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 5109 matches)

Next   displayed columns for results
Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.61.abe_nj $2$ $\F_{61}$ $( 1 - 15 x + 61 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-19}) \) $C_2$ 1.61.ap 2
2.61.abd_mt $2$ $\F_{61}$ $1 - 29 x + 331 x^{2} - 1769 x^{3} + 3721 x^{4}$ $2$ \(\Q(\zeta_{5})\) $C_4$ simple
2.61.abd_mu $2$ $\F_{61}$ $( 1 - 15 x + 61 x^{2} )( 1 - 14 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.61.ap $\times$ 1.61.ao
2.61.abc_me $2$ $\F_{61}$ $1 - 28 x + 316 x^{2} - 1708 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-26 +8 \sqrt{2}})\) $D_{4}$ simple
2.61.abc_mf $2$ $\F_{61}$ $( 1 - 15 x + 61 x^{2} )( 1 - 13 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.61.ap $\times$ 1.61.an
2.61.abc_mg $2$ $\F_{61}$ $( 1 - 14 x + 61 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.61.ao 2
2.61.abb_lo $2$ $\F_{61}$ $1 - 27 x + 300 x^{2} - 1647 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-9 +2 \sqrt{17}})\) $D_{4}$ simple
2.61.abb_lp $2$ $\F_{61}$ $1 - 27 x + 301 x^{2} - 1647 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-26 -6 \sqrt{13}})\) $C_4$ simple
2.61.abb_lq $2$ $\F_{61}$ $( 1 - 15 x + 61 x^{2} )( 1 - 12 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.61.ap $\times$ 1.61.am
2.61.abb_lr $2$ $\F_{61}$ $1 - 27 x + 303 x^{2} - 1647 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-57 +10 \sqrt{5}})\) $D_{4}$ simple
2.61.abb_ls $2$ $\F_{61}$ $( 1 - 14 x + 61 x^{2} )( 1 - 13 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.61.ao $\times$ 1.61.an
2.61.aba_kz $2$ $\F_{61}$ $1 - 26 x + 285 x^{2} - 1586 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-66 +16 \sqrt{6}})\) $D_{4}$ simple
2.61.aba_la $2$ $\F_{61}$ $1 - 26 x + 286 x^{2} - 1586 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-10 + \sqrt{5}})\) $D_{4}$ simple
2.61.aba_lb $2$ $\F_{61}$ $( 1 - 15 x + 61 x^{2} )( 1 - 11 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.61.ap $\times$ 1.61.al
2.61.aba_lc $2$ $\F_{61}$ $1 - 26 x + 288 x^{2} - 1586 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-72 -26 \sqrt{3}})\) $D_{4}$ simple
2.61.aba_ld $2$ $\F_{61}$ $1 - 26 x + 289 x^{2} - 1586 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-73 -26 \sqrt{2}})\) $D_{4}$ simple
2.61.aba_le $2$ $\F_{61}$ $( 1 - 14 x + 61 x^{2} )( 1 - 12 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.61.ao $\times$ 1.61.am
2.61.aba_lf $2$ $\F_{61}$ $( 1 - 13 x + 61 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.61.an 2
2.61.az_kj $2$ $\F_{61}$ $1 - 25 x + 269 x^{2} - 1525 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-69 +6 \sqrt{37}})\) $D_{4}$ simple
2.61.az_kk $2$ $\F_{61}$ $1 - 25 x + 270 x^{2} - 1525 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-318 +50 \sqrt{33}})\) $D_{4}$ simple
2.61.az_kl $2$ $\F_{61}$ $1 - 25 x + 271 x^{2} - 1525 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-322 +50 \sqrt{29}})\) $D_{4}$ simple
2.61.az_km $2$ $\F_{61}$ $( 1 - 15 x + 61 x^{2} )( 1 - 10 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.61.ap $\times$ 1.61.ak
2.61.az_kn $2$ $\F_{61}$ $1 - 25 x + 273 x^{2} - 1525 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-330 +50 \sqrt{21}})\) $D_{4}$ simple
2.61.az_ko $2$ $\F_{61}$ $1 - 25 x + 274 x^{2} - 1525 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-334 +50 \sqrt{17}})\) $D_{4}$ simple
