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 6683 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.73.abi_qt $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.73.ar 2
2.73.abh_qc $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )( 1 - 16 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.73.ar $\times$ 1.73.aq
2.73.abg_pl $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )( 1 - 15 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.73.ar $\times$ 1.73.ap
2.73.abg_pm $2$ $\F_{73}$ $( 1 - 16 x + 73 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.73.aq 2
2.73.abf_ou $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )( 1 - 14 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) $C_2$, $C_2$ 1.73.ar $\times$ 1.73.ao
2.73.abf_ov $2$ $\F_{73}$ $1 - 31 x + 385 x^{2} - 2263 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-37 +2 \sqrt{5}})\) $D_{4}$ simple
2.73.abf_ow $2$ $\F_{73}$ $( 1 - 16 x + 73 x^{2} )( 1 - 15 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.73.aq $\times$ 1.73.ap
2.73.abe_od $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.73.ar $\times$ 1.73.an
2.73.abe_oe $2$ $\F_{73}$ $1 - 30 x + 368 x^{2} - 2190 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-64 -30 \sqrt{3}})\) $D_{4}$ simple
2.73.abe_of $2$ $\F_{73}$ $1 - 30 x + 369 x^{2} - 2190 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-65 -30 \sqrt{2}})\) $D_{4}$ simple
2.73.abe_og $2$ $\F_{73}$ $( 1 - 16 x + 73 x^{2} )( 1 - 14 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \) $C_2$, $C_2$ 1.73.aq $\times$ 1.73.ao
2.73.abe_oh $2$ $\F_{73}$ $( 1 - 15 x + 73 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-67}) \) $C_2$ 1.73.ap 2
2.73.abd_nm $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )( 1 - 12 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-37}) \) $C_2$, $C_2$ 1.73.ar $\times$ 1.73.am
2.73.abd_nn $2$ $\F_{73}$ $1 - 29 x + 351 x^{2} - 2117 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-306 +58 \sqrt{21}})\) $D_{4}$ simple
2.73.abd_no $2$ $\F_{73}$ $1 - 29 x + 352 x^{2} - 2117 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-26 +2 \sqrt{17}})\) $D_{4}$ simple
2.73.abd_np $2$ $\F_{73}$ $1 - 29 x + 353 x^{2} - 2117 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-122 +26 \sqrt{13}})\) $D_{4}$ simple
2.73.abd_nq $2$ $\F_{73}$ $( 1 - 16 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.73.aq $\times$ 1.73.an
2.73.abd_nr $2$ $\F_{73}$ $1 - 29 x + 355 x^{2} - 2117 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-322 +58 \sqrt{5}})\) $D_{4}$ simple
2.73.abd_ns $2$ $\F_{73}$ $( 1 - 15 x + 73 x^{2} )( 1 - 14 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-6}) \) $C_2$, $C_2$ 1.73.ap $\times$ 1.73.ao
2.73.abc_mv $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )( 1 - 11 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.73.ar $\times$ 1.73.al
2.73.abc_mw $2$ $\F_{73}$ $1 - 28 x + 334 x^{2} - 2044 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-5 + \sqrt{2}})\) $D_{4}$ simple
2.73.abc_mx $2$ $\F_{73}$ $1 - 28 x + 335 x^{2} - 2044 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-89 +28 \sqrt{7}})\) $D_{4}$ simple
2.73.abc_my $2$ $\F_{73}$ $1 - 28 x + 336 x^{2} - 2044 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-90 +28 \sqrt{6}})\) $D_{4}$ simple
2.73.abc_mz $2$ $\F_{73}$ $1 - 28 x + 337 x^{2} - 2044 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-266 -14 \sqrt{5}})\) $D_{4}$ simple
2.73.abc_na $2$ $\F_{73}$ $( 1 - 16 x + 73 x^{2} )( 1 - 12 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-37}) \) $C_2$, $C_2$ 1.73.aq $\times$ 1.73.am
