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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

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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
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Results (9 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
1.4.ae $1$ $\F_{2^{2}}$ $( 1 - 2 x )^{2}$ $0$ \(\Q\) Trivial simple
1.4.ad $1$ $\F_{2^{2}}$ $1 - 3 x + 4 x^{2}$ $1$ \(\Q(\sqrt{-7}) \) $C_2$ simple
1.4.ac $1$ $\F_{2^{2}}$ $1 - 2 x + 4 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.4.ab $1$ $\F_{2^{2}}$ $1 - x + 4 x^{2}$ $1$ \(\Q(\sqrt{-15}) \) $C_2$ simple
1.4.a $1$ $\F_{2^{2}}$ $1 + 4 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.4.b $1$ $\F_{2^{2}}$ $1 + x + 4 x^{2}$ $1$ \(\Q(\sqrt{-15}) \) $C_2$ simple
1.4.c $1$ $\F_{2^{2}}$ $1 + 2 x + 4 x^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.4.d $1$ $\F_{2^{2}}$ $1 + 3 x + 4 x^{2}$ $1$ \(\Q(\sqrt{-7}) \) $C_2$ simple
1.4.e $1$ $\F_{2^{2}}$ $( 1 + 2 x )^{2}$ $0$ \(\Q\) Trivial simple
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