↑

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 4861 matches)

Next   displayed columns for results
Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.59.abe_nf $2$ $\F_{59}$ $( 1 - 15 x + 59 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-11}) \) $C_2$ 1.59.ap 2
2.59.abd_mq $2$ $\F_{59}$ $( 1 - 15 x + 59 x^{2} )( 1 - 14 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.59.ap $\times$ 1.59.ao
2.59.abc_mb $2$ $\F_{59}$ $( 1 - 15 x + 59 x^{2} )( 1 - 13 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.59.ap $\times$ 1.59.an
2.59.abc_mc $2$ $\F_{59}$ $( 1 - 14 x + 59 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-10}) \) $C_2$ 1.59.ao 2
2.59.abb_ll $2$ $\F_{59}$ $1 - 27 x + 297 x^{2} - 1593 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-58 -6 \sqrt{13}})\) $D_{4}$ simple
2.59.abb_lm $2$ $\F_{59}$ $( 1 - 15 x + 59 x^{2} )( 1 - 12 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-23}) \) $C_2$, $C_2$ 1.59.ap $\times$ 1.59.am
2.59.abb_ln $2$ $\F_{59}$ $1 - 27 x + 299 x^{2} - 1593 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-45 +6 \sqrt{5}})\) $D_{4}$ simple
2.59.abb_lo $2$ $\F_{59}$ $( 1 - 14 x + 59 x^{2} )( 1 - 13 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.59.ao $\times$ 1.59.an
2.59.aba_kw $2$ $\F_{59}$ $1 - 26 x + 282 x^{2} - 1534 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-22 +2 \sqrt{5}})\) $D_{4}$ simple
2.59.aba_kx $2$ $\F_{59}$ $( 1 - 15 x + 59 x^{2} )( 1 - 11 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.59.ap $\times$ 1.59.al
2.59.aba_ky $2$ $\F_{59}$ $1 - 26 x + 284 x^{2} - 1534 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-64 -26 \sqrt{3}})\) $D_{4}$ simple
2.59.aba_kz $2$ $\F_{59}$ $1 - 26 x + 285 x^{2} - 1534 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-65 -26 \sqrt{2}})\) $D_{4}$ simple
2.59.aba_la $2$ $\F_{59}$ $( 1 - 14 x + 59 x^{2} )( 1 - 12 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-23}) \) $C_2$, $C_2$ 1.59.ao $\times$ 1.59.am
2.59.aba_lb $2$ $\F_{59}$ $( 1 - 13 x + 59 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-67}) \) $C_2$ 1.59.an 2
2.59.az_kh $2$ $\F_{59}$ $1 - 25 x + 267 x^{2} - 1475 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-290 +50 \sqrt{29}})\) $C_4$ simple
2.59.az_ki $2$ $\F_{59}$ $( 1 - 15 x + 59 x^{2} )( 1 - 10 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-34}) \) $C_2$, $C_2$ 1.59.ap $\times$ 1.59.ak
2.59.az_kj $2$ $\F_{59}$ $1 - 25 x + 269 x^{2} - 1475 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-298 +50 \sqrt{21}})\) $D_{4}$ simple
2.59.az_kk $2$ $\F_{59}$ $1 - 25 x + 270 x^{2} - 1475 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-43 +8 \sqrt{17}})\) $D_{4}$ simple
2.59.az_kl $2$ $\F_{59}$ $1 - 25 x + 271 x^{2} - 1475 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-306 +50 \sqrt{13}})\) $D_{4}$ simple
2.59.az_km $2$ $\F_{59}$ $( 1 - 14 x + 59 x^{2} )( 1 - 11 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.59.ao $\times$ 1.59.al
2.59.az_kn $2$ $\F_{59}$ $1 - 25 x + 273 x^{2} - 1475 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-314 +50 \sqrt{5}})\) $D_{4}$ simple
2.59.az_ko $2$ $\F_{59}$ $( 1 - 13 x + 59 x^{2} )( 1 - 12 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-23}) \) $C_2$, $C_2$ 1.59.an $\times$ 1.59.am
2.59.ay_jr $2$ $\F_{59}$ $1 - 24 x + 251 x^{2} - 1416 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{11})\) $C_2^2$ simple
2.59.ay_js $2$ $\F_{59}$ $1 - 24 x + 252 x^{2} - 1416 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-82 +24 \sqrt{10}})\) $D_{4}$ simple
