The results below are complete, since the LMFDB contains all isogeny classes of abelian varieties of dimension at most 2 over fields of cardinality at most 211 or 243, 256, 343, 512, 625, 729, 1024

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Results (1-50 of 3461 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.47.aba_kd $2$ $\F_{47}$ $( 1 - 13 x + 47 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-19}) \) $C_2$ 1.47.an 2
2.47.az_jp $2$ $\F_{47}$ $1 - 25 x + 249 x^{2} - 1175 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-13 +2 \sqrt{5}})\) $D_{4}$ simple
2.47.az_jq $2$ $\F_{47}$ $( 1 - 13 x + 47 x^{2} )( 1 - 12 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.47.an $\times$ 1.47.am
2.47.ay_jc $2$ $\F_{47}$ $1 - 24 x + 236 x^{2} - 1128 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-30 +12 \sqrt{2}})\) $D_{4}$ simple
2.47.ay_jd $2$ $\F_{47}$ $( 1 - 13 x + 47 x^{2} )( 1 - 11 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.47.an $\times$ 1.47.al
2.47.ay_je $2$ $\F_{47}$ $( 1 - 12 x + 47 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-11}) \) $C_2$ 1.47.am 2
2.47.ax_io $2$ $\F_{47}$ $1 - 23 x + 222 x^{2} - 1081 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-13 +2 \sqrt{17}})\) $D_{4}$ simple
2.47.ax_ip $2$ $\F_{47}$ $1 - 23 x + 223 x^{2} - 1081 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-210 -46 \sqrt{13}})\) $D_{4}$ simple
2.47.ax_iq $2$ $\F_{47}$ $( 1 - 13 x + 47 x^{2} )( 1 - 10 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.47.an $\times$ 1.47.ak
2.47.ax_ir $2$ $\F_{47}$ $1 - 23 x + 225 x^{2} - 1081 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-53 +10 \sqrt{5}})\) $D_{4}$ simple
2.47.ax_is $2$ $\F_{47}$ $( 1 - 12 x + 47 x^{2} )( 1 - 11 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.47.am $\times$ 1.47.al
2.47.aw_ia $2$ $\F_{47}$ $1 - 22 x + 208 x^{2} - 1034 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-9 +2 \sqrt{7}})\) $D_{4}$ simple
2.47.aw_ib $2$ $\F_{47}$ $1 - 22 x + 209 x^{2} - 1034 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-61 -22 \sqrt{6}})\) $D_{4}$ simple
2.47.aw_ic $2$ $\F_{47}$ $1 - 22 x + 210 x^{2} - 1034 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-38 +2 \sqrt{5}})\) $D_{4}$ simple
2.47.aw_id $2$ $\F_{47}$ $( 1 - 13 x + 47 x^{2} )( 1 - 9 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-107}) \) $C_2$, $C_2$ 1.47.an $\times$ 1.47.aj
2.47.aw_ie $2$ $\F_{47}$ $1 - 22 x + 212 x^{2} - 1034 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-64 -22 \sqrt{3}})\) $D_{4}$ simple
2.47.aw_if $2$ $\F_{47}$ $1 - 22 x + 213 x^{2} - 1034 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-65 -22 \sqrt{2}})\) $D_{4}$ simple
2.47.aw_ig $2$ $\F_{47}$ $( 1 - 12 x + 47 x^{2} )( 1 - 10 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.47.am $\times$ 1.47.ak
2.47.aw_ih $2$ $\F_{47}$ $( 1 - 11 x + 47 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-67}) \) $C_2$ 1.47.al 2
2.47.av_hm $2$ $\F_{47}$ $1 - 21 x + 194 x^{2} - 987 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{41})\) $C_2^2$ simple
2.47.av_hn $2$ $\F_{47}$ $1 - 21 x + 195 x^{2} - 987 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-274 +42 \sqrt{37}})\) $D_{4}$ simple
2.47.av_ho $2$ $\F_{47}$ $1 - 21 x + 196 x^{2} - 987 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-278 +42 \sqrt{33}})\) $D_{4}$ simple
2.47.av_hp $2$ $\F_{47}$ $1 - 21 x + 197 x^{2} - 987 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-282 +42 \sqrt{29}})\) $D_{4}$ simple
2.47.av_hq $2$ $\F_{47}$ $( 1 - 13 x + 47 x^{2} )( 1 - 8 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-31}) \) $C_2$, $C_2$ 1.47.an $\times$ 1.47.ai
