↑

Learn more

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

Refine search

Base field Base char. Dimension $p$-rank Initial coefficients
Simple Geom. simple Primitive Princ. polarizable Jacobian
Slopes Points on variety Points on curve Simple factors
Newton elevation # Jacobians # Hyp. Jacobians # twists Max twist degree
Angle rank Angle corank End. degree $p$-corank (Geom.) Sq.free
Cyclic group of points Non-cyclic primes
Use Geometric decomposition in the following inputs
Dim 1 factors Dim 2 factors Dim 3 factors Dim 4 factors Dim 5 factors
(distinct) (distinct) (distinct) Number field Galois group
Sort order Select

Results (1-50 of 5877 matches)

Next   displayed columns for results
Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.67.abg_pa $2$ $\F_{67}$ $( 1 - 16 x + 67 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.67.aq 2
2.67.abf_ok $2$ $\F_{67}$ $( 1 - 16 x + 67 x^{2} )( 1 - 15 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.67.aq $\times$ 1.67.ap
2.67.abe_nu $2$ $\F_{67}$ $( 1 - 16 x + 67 x^{2} )( 1 - 14 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.67.aq $\times$ 1.67.ao
2.67.abe_nv $2$ $\F_{67}$ $( 1 - 15 x + 67 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-43}) \) $C_2$ 1.67.ap 2
2.67.abd_nd $2$ $\F_{67}$ $1 - 29 x + 341 x^{2} - 1943 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-17 +2 \sqrt{13}})\) $D_{4}$ simple
2.67.abd_ne $2$ $\F_{67}$ $( 1 - 16 x + 67 x^{2} )( 1 - 13 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.67.aq $\times$ 1.67.an
2.67.abd_nf $2$ $\F_{67}$ $1 - 29 x + 343 x^{2} - 1943 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-194 +26 \sqrt{5}})\) $D_{4}$ simple
2.67.abd_ng $2$ $\F_{67}$ $( 1 - 15 x + 67 x^{2} )( 1 - 14 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.67.ap $\times$ 1.67.ao
2.67.abc_mn $2$ $\F_{67}$ $1 - 28 x + 325 x^{2} - 1876 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-98 +10 \sqrt{5}})\) $D_{4}$ simple
2.67.abc_mo $2$ $\F_{67}$ $( 1 - 16 x + 67 x^{2} )( 1 - 12 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-31}) \) $C_2$, $C_2$ 1.67.aq $\times$ 1.67.am
2.67.abc_mp $2$ $\F_{67}$ $1 - 28 x + 327 x^{2} - 1876 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-69 +28 \sqrt{3}})\) $D_{4}$ simple
2.67.abc_mq $2$ $\F_{67}$ $1 - 28 x + 328 x^{2} - 1876 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-70 +28 \sqrt{2}})\) $D_{4}$ simple
2.67.abc_mr $2$ $\F_{67}$ $( 1 - 15 x + 67 x^{2} )( 1 - 13 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.67.ap $\times$ 1.67.an
2.67.abc_ms $2$ $\F_{67}$ $( 1 - 14 x + 67 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-2}) \) $C_2$ 1.67.ao 2
2.67.abb_lx $2$ $\F_{67}$ $1 - 27 x + 309 x^{2} - 1809 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-81 +14 \sqrt{29}})\) $D_{4}$ simple
2.67.abb_ly $2$ $\F_{67}$ $( 1 - 16 x + 67 x^{2} )( 1 - 11 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.67.aq $\times$ 1.67.al
2.67.abb_lz $2$ $\F_{67}$ $1 - 27 x + 311 x^{2} - 1809 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-322 -54 \sqrt{21}})\) $D_{4}$ simple
2.67.abb_ma $2$ $\F_{67}$ $1 - 27 x + 312 x^{2} - 1809 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-326 -54 \sqrt{17}})\) $D_{4}$ simple
2.67.abb_mb $2$ $\F_{67}$ $1 - 27 x + 313 x^{2} - 1809 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-330 -54 \sqrt{13}})\) $D_{4}$ simple
2.67.abb_mc $2$ $\F_{67}$ $( 1 - 15 x + 67 x^{2} )( 1 - 12 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-31}) \) $C_2$, $C_2$ 1.67.ap $\times$ 1.67.am
2.67.abb_md $2$ $\F_{67}$ $1 - 27 x + 315 x^{2} - 1809 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-338 -54 \sqrt{5}})\) $D_{4}$ simple
2.67.abb_me $2$ $\F_{67}$ $( 1 - 14 x + 67 x^{2} )( 1 - 13 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.67.ao $\times$ 1.67.an
2.67.aba_lg $2$ $\F_{67}$ $1 - 26 x + 292 x^{2} - 1742 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-11 +2 \sqrt{11}})\) $D_{4}$ simple
