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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 (33 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
1.71.aq $1$ $\F_{71}$ $1 - 16 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-7}) \) $C_2$ simple
1.71.ap $1$ $\F_{71}$ $1 - 15 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-59}) \) $C_2$ simple
1.71.ao $1$ $\F_{71}$ $1 - 14 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-22}) \) $C_2$ simple
1.71.an $1$ $\F_{71}$ $1 - 13 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-115}) \) $C_2$ simple
1.71.am $1$ $\F_{71}$ $1 - 12 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-35}) \) $C_2$ simple
1.71.al $1$ $\F_{71}$ $1 - 11 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-163}) \) $C_2$ simple
1.71.ak $1$ $\F_{71}$ $1 - 10 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-46}) \) $C_2$ simple
1.71.aj $1$ $\F_{71}$ $1 - 9 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-203}) \) $C_2$ simple
1.71.ai $1$ $\F_{71}$ $1 - 8 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-55}) \) $C_2$ simple
1.71.ah $1$ $\F_{71}$ $1 - 7 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-235}) \) $C_2$ simple
1.71.ag $1$ $\F_{71}$ $1 - 6 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-62}) \) $C_2$ simple
1.71.af $1$ $\F_{71}$ $1 - 5 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-259}) \) $C_2$ simple
1.71.ae $1$ $\F_{71}$ $1 - 4 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-67}) \) $C_2$ simple
1.71.ad $1$ $\F_{71}$ $1 - 3 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-11}) \) $C_2$ simple
1.71.ac $1$ $\F_{71}$ $1 - 2 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-70}) \) $C_2$ simple
1.71.ab $1$ $\F_{71}$ $1 - x + 71 x^{2}$ $1$ \(\Q(\sqrt{-283}) \) $C_2$ simple
1.71.a $1$ $\F_{71}$ $1 + 71 x^{2}$ $0$ \(\Q(\sqrt{-71}) \) $C_2$ simple
1.71.b $1$ $\F_{71}$ $1 + x + 71 x^{2}$ $1$ \(\Q(\sqrt{-283}) \) $C_2$ simple
1.71.c $1$ $\F_{71}$ $1 + 2 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-70}) \) $C_2$ simple
1.71.d $1$ $\F_{71}$ $1 + 3 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-11}) \) $C_2$ simple
1.71.e $1$ $\F_{71}$ $1 + 4 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-67}) \) $C_2$ simple
1.71.f $1$ $\F_{71}$ $1 + 5 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-259}) \) $C_2$ simple
1.71.g $1$ $\F_{71}$ $1 + 6 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-62}) \) $C_2$ simple
1.71.h $1$ $\F_{71}$ $1 + 7 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-235}) \) $C_2$ simple
1.71.i $1$ $\F_{71}$ $1 + 8 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-55}) \) $C_2$ simple
1.71.j $1$ $\F_{71}$ $1 + 9 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-203}) \) $C_2$ simple
1.71.k $1$ $\F_{71}$ $1 + 10 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-46}) \) $C_2$ simple
1.71.l $1$ $\F_{71}$ $1 + 11 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-163}) \) $C_2$ simple
1.71.m $1$ $\F_{71}$ $1 + 12 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-35}) \) $C_2$ simple
1.71.n $1$ $\F_{71}$ $1 + 13 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-115}) \) $C_2$ simple
1.71.o $1$ $\F_{71}$ $1 + 14 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-22}) \) $C_2$ simple
1.71.p $1$ $\F_{71}$ $1 + 15 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-59}) \) $C_2$ simple
1.71.q $1$ $\F_{71}$ $1 + 16 x + 71 x^{2}$ $1$ \(\Q(\sqrt{-7}) \) $C_2$ simple
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