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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 34650.dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34650.dy1 | 34650cp1 | \([1, -1, 1, -5780, -62153]\) | \(69426531/34496\) | \(10609137000000\) | \([2]\) | \(73728\) | \(1.1924\) | \(\Gamma_0(N)\)-optimal |
34650.dy2 | 34650cp2 | \([1, -1, 1, 21220, -494153]\) | \(3436115229/2324168\) | \(-714790605375000\) | \([2]\) | \(147456\) | \(1.5389\) |
Rank
sage: E.rank()
The elliptic curves in class 34650.dy have rank \(1\).
Complex multiplication
The elliptic curves in class 34650.dy do not have complex multiplication.Modular form 34650.2.a.dy
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.