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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 (39 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
1.97.at $1$ $\F_{97}$ $1 - 19 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.97.as $1$ $\F_{97}$ $1 - 18 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.97.ar $1$ $\F_{97}$ $1 - 17 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-11}) \) $C_2$ simple
1.97.aq $1$ $\F_{97}$ $1 - 16 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-33}) \) $C_2$ simple
1.97.ap $1$ $\F_{97}$ $1 - 15 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-163}) \) $C_2$ simple
1.97.ao $1$ $\F_{97}$ $1 - 14 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.97.an $1$ $\F_{97}$ $1 - 13 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-219}) \) $C_2$ simple
1.97.am $1$ $\F_{97}$ $1 - 12 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-61}) \) $C_2$ simple
1.97.al $1$ $\F_{97}$ $1 - 11 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-267}) \) $C_2$ simple
1.97.ak $1$ $\F_{97}$ $1 - 10 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-2}) \) $C_2$ simple
1.97.aj $1$ $\F_{97}$ $1 - 9 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-307}) \) $C_2$ simple
1.97.ai $1$ $\F_{97}$ $1 - 8 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.97.ah $1$ $\F_{97}$ $1 - 7 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-339}) \) $C_2$ simple
1.97.ag $1$ $\F_{97}$ $1 - 6 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-22}) \) $C_2$ simple
1.97.af $1$ $\F_{97}$ $1 - 5 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.97.ae $1$ $\F_{97}$ $1 - 4 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-93}) \) $C_2$ simple
1.97.ad $1$ $\F_{97}$ $1 - 3 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-379}) \) $C_2$ simple
1.97.ac $1$ $\F_{97}$ $1 - 2 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-6}) \) $C_2$ simple
1.97.ab $1$ $\F_{97}$ $1 - x + 97 x^{2}$ $1$ \(\Q(\sqrt{-43}) \) $C_2$ simple
1.97.a $1$ $\F_{97}$ $1 + 97 x^{2}$ $0$ \(\Q(\sqrt{-97}) \) $C_2$ simple
1.97.b $1$ $\F_{97}$ $1 + x + 97 x^{2}$ $1$ \(\Q(\sqrt{-43}) \) $C_2$ simple
1.97.c $1$ $\F_{97}$ $1 + 2 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-6}) \) $C_2$ simple
1.97.d $1$ $\F_{97}$ $1 + 3 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-379}) \) $C_2$ simple
1.97.e $1$ $\F_{97}$ $1 + 4 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-93}) \) $C_2$ simple
1.97.f $1$ $\F_{97}$ $1 + 5 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.97.g $1$ $\F_{97}$ $1 + 6 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-22}) \) $C_2$ simple
1.97.h $1$ $\F_{97}$ $1 + 7 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-339}) \) $C_2$ simple
1.97.i $1$ $\F_{97}$ $1 + 8 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.97.j $1$ $\F_{97}$ $1 + 9 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-307}) \) $C_2$ simple
1.97.k $1$ $\F_{97}$ $1 + 10 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-2}) \) $C_2$ simple
1.97.l $1$ $\F_{97}$ $1 + 11 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-267}) \) $C_2$ simple
1.97.m $1$ $\F_{97}$ $1 + 12 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-61}) \) $C_2$ simple
1.97.n $1$ $\F_{97}$ $1 + 13 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-219}) \) $C_2$ simple
1.97.o $1$ $\F_{97}$ $1 + 14 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
1.97.p $1$ $\F_{97}$ $1 + 15 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-163}) \) $C_2$ simple
1.97.q $1$ $\F_{97}$ $1 + 16 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-33}) \) $C_2$ simple
1.97.r $1$ $\F_{97}$ $1 + 17 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-11}) \) $C_2$ simple
1.97.s $1$ $\F_{97}$ $1 + 18 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-1}) \) $C_2$ simple
1.97.t $1$ $\F_{97}$ $1 + 19 x + 97 x^{2}$ $1$ \(\Q(\sqrt{-3}) \) $C_2$ simple
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