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Results (1-50 of 30250 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.2.ae_i $2$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ 1.2.ac 2
2.2.ac_c $2$ $\F_{2}$ $1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.2.ac_e $2$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.2.ac $\times$ 1.2.a
2.2.a_ae $2$ $\F_{2}$ $( 1 - 2 x^{2} )^{2}$ $0$ \(\Q(\sqrt{2}) \) $C_2$ simple
2.2.a_ac $2$ $\F_{2}$ $1 - 2 x^{2} + 4 x^{4}$ $0$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.2.a_a $2$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.2.ac $\times$ 1.2.c
2.2.a_c $2$ $\F_{2}$ $1 + 2 x^{2} + 4 x^{4}$ $0$ \(\Q(\sqrt{2}, \sqrt{-3})\) $C_2^2$ simple
2.2.a_e $2$ $\F_{2}$ $( 1 + 2 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-2}) \) $C_2$ 1.2.a 2
2.2.c_c $2$ $\F_{2}$ $1 + 2 x + 2 x^{2} + 4 x^{3} + 4 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.2.c_e $2$ $\F_{2}$ $( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ $0$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.2.a $\times$ 1.2.c
2.2.e_i $2$ $\F_{2}$ $( 1 + 2 x + 2 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ 1.2.c 2
2.3.ag_p $2$ $\F_{3}$ $( 1 - 3 x + 3 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ 1.3.ad 2
2.3.ae_i $2$ $\F_{3}$ $1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.3.ad_g $2$ $\F_{3}$ $( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.3.ad $\times$ 1.3.a
2.3.ac_b $2$ $\F_{3}$ $1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4}$ $2$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.3.a_ad $2$ $\F_{3}$ $( 1 - 3 x + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.3.ad $\times$ 1.3.d
2.3.a_a $2$ $\F_{3}$ $1 + 9 x^{4}$ $0$ \(\Q(i, \sqrt{6})\) $C_2^2$ simple
2.3.a_d $2$ $\F_{3}$ $1 + 3 x^{2} + 9 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.3.c_b $2$ $\F_{3}$ $1 + 2 x + x^{2} + 6 x^{3} + 9 x^{4}$ $2$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.3.d_g $2$ $\F_{3}$ $( 1 + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.3.a $\times$ 1.3.d
2.3.e_i $2$ $\F_{3}$ $1 + 4 x + 8 x^{2} + 12 x^{3} + 9 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.3.g_p $2$ $\F_{3}$ $( 1 + 3 x + 3 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ 1.3.d 2
2.5.ag_r $2$ $\F_{5}$ $1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4}$ $2$ \(\Q(\sqrt{2}, \sqrt{-3})\) $C_2^2$ simple
2.5.ae_i $2$ $\F_{5}$ $1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4}$ $2$ \(\Q(i, \sqrt{6})\) $C_2^2$ simple
2.5.ae_l $2$ $\F_{5}$ $1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4}$ $2$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.5.ac_ab $2$ $\F_{5}$ $1 - 2 x - x^{2} - 10 x^{3} + 25 x^{4}$ $2$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.5.a_ai $2$ $\F_{5}$ $1 - 8 x^{2} + 25 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.5.a_i $2$ $\F_{5}$ $1 + 8 x^{2} + 25 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.5.c_ab $2$ $\F_{5}$ $1 + 2 x - x^{2} + 10 x^{3} + 25 x^{4}$ $2$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.5.e_i $2$ $\F_{5}$ $1 + 4 x + 8 x^{2} + 20 x^{3} + 25 x^{4}$ $2$ \(\Q(i, \sqrt{6})\) $C_2^2$ simple
2.5.e_l $2$ $\F_{5}$ $1 + 4 x + 11 x^{2} + 20 x^{3} + 25 x^{4}$ $2$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.5.g_r $2$ $\F_{5}$ $1 + 6 x + 17 x^{2} + 30 x^{3} + 25 x^{4}$ $2$ \(\Q(\sqrt{2}, \sqrt{-3})\) $C_2^2$ simple
2.7.a_ah $2$ $\F_{7}$ $1 - 7 x^{2} + 49 x^{4}$ $0$ \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2^2$ simple
2.7.a_a $2$ $\F_{7}$ $1 + 49 x^{4}$ $0$ \(\Q(i, \sqrt{14})\) $C_2^2$ simple
2.7.a_h $2$ $\F_{7}$ $1 + 7 x^{2} + 49 x^{4}$ $0$ \(\Q(\sqrt{-3}, \sqrt{7})\) $C_2^2$ simple
2.8.ai_bg $2$ $\F_{2^{3}}$ $( 1 - 4 x + 8 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ 1.8.ae 2
2.8.ae_i $2$ $\F_{2^{3}}$ $1 - 4 x + 8 x^{2} - 32 x^{3} + 64 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.8.ae_q $2$ $\F_{2^{3}}$ $( 1 - 4 x + 8 x^{2} )( 1 + 8 x^{2} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.8.ae $\times$ 1.8.a
2.8.a_aq $2$ $\F_{2^{3}}$ $( 1 - 8 x^{2} )^{2}$ $0$ \(\Q(\sqrt{2}) \) $C_2$ simple
2.8.a_ai $2$ $\F_{2^{3}}$ $1 - 8 x^{2} + 64 x^{4}$ $0$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.8.a_a $2$ $\F_{2^{3}}$ $( 1 - 4 x + 8 x^{2} )( 1 + 4 x + 8 x^{2} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.8.ae $\times$ 1.8.e
2.8.a_i $2$ $\F_{2^{3}}$ $1 + 8 x^{2} + 64 x^{4}$ $0$ \(\Q(\sqrt{2}, \sqrt{-3})\) $C_2^2$ simple
2.8.a_q $2$ $\F_{2^{3}}$ $( 1 + 8 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-2}) \) $C_2$ 1.8.a 2
2.8.e_i $2$ $\F_{2^{3}}$ $1 + 4 x + 8 x^{2} + 32 x^{3} + 64 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.8.e_q $2$ $\F_{2^{3}}$ $( 1 + 8 x^{2} )( 1 + 4 x + 8 x^{2} )$ $0$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.8.a $\times$ 1.8.e
2.8.i_bg $2$ $\F_{2^{3}}$ $( 1 + 4 x + 8 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ 1.8.e 2
2.9.ai_bg $2$ $\F_{3^{2}}$ $1 - 8 x + 32 x^{2} - 72 x^{3} + 81 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.9.ac_af $2$ $\F_{3^{2}}$ $1 - 2 x - 5 x^{2} - 18 x^{3} + 81 x^{4}$ $2$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.9.c_af $2$ $\F_{3^{2}}$ $1 + 2 x - 5 x^{2} + 18 x^{3} + 81 x^{4}$ $2$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.9.i_bg $2$ $\F_{3^{2}}$ $1 + 8 x + 32 x^{2} + 72 x^{3} + 81 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
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