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 6409 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.71.abg_pi $2$ $\F_{71}$ $( 1 - 16 x + 71 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-7}) \) $C_2$ 1.71.aq 2
2.71.abf_or $2$ $\F_{71}$ $1 - 31 x + 381 x^{2} - 2201 x^{3} + 5041 x^{4}$ $2$ \(\Q(\zeta_{5})\) $C_4$ simple
2.71.abf_os $2$ $\F_{71}$ $( 1 - 16 x + 71 x^{2} )( 1 - 15 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-59}) \) $C_2$, $C_2$ 1.71.aq $\times$ 1.71.ap
2.71.abe_oa $2$ $\F_{71}$ $1 - 30 x + 364 x^{2} - 2130 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-32 -14 \sqrt{3}})\) $D_{4}$ simple
2.71.abe_ob $2$ $\F_{71}$ $1 - 30 x + 365 x^{2} - 2130 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-51 +24 \sqrt{2}})\) $D_{4}$ simple
2.71.abe_oc $2$ $\F_{71}$ $( 1 - 16 x + 71 x^{2} )( 1 - 14 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.71.aq $\times$ 1.71.ao
2.71.abe_od $2$ $\F_{71}$ $( 1 - 15 x + 71 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-59}) \) $C_2$ 1.71.ap 2
2.71.abd_nj $2$ $\F_{71}$ $1 - 29 x + 347 x^{2} - 2059 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-106 +18 \sqrt{21}})\) $D_{4}$ simple
2.71.abd_nk $2$ $\F_{71}$ $1 - 29 x + 348 x^{2} - 2059 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-278 +58 \sqrt{17}})\) $D_{4}$ simple
2.71.abd_nl $2$ $\F_{71}$ $1 - 29 x + 349 x^{2} - 2059 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-282 +58 \sqrt{13}})\) $D_{4}$ simple
2.71.abd_nm $2$ $\F_{71}$ $( 1 - 16 x + 71 x^{2} )( 1 - 13 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.71.aq $\times$ 1.71.an
2.71.abd_nn $2$ $\F_{71}$ $1 - 29 x + 351 x^{2} - 2059 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-290 +58 \sqrt{5}})\) $C_4$ simple
2.71.abd_no $2$ $\F_{71}$ $( 1 - 15 x + 71 x^{2} )( 1 - 14 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.71.ap $\times$ 1.71.ao
2.71.abc_ms $2$ $\F_{71}$ $1 - 28 x + 330 x^{2} - 1988 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-2 + \sqrt{2}})\) $C_4$ simple
2.71.abc_mt $2$ $\F_{71}$ $1 - 28 x + 331 x^{2} - 1988 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-81 +28 \sqrt{7}})\) $D_{4}$ simple
2.71.abc_mu $2$ $\F_{71}$ $1 - 28 x + 332 x^{2} - 1988 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-82 +28 \sqrt{6}})\) $D_{4}$ simple
2.71.abc_mv $2$ $\F_{71}$ $1 - 28 x + 333 x^{2} - 1988 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-218 +2 \sqrt{5}})\) $D_{4}$ simple
2.71.abc_mw $2$ $\F_{71}$ $( 1 - 16 x + 71 x^{2} )( 1 - 12 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \) $C_2$, $C_2$ 1.71.aq $\times$ 1.71.am
2.71.abc_mx $2$ $\F_{71}$ $1 - 28 x + 335 x^{2} - 1988 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-85 +28 \sqrt{3}})\) $D_{4}$ simple
2.71.abc_my $2$ $\F_{71}$ $1 - 28 x + 336 x^{2} - 1988 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-86 +28 \sqrt{2}})\) $D_{4}$ simple
2.71.abc_mz $2$ $\F_{71}$ $( 1 - 15 x + 71 x^{2} )( 1 - 13 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.71.ap $\times$ 1.71.an
2.71.abc_na $2$ $\F_{71}$ $( 1 - 14 x + 71 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-22}) \) $C_2$ 1.71.ao 2
2.71.abb_mc $2$ $\F_{71}$ $1 - 27 x + 314 x^{2} - 1917 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{41})\) $C_2^2$ simple
2.71.abb_md $2$ $\F_{71}$ $1 - 27 x + 315 x^{2} - 1917 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-74 +2 \sqrt{37}})\) $C_4$ simple
2.71.abb_me $2$ $\F_{71}$ $1 - 27 x + 316 x^{2} - 1917 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-374 -54 \sqrt{33}})\) $D_{4}$ simple
