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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 9702.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.cd1 | 9702bc1 | \([1, -1, 1, -329951, 73031879]\) | \(-61279455929796531/681472\) | \(-44177785344\) | \([3]\) | \(51840\) | \(1.6117\) | \(\Gamma_0(N)\)-optimal |
9702.cd2 | 9702bc2 | \([1, -1, 1, -312311, 81173719]\) | \(-71285434106859/18863581528\) | \(-891471792392713224\) | \([]\) | \(155520\) | \(2.1610\) |
Rank
sage: E.rank()
The elliptic curves in class 9702.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.cd do not have complex multiplication.Modular form 9702.2.a.cd
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.