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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 (27 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
1.49.ao $1$ $\F_{7^{2}}$ $( 1 - 7 x )^{2}$ $0$ \(\Q\) Trivial simple
1.49.an $1$ $\F_{7^{2}}$ $1 - 13 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.49.am $1$ $\F_{7^{2}}$ $1 - 12 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-13}) \) $C_2$ simple
1.49.al $1$ $\F_{7^{2}}$ $1 - 11 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.49.ak $1$ $\F_{7^{2}}$ $1 - 10 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-6}) \) $C_2$ simple
1.49.aj $1$ $\F_{7^{2}}$ $1 - 9 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-115}) \) $C_2$ simple
1.49.ai $1$ $\F_{7^{2}}$ $1 - 8 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-33}) \) $C_2$ simple
1.49.ag $1$ $\F_{7^{2}}$ $1 - 6 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-10}) \) $C_2$ simple
1.49.af $1$ $\F_{7^{2}}$ $1 - 5 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-19}) \) $C_2$ simple
1.49.ae $1$ $\F_{7^{2}}$ $1 - 4 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-5}) \) $C_2$ simple
1.49.ad $1$ $\F_{7^{2}}$ $1 - 3 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-187}) \) $C_2$ simple
1.49.ac $1$ $\F_{7^{2}}$ $1 - 2 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.49.ab $1$ $\F_{7^{2}}$ $1 - x + 49 x^{2}$ $1$ \(\Q(\sqrt{-195}) \) $C_2$ simple
1.49.a $1$ $\F_{7^{2}}$ $1 + 49 x^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.49.b $1$ $\F_{7^{2}}$ $1 + x + 49 x^{2}$ $1$ \(\Q(\sqrt{-195}) \) $C_2$ simple
1.49.c $1$ $\F_{7^{2}}$ $1 + 2 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.49.d $1$ $\F_{7^{2}}$ $1 + 3 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-187}) \) $C_2$ simple
1.49.e $1$ $\F_{7^{2}}$ $1 + 4 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-5}) \) $C_2$ simple
1.49.f $1$ $\F_{7^{2}}$ $1 + 5 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-19}) \) $C_2$ simple
1.49.g $1$ $\F_{7^{2}}$ $1 + 6 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-10}) \) $C_2$ simple
1.49.i $1$ $\F_{7^{2}}$ $1 + 8 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-33}) \) $C_2$ simple
1.49.j $1$ $\F_{7^{2}}$ $1 + 9 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-115}) \) $C_2$ simple
1.49.k $1$ $\F_{7^{2}}$ $1 + 10 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-6}) \) $C_2$ simple
1.49.l $1$ $\F_{7^{2}}$ $1 + 11 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.49.m $1$ $\F_{7^{2}}$ $1 + 12 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-13}) \) $C_2$ simple
1.49.n $1$ $\F_{7^{2}}$ $1 + 13 x + 49 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.49.o $1$ $\F_{7^{2}}$ $( 1 + 7 x )^{2}$ $0$ \(\Q\) Trivial simple
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