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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 417450.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
417450.y1 | 417450y2 | \([1, 1, 0, -1056434425, 13215921785125]\) | \(4710588959856854135593/81253269504\) | \(2249142552746496000000\) | \([]\) | \(111974400\) | \(3.6383\) | \(\Gamma_0(N)\)-optimal* |
417450.y2 | 417450y1 | \([1, 1, 0, -13853050, 15742640500]\) | \(10621450496611513/2276047011744\) | \(63002439377690818500000\) | \([]\) | \(37324800\) | \(3.0890\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 417450.y have rank \(0\).
Complex multiplication
The elliptic curves in class 417450.y do not have complex multiplication.Modular form 417450.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.