2.71.abb_mf $2$ $\F_{71}$ $1 - 27 x + 317 x^{2} - 1917 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-42 -6 \sqrt{29}})\) $D_{4}$ simple
2.71.abb_mg $2$ $\F_{71}$ $( 1 - 16 x + 71 x^{2} )( 1 - 11 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-163}) \) $C_2$, $C_2$ 1.71.aq $\times$ 1.71.al
2.71.abb_mh $2$ $\F_{71}$ $1 - 27 x + 319 x^{2} - 1917 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-386 -54 \sqrt{21}})\) $D_{4}$ simple
2.71.abb_mi $2$ $\F_{71}$ $1 - 27 x + 320 x^{2} - 1917 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-390 -54 \sqrt{17}})\) $D_{4}$ simple
2.71.abb_mj $2$ $\F_{71}$ $1 - 27 x + 321 x^{2} - 1917 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-394 -54 \sqrt{13}})\) $D_{4}$ simple
2.71.abb_mk $2$ $\F_{71}$ $( 1 - 15 x + 71 x^{2} )( 1 - 12 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-35}) \) $C_2$, $C_2$ 1.71.ap $\times$ 1.71.am
2.71.abb_ml $2$ $\F_{71}$ $1 - 27 x + 323 x^{2} - 1917 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-402 -54 \sqrt{5}})\) $D_{4}$ simple
2.71.abb_mm $2$ $\F_{71}$ $( 1 - 14 x + 71 x^{2} )( 1 - 13 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-22}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.71.ao $\times$ 1.71.an
2.71.aba_ll $2$ $\F_{71}$ $1 - 26 x + 297 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-101 -26 \sqrt{14}})\) $D_{4}$ simple
2.71.aba_lm $2$ $\F_{71}$ $1 - 26 x + 298 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-54 +10 \sqrt{13}})\) $D_{4}$ simple
2.71.aba_ln $2$ $\F_{71}$ $1 - 26 x + 299 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-97 +48 \sqrt{3}})\) $D_{4}$ simple
2.71.aba_lo $2$ $\F_{71}$ $1 - 26 x + 300 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-104 -26 \sqrt{11}})\) $D_{4}$ simple
2.71.aba_lp $2$ $\F_{71}$ $1 - 26 x + 301 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-105 -26 \sqrt{10}})\) $D_{4}$ simple
2.71.aba_lq $2$ $\F_{71}$ $( 1 - 16 x + 71 x^{2} )( 1 - 10 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-46}) \) $C_2$, $C_2$ 1.71.aq $\times$ 1.71.ak
2.71.aba_lr $2$ $\F_{71}$ $1 - 26 x + 303 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-107 +52 \sqrt{2}})\) $D_{4}$ simple
2.71.aba_ls $2$ $\F_{71}$ $1 - 26 x + 304 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-108 -26 \sqrt{7}})\) $D_{4}$ simple
2.71.aba_lt $2$ $\F_{71}$ $1 - 26 x + 305 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-43 +16 \sqrt{6}})\) $D_{4}$ simple
2.71.aba_lu $2$ $\F_{71}$ $1 - 26 x + 306 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-25 +4 \sqrt{5}})\) $D_{4}$ simple
2.71.aba_lv $2$ $\F_{71}$ $( 1 - 15 x + 71 x^{2} )( 1 - 11 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-163}) \) $C_2$, $C_2$ 1.71.ap $\times$ 1.71.al
2.71.aba_lw $2$ $\F_{71}$ $1 - 26 x + 308 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-112 -26 \sqrt{3}})\) $D_{4}$ simple
2.71.aba_lx $2$ $\F_{71}$ $1 - 26 x + 309 x^{2} - 1846 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-19 +8 \sqrt{2}})\) $D_{4}$ simple
2.71.aba_ly $2$ $\F_{71}$ $( 1 - 14 x + 71 x^{2} )( 1 - 12 x + 71 x^{2} )$ $2$ \(\Q(\sqrt{-22}) \), \(\Q(\sqrt{-35}) \) $C_2$, $C_2$ 1.71.ao $\times$ 1.71.am
2.71.aba_lz $2$ $\F_{71}$ $( 1 - 13 x + 71 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-115}) \) $C_2$ 1.71.an 2
2.71.az_ku $2$ $\F_{71}$ $1 - 25 x + 280 x^{2} - 1775 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-438 +50 \sqrt{73}})\) $D_{4}$ simple
2.71.az_kv $2$ $\F_{71}$ $1 - 25 x + 281 x^{2} - 1775 x^{3} + 5041 x^{4}$ $2$ \(\Q(\sqrt{-442 +50 \sqrt{69}})\) $D_{4}$ simple
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