 1 - 2 x + 4 x^{2} )$ $1$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.4.ad $\times$ 1.4.ac
2.4.ad_f $2$ $\F_{2^{2}}$ $1 - 3 x + 5 x^{2} - 12 x^{3} + 16 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2^2$ simple
2.4.ad_h $2$ $\F_{2^{2}}$ $1 - 3 x + 7 x^{2} - 12 x^{3} + 16 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{13})\) $C_2^2$ simple
2.4.ad_i $2$ $\F_{2^{2}}$ $( 1 - 3 x + 4 x^{2} )( 1 + 4 x^{2} )$ $1$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.4.ad $\times$ 1.4.a
2.4.ad_k $2$ $\F_{2^{2}}$ $( 1 - 2 x + 4 x^{2} )( 1 - x + 4 x^{2} )$ $1$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) $C_2$, $C_2$ 1.4.ac $\times$ 1.4.ab
2.4.ab_ad $2$ $\F_{2^{2}}$ $1 - x - 3 x^{2} - 4 x^{3} + 16 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ simple
2.4.ab_c $2$ $\F_{2^{2}}$ $( 1 - 3 x + 4 x^{2} )( 1 + 2 x + 4 x^{2} )$ $1$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.4.ad $\times$ 1.4.c
2.4.ab_g $2$ $\F_{2^{2}}$ $( 1 - 2 x + 4 x^{2} )( 1 + x + 4 x^{2} )$ $1$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) $C_2$, $C_2$ 1.4.ac $\times$ 1.4.b
2.4.ab_i $2$ $\F_{2^{2}}$ $( 1 - x + 4 x^{2} )( 1 + 4 x^{2} )$ $1$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.4.ab $\times$ 1.4.a
2.4.a_ai $2$ $\F_{2^{2}}$ $( 1 - 2 x )^{2}( 1 + 2 x )^{2}$ $0$ \(\Q\), \(\Q\) Trivial, Trivial 1.4.ae $\times$ 1.4.e
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