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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 98736dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98736.cq1 | 98736dm1 | \([0, 1, 0, -17464, -437164]\) | \(81182737/35904\) | \(260530692685824\) | \([2]\) | \(276480\) | \(1.4619\) | \(\Gamma_0(N)\)-optimal |
98736.cq2 | 98736dm2 | \([0, 1, 0, 59976, -3194028]\) | \(3288008303/2517768\) | \(-18269714824593408\) | \([2]\) | \(552960\) | \(1.8084\) |
Rank
sage: E.rank()
The elliptic curves in class 98736dm have rank \(1\).
Complex multiplication
The elliptic curves in class 98736dm do not have complex multiplication.Modular form 98736.2.a.dm
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 Cremona 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 Cremona labels.