2.67.aba_lh $2$ $\F_{67}$ $1 - 26 x + 293 x^{2} - 1742 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-26 +4 \sqrt{10}})\) $D_{4}$ simple
2.67.aba_li $2$ $\F_{67}$ $( 1 - 16 x + 67 x^{2} )( 1 - 10 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-42}) \) $C_2$, $C_2$ 1.67.aq $\times$ 1.67.ak
2.67.aba_lj $2$ $\F_{67}$ $1 - 26 x + 295 x^{2} - 1742 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-65 -26 \sqrt{2}})\) $D_{4}$ simple
2.67.aba_lk $2$ $\F_{67}$ $1 - 26 x + 296 x^{2} - 1742 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-92 -26 \sqrt{7}})\) $D_{4}$ simple
2.67.aba_ll $2$ $\F_{67}$ $1 - 26 x + 297 x^{2} - 1742 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-93 -26 \sqrt{6}})\) $D_{4}$ simple
2.67.aba_lm $2$ $\F_{67}$ $1 - 26 x + 298 x^{2} - 1742 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-19 +2 \sqrt{5}})\) $D_{4}$ simple
2.67.aba_ln $2$ $\F_{67}$ $( 1 - 15 x + 67 x^{2} )( 1 - 11 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.67.ap $\times$ 1.67.al
2.67.aba_lo $2$ $\F_{67}$ $1 - 26 x + 300 x^{2} - 1742 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-96 -26 \sqrt{3}})\) $D_{4}$ simple
2.67.aba_lp $2$ $\F_{67}$ $1 - 26 x + 301 x^{2} - 1742 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-97 -26 \sqrt{2}})\) $D_{4}$ simple
2.67.aba_lq $2$ $\F_{67}$ $( 1 - 14 x + 67 x^{2} )( 1 - 12 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-31}) \) $C_2$, $C_2$ 1.67.ao $\times$ 1.67.am
2.67.aba_lr $2$ $\F_{67}$ $( 1 - 13 x + 67 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-11}) \) $C_2$ 1.67.an 2
2.67.az_kq $2$ $\F_{67}$ $1 - 25 x + 276 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-90 +10 \sqrt{57}})\) $D_{4}$ simple
2.67.az_kr $2$ $\F_{67}$ $1 - 25 x + 277 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-26 +2 \sqrt{53}})\) $D_{4}$ simple
2.67.az_ks $2$ $\F_{67}$ $( 1 - 16 x + 67 x^{2} )( 1 - 9 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-187}) \) $C_2$, $C_2$ 1.67.aq $\times$ 1.67.aj
2.67.az_kt $2$ $\F_{67}$ $1 - 25 x + 279 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-57 +6 \sqrt{5}})\) $D_{4}$ simple
2.67.az_ku $2$ $\F_{67}$ $1 - 25 x + 280 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-406 +50 \sqrt{41}})\) $D_{4}$ simple
2.67.az_kv $2$ $\F_{67}$ $1 - 25 x + 281 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-65 +10 \sqrt{37}})\) $D_{4}$ simple
2.67.az_kw $2$ $\F_{67}$ $1 - 25 x + 282 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-414 +50 \sqrt{33}})\) $D_{4}$ simple
2.67.az_kx $2$ $\F_{67}$ $1 - 25 x + 283 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-418 +50 \sqrt{29}})\) $D_{4}$ simple
2.67.az_ky $2$ $\F_{67}$ $( 1 - 15 x + 67 x^{2} )( 1 - 10 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-42}) \) $C_2$, $C_2$ 1.67.ap $\times$ 1.67.ak
2.67.az_kz $2$ $\F_{67}$ $1 - 25 x + 285 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-426 +50 \sqrt{21}})\) $D_{4}$ simple
2.67.az_la $2$ $\F_{67}$ $1 - 25 x + 286 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-95 +20 \sqrt{17}})\) $D_{4}$ simple
2.67.az_lb $2$ $\F_{67}$ $1 - 25 x + 287 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-434 +50 \sqrt{13}})\) $D_{4}$ simple
2.67.az_lc $2$ $\F_{67}$ $( 1 - 14 x + 67 x^{2} )( 1 - 11 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.67.ao $\times$ 1.67.al
2.67.az_ld $2$ $\F_{67}$ $1 - 25 x + 289 x^{2} - 1675 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-442 +50 \sqrt{5}})\) $D_{4}$ simple
2.67.az_le $2$ $\F_{67}$ $( 1 - 13 x + 67 x^{2} )( 1 - 12 x + 67 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-31}) \) $C_2$, $C_2$ 1.67.an $\times$ 1.67.am
2.67.ay_jz $2$ $\F_{67}$ $1 - 24 x + 259 x^{2} - 1608 x^{3} + 4489 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{19})\) $C_2^2$ simple
Next   displayed columns for results