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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 47610.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47610.n1 | 47610q2 | \([1, -1, 0, -552375, 151751461]\) | \(172715635009/7935000\) | \(856330624047735000\) | \([2]\) | \(811008\) | \(2.2026\) | |
47610.n2 | 47610q1 | \([1, -1, 0, 18945, 9035725]\) | \(6967871/331200\) | \(-35742495612427200\) | \([2]\) | \(405504\) | \(1.8560\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47610.n have rank \(1\).
Complex multiplication
The elliptic curves in class 47610.n do not have complex multiplication.Modular form 47610.2.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.