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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 259920.eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259920.eo1 | 259920eo1 | \([0, 0, 0, -2993412, -1859138809]\) | \(5405726654464/407253125\) | \(223477365096846450000\) | \([2]\) | \(8294400\) | \(2.6499\) | \(\Gamma_0(N)\)-optimal |
259920.eo2 | 259920eo2 | \([0, 0, 0, 2871033, -8254902526]\) | \(298091207216/3525390625\) | \(-30952543642222500000000\) | \([2]\) | \(16588800\) | \(2.9965\) |
Rank
sage: E.rank()
The elliptic curves in class 259920.eo have rank \(1\).
Complex multiplication
The elliptic curves in class 259920.eo do not have complex multiplication.Modular form 259920.2.a.eo
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.