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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 468270.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468270.n1 | 468270n2 | \([1, -1, 0, -552690, -157970444]\) | \(14457238157881/4437600\) | \(5731018259234400\) | \([2]\) | \(5529600\) | \(2.0006\) | \(\Gamma_0(N)\)-optimal* |
468270.n2 | 468270n1 | \([1, -1, 0, -29970, -3140780]\) | \(-2305199161/1981440\) | \(-2558966292495360\) | \([2]\) | \(2764800\) | \(1.6540\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 468270.n have rank \(0\).
Complex multiplication
The elliptic curves in class 468270.n do not have complex multiplication.Modular form 468270.2.a.n
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.