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SageMath
E = EllipticCurve("fd1")
E.isogeny_class()
Elliptic curves in class 20160.fd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.fd1 | 20160dm1 | \([0, 0, 0, -2951532, 1947510864]\) | \(551105805571803/1376829440\) | \(7104137492567162880\) | \([2]\) | \(645120\) | \(2.4946\) | \(\Gamma_0(N)\)-optimal |
20160.fd2 | 20160dm2 | \([0, 0, 0, -1845612, 3424577616]\) | \(-134745327251163/903920796800\) | \(-4664032767092824473600\) | \([2]\) | \(1290240\) | \(2.8412\) |
Rank
sage: E.rank()
The elliptic curves in class 20160.fd have rank \(0\).
Complex multiplication
The elliptic curves in class 20160.fd do not have complex multiplication.Modular form 20160.2.a.fd
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.