2.73.abc_nb $2$ $\F_{73}$ $1 - 28 x + 339 x^{2} - 2044 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-93 +28 \sqrt{3}})\) $D_{4}$ simple
2.73.abc_nc $2$ $\F_{73}$ $1 - 28 x + 340 x^{2} - 2044 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-94 +28 \sqrt{2}})\) $D_{4}$ simple
2.73.abc_nd $2$ $\F_{73}$ $( 1 - 15 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.73.ap $\times$ 1.73.an
2.73.abc_ne $2$ $\F_{73}$ $( 1 - 14 x + 73 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-6}) \) $C_2$ 1.73.ao 2
2.73.abb_me $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )( 1 - 10 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.73.ar $\times$ 1.73.ak
2.73.abb_mf $2$ $\F_{73}$ $1 - 27 x + 317 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-41 +6 \sqrt{5}})\) $D_{4}$ simple
2.73.abb_mg $2$ $\F_{73}$ $1 - 27 x + 318 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-398 -54 \sqrt{41}})\) $D_{4}$ simple
2.73.abb_mh $2$ $\F_{73}$ $1 - 27 x + 319 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-402 -54 \sqrt{37}})\) $D_{4}$ simple
2.73.abb_mi $2$ $\F_{73}$ $1 - 27 x + 320 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-10 + \sqrt{33}})\) $D_{4}$ simple
2.73.abb_mj $2$ $\F_{73}$ $1 - 27 x + 321 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-410 -54 \sqrt{29}})\) $D_{4}$ simple
2.73.abb_mk $2$ $\F_{73}$ $( 1 - 16 x + 73 x^{2} )( 1 - 11 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.73.aq $\times$ 1.73.al
2.73.abb_ml $2$ $\F_{73}$ $1 - 27 x + 323 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-418 -54 \sqrt{21}})\) $D_{4}$ simple
2.73.abb_mm $2$ $\F_{73}$ $1 - 27 x + 324 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-90 +2 \sqrt{17}})\) $D_{4}$ simple
2.73.abb_mn $2$ $\F_{73}$ $1 - 27 x + 325 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-426 -54 \sqrt{13}})\) $D_{4}$ simple
2.73.abb_mo $2$ $\F_{73}$ $( 1 - 15 x + 73 x^{2} )( 1 - 12 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-37}) \) $C_2$, $C_2$ 1.73.ap $\times$ 1.73.am
2.73.abb_mp $2$ $\F_{73}$ $1 - 27 x + 327 x^{2} - 1971 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-434 -54 \sqrt{5}})\) $D_{4}$ simple
2.73.abb_mq $2$ $\F_{73}$ $( 1 - 14 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.73.ao $\times$ 1.73.an
2.73.aba_ln $2$ $\F_{73}$ $( 1 - 17 x + 73 x^{2} )( 1 - 9 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-211}) \) $C_2$, $C_2$ 1.73.ar $\times$ 1.73.aj
2.73.aba_lo $2$ $\F_{73}$ $1 - 26 x + 300 x^{2} - 1898 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-108 -26 \sqrt{15}})\) $D_{4}$ simple
2.73.aba_lp $2$ $\F_{73}$ $1 - 26 x + 301 x^{2} - 1898 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-109 -26 \sqrt{14}})\) $D_{4}$ simple
2.73.aba_lq $2$ $\F_{73}$ $1 - 26 x + 302 x^{2} - 1898 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-6 + \sqrt{13}})\) $D_{4}$ simple
2.73.aba_lr $2$ $\F_{73}$ $1 - 26 x + 303 x^{2} - 1898 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-111 +52 \sqrt{3}})\) $D_{4}$ simple
2.73.aba_ls $2$ $\F_{73}$ $1 - 26 x + 304 x^{2} - 1898 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-112 -26 \sqrt{11}})\) $D_{4}$ simple
2.73.aba_lt $2$ $\F_{73}$ $1 - 26 x + 305 x^{2} - 1898 x^{3} + 5329 x^{4}$ $2$ \(\Q(\sqrt{-113 -26 \sqrt{10}})\) $D_{4}$ simple
2.73.aba_lu $2$ $\F_{73}$ $( 1 - 16 x + 73 x^{2} )( 1 - 10 x + 73 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.73.aq $\times$ 1.73.ak
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