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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3570.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3570.n1 | 3570q2 | \([1, 0, 1, -54048, 4606756]\) | \(17460273607244690041/918397653311250\) | \(918397653311250\) | \([2]\) | \(30720\) | \(1.6282\) | |
3570.n2 | 3570q1 | \([1, 0, 1, 2202, 286756]\) | \(1181569139409959/36161310937500\) | \(-36161310937500\) | \([2]\) | \(15360\) | \(1.2816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3570.n have rank \(1\).
Complex multiplication
The elliptic curves in class 3570.n do not have complex multiplication.Modular form 3570.2.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.