2.59.ay_jt $2$ $\F_{59}$ $( 1 - 15 x + 59 x^{2} )( 1 - 9 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-155}) \) $C_2$, $C_2$ 1.59.ap $\times$ 1.59.aj
2.59.ay_ju $2$ $\F_{59}$ $1 - 24 x + 254 x^{2} - 1416 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-30 +12 \sqrt{2}})\) $D_{4}$ simple
2.59.ay_jv $2$ $\F_{59}$ $1 - 24 x + 255 x^{2} - 1416 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-85 +24 \sqrt{7}})\) $D_{4}$ simple
2.59.ay_jw $2$ $\F_{59}$ $1 - 24 x + 256 x^{2} - 1416 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-86 +24 \sqrt{6}})\) $D_{4}$ simple
2.59.ay_jx $2$ $\F_{59}$ $1 - 24 x + 257 x^{2} - 1416 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-282 -30 \sqrt{5}})\) $D_{4}$ simple
2.59.ay_jy $2$ $\F_{59}$ $( 1 - 14 x + 59 x^{2} )( 1 - 10 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-34}) \) $C_2$, $C_2$ 1.59.ao $\times$ 1.59.ak
2.59.ay_jz $2$ $\F_{59}$ $1 - 24 x + 259 x^{2} - 1416 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-89 +24 \sqrt{3}})\) $D_{4}$ simple
2.59.ay_ka $2$ $\F_{59}$ $1 - 24 x + 260 x^{2} - 1416 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-90 +24 \sqrt{2}})\) $D_{4}$ simple
2.59.ay_kb $2$ $\F_{59}$ $( 1 - 13 x + 59 x^{2} )( 1 - 11 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.59.an $\times$ 1.59.al
2.59.ay_kc $2$ $\F_{59}$ $( 1 - 12 x + 59 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-23}) \) $C_2$ 1.59.am 2
2.59.ax_jc $2$ $\F_{59}$ $1 - 23 x + 236 x^{2} - 1357 x^{3} + 3481 x^{4}$ $1$ \(\Q(\sqrt{-310 +34 \sqrt{57}})\) $D_{4}$ simple
2.59.ax_jd $2$ $\F_{59}$ $1 - 23 x + 237 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-362 -46 \sqrt{53}})\) $D_{4}$ simple
2.59.ax_je $2$ $\F_{59}$ $( 1 - 15 x + 59 x^{2} )( 1 - 8 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.59.ap $\times$ 1.59.ai
2.59.ax_jf $2$ $\F_{59}$ $1 - 23 x + 239 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-210 -22 \sqrt{5}})\) $D_{4}$ simple
2.59.ax_jg $2$ $\F_{59}$ $1 - 23 x + 240 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-374 -46 \sqrt{41}})\) $D_{4}$ simple
2.59.ax_jh $2$ $\F_{59}$ $1 - 23 x + 241 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-378 -46 \sqrt{37}})\) $D_{4}$ simple
2.59.ax_ji $2$ $\F_{59}$ $1 - 23 x + 242 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-382 -46 \sqrt{33}})\) $D_{4}$ simple
2.59.ax_jj $2$ $\F_{59}$ $1 - 23 x + 243 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-386 -46 \sqrt{29}})\) $D_{4}$ simple
2.59.ax_jk $2$ $\F_{59}$ $( 1 - 14 x + 59 x^{2} )( 1 - 9 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-155}) \) $C_2$, $C_2$ 1.59.ao $\times$ 1.59.aj
2.59.ax_jl $2$ $\F_{59}$ $1 - 23 x + 245 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-106 +18 \sqrt{21}})\) $D_{4}$ simple
2.59.ax_jm $2$ $\F_{59}$ $1 - 23 x + 246 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-350 +2 \sqrt{17}})\) $D_{4}$ simple
2.59.ax_jn $2$ $\F_{59}$ $1 - 23 x + 247 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-9 +2 \sqrt{13}})\) $D_{4}$ simple
2.59.ax_jo $2$ $\F_{59}$ $( 1 - 13 x + 59 x^{2} )( 1 - 10 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-34}) \) $C_2$, $C_2$ 1.59.an $\times$ 1.59.ak
2.59.ax_jp $2$ $\F_{59}$ $1 - 23 x + 249 x^{2} - 1357 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-410 -46 \sqrt{5}})\) $D_{4}$ simple
2.59.ax_jq $2$ $\F_{59}$ $( 1 - 12 x + 59 x^{2} )( 1 - 11 x + 59 x^{2} )$ $2$ \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.59.am $\times$ 1.59.al
2.59.aw_im $2$ $\F_{59}$ $1 - 22 x + 220 x^{2} - 1298 x^{3} + 3481 x^{4}$ $2$ \(\Q(\sqrt{-9 +2 \sqrt{19}})\) $D_{4}$ simple
Next   displayed columns for results