The results below are complete, since the LMFDB contains all isogeny classes of elliptic curves over fields of cardinality less than 500 or 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 (9 matches)

  displayed columns for results
Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
1.5.ae $1$ $\F_{5}$ $1 - 4 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.5.ad $1$ $\F_{5}$ $1 - 3 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-11}) \) $C_2$ simple
1.5.ac $1$ $\F_{5}$ $1 - 2 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.5.ab $1$ $\F_{5}$ $1 - x + 5 x^{2}$ $1$ \(\Q(\sqrt{-19}) \) $C_2$ simple
1.5.a $1$ $\F_{5}$ $1 + 5 x^{2}$ $0$ \(\Q(\sqrt{-5}) \) $C_2$ simple
1.5.b $1$ $\F_{5}$ $1 + x + 5 x^{2}$ $1$ \(\Q(\sqrt{-19}) \) $C_2$ simple
1.5.c $1$ $\F_{5}$ $1 + 2 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.5.d $1$ $\F_{5}$ $1 + 3 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-11}) \) $C_2$ simple
1.5.e $1$ $\F_{5}$ $1 + 4 x + 5 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
  displayed columns for results