2.61.az_kp $2$ $\F_{61}$ $1 - 25 x + 275 x^{2} - 1525 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-338 +50 \sqrt{13}})\) $D_{4}$ simple
2.61.az_kq $2$ $\F_{61}$ $( 1 - 14 x + 61 x^{2} )( 1 - 11 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.61.ao $\times$ 1.61.al
2.61.az_kr $2$ $\F_{61}$ $1 - 25 x + 277 x^{2} - 1525 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-346 +50 \sqrt{5}})\) $D_{4}$ simple
2.61.az_ks $2$ $\F_{61}$ $( 1 - 13 x + 61 x^{2} )( 1 - 12 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.61.an $\times$ 1.61.am
2.61.ay_jt $2$ $\F_{61}$ $1 - 24 x + 253 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{13})\) $C_2^2$ simple
2.61.ay_ju $2$ $\F_{61}$ $1 - 24 x + 254 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-4 + \sqrt{3}})\) $D_{4}$ simple
2.61.ay_jv $2$ $\F_{61}$ $1 - 24 x + 255 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-89 +24 \sqrt{11}})\) $D_{4}$ simple
2.61.ay_jw $2$ $\F_{61}$ $1 - 24 x + 256 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-90 +24 \sqrt{10}})\) $D_{4}$ simple
2.61.ay_jx $2$ $\F_{61}$ $( 1 - 15 x + 61 x^{2} )( 1 - 9 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-163}) \) $C_2$, $C_2$ 1.61.ap $\times$ 1.61.aj
2.61.ay_jy $2$ $\F_{61}$ $1 - 24 x + 258 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-23 +12 \sqrt{2}})\) $D_{4}$ simple
2.61.ay_jz $2$ $\F_{61}$ $1 - 24 x + 259 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-16 -2 \sqrt{7}})\) $D_{4}$ simple
2.61.ay_ka $2$ $\F_{61}$ $1 - 24 x + 260 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-94 +24 \sqrt{6}})\) $D_{4}$ simple
2.61.ay_kb $2$ $\F_{61}$ $1 - 24 x + 261 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-330 -46 \sqrt{5}})\) $D_{4}$ simple
2.61.ay_kc $2$ $\F_{61}$ $( 1 - 14 x + 61 x^{2} )( 1 - 10 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.61.ao $\times$ 1.61.ak
2.61.ay_kd $2$ $\F_{61}$ $1 - 24 x + 263 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-97 +24 \sqrt{3}})\) $D_{4}$ simple
2.61.ay_ke $2$ $\F_{61}$ $1 - 24 x + 264 x^{2} - 1464 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-98 +24 \sqrt{2}})\) $D_{4}$ simple
2.61.ay_kf $2$ $\F_{61}$ $( 1 - 13 x + 61 x^{2} )( 1 - 11 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.61.an $\times$ 1.61.al
2.61.ay_kg $2$ $\F_{61}$ $( 1 - 12 x + 61 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.61.am 2
2.61.ax_je $2$ $\F_{61}$ $1 - 23 x + 238 x^{2} - 1403 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-382 -46 \sqrt{65}})\) $D_{4}$ simple
2.61.ax_jf $2$ $\F_{61}$ $1 - 23 x + 239 x^{2} - 1403 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-386 -46 \sqrt{61}})\) $D_{4}$ simple
2.61.ax_jg $2$ $\F_{61}$ $1 - 23 x + 240 x^{2} - 1403 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-90 +2 \sqrt{57}})\) $D_{4}$ simple
2.61.ax_jh $2$ $\F_{61}$ $1 - 23 x + 241 x^{2} - 1403 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-394 -46 \sqrt{53}})\) $D_{4}$ simple
2.61.ax_ji $2$ $\F_{61}$ $( 1 - 15 x + 61 x^{2} )( 1 - 8 x + 61 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-5}) \) $C_2$, $C_2$ 1.61.ap $\times$ 1.61.ai
2.61.ax_jj $2$ $\F_{61}$ $1 - 23 x + 243 x^{2} - 1403 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-258 -6 \sqrt{5}})\) $D_{4}$ simple
2.61.ax_jk $2$ $\F_{61}$ $1 - 23 x + 244 x^{2} - 1403 x^{3} + 3721 x^{4}$ $1$ \(\Q(\sqrt{-31 +4 \sqrt{41}})\) $D_{4}$ simple
2.61.ax_jl $2$ $\F_{61}$ $1 - 23 x + 245 x^{2} - 1403 x^{3} + 3721 x^{4}$ $2$ \(\Q(\sqrt{-410 -46 \sqrt{37}})\) $D_{4}$ simple
Next   displayed columns for results