2.47.av_hr $2$ $\F_{47}$ $1 - 21 x + 199 x^{2} - 987 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-290 +42 \sqrt{21}})\) $D_{4}$ simple
2.47.av_hs $2$ $\F_{47}$ $1 - 21 x + 200 x^{2} - 987 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-294 +42 \sqrt{17}})\) $D_{4}$ simple
2.47.av_ht $2$ $\F_{47}$ $1 - 21 x + 201 x^{2} - 987 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-298 +42 \sqrt{13}})\) $D_{4}$ simple
2.47.av_hu $2$ $\F_{47}$ $( 1 - 12 x + 47 x^{2} )( 1 - 9 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-107}) \) $C_2$, $C_2$ 1.47.am $\times$ 1.47.aj
2.47.av_hv $2$ $\F_{47}$ $1 - 21 x + 203 x^{2} - 987 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-306 +42 \sqrt{5}})\) $D_{4}$ simple
2.47.av_hw $2$ $\F_{47}$ $( 1 - 11 x + 47 x^{2} )( 1 - 10 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.47.al $\times$ 1.47.ak
2.47.au_gz $2$ $\F_{47}$ $1 - 20 x + 181 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-90 +10 \sqrt{13}})\) $D_{4}$ simple
2.47.au_ha $2$ $\F_{47}$ $1 - 20 x + 182 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-16 -2 \sqrt{3}})\) $D_{4}$ simple
2.47.au_hb $2$ $\F_{47}$ $1 - 20 x + 183 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-77 +20 \sqrt{11}})\) $D_{4}$ simple
2.47.au_hc $2$ $\F_{47}$ $1 - 20 x + 184 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-78 +20 \sqrt{10}})\) $D_{4}$ simple
2.47.au_hd $2$ $\F_{47}$ $( 1 - 13 x + 47 x^{2} )( 1 - 7 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-139}) \) $C_2$, $C_2$ 1.47.an $\times$ 1.47.ah
2.47.au_he $2$ $\F_{47}$ $1 - 20 x + 186 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-10 +5 \sqrt{2}})\) $C_4$ simple
2.47.au_hf $2$ $\F_{47}$ $1 - 20 x + 187 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-81 +20 \sqrt{7}})\) $D_{4}$ simple
2.47.au_hg $2$ $\F_{47}$ $1 - 20 x + 188 x^{2} - 940 x^{3} + 2209 x^{4}$ $1$ \(\Q(\sqrt{-82 +20 \sqrt{6}})\) $D_{4}$ simple
2.47.au_hh $2$ $\F_{47}$ $1 - 20 x + 189 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-298 -46 \sqrt{5}})\) $D_{4}$ simple
2.47.au_hi $2$ $\F_{47}$ $( 1 - 12 x + 47 x^{2} )( 1 - 8 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-31}) \) $C_2$, $C_2$ 1.47.am $\times$ 1.47.ai
2.47.au_hj $2$ $\F_{47}$ $1 - 20 x + 191 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-85 +20 \sqrt{3}})\) $D_{4}$ simple
2.47.au_hk $2$ $\F_{47}$ $1 - 20 x + 192 x^{2} - 940 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-86 +20 \sqrt{2}})\) $D_{4}$ simple
2.47.au_hl $2$ $\F_{47}$ $( 1 - 11 x + 47 x^{2} )( 1 - 9 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-107}) \) $C_2$, $C_2$ 1.47.al $\times$ 1.47.aj
2.47.au_hm $2$ $\F_{47}$ $( 1 - 10 x + 47 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-22}) \) $C_2$ 1.47.ak 2
2.47.at_gl $2$ $\F_{47}$ $1 - 19 x + 167 x^{2} - 893 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-69 +6 \sqrt{69}})\) $D_{4}$ simple
2.47.at_gm $2$ $\F_{47}$ $1 - 19 x + 168 x^{2} - 893 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-326 -38 \sqrt{65}})\) $D_{4}$ simple
2.47.at_gn $2$ $\F_{47}$ $1 - 19 x + 169 x^{2} - 893 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-330 -38 \sqrt{61}})\) $D_{4}$ simple
2.47.at_go $2$ $\F_{47}$ $1 - 19 x + 170 x^{2} - 893 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-334 -38 \sqrt{57}})\) $D_{4}$ simple
2.47.at_gp $2$ $\F_{47}$ $1 - 19 x + 171 x^{2} - 893 x^{3} + 2209 x^{4}$ $2$ \(\Q(\sqrt{-338 -38 \sqrt{53}})\) $D_{4}$ simple
2.47.at_gq $2$ $\F_{47}$ $( 1 - 13 x + 47 x^{2} )( 1 - 6 x + 47 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-38}) \) $C_2$, $C_2$ 1.47.an $\times$ 1.47.ag
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