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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 485100.dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.dv1 | 485100dv2 | \([0, 0, 0, -2492175, -1514308250]\) | \(1711503051568/7425\) | \(7426395900000000\) | \([2]\) | \(6193152\) | \(2.2521\) | \(\Gamma_0(N)\)-optimal* |
485100.dv2 | 485100dv1 | \([0, 0, 0, -153300, -24444875]\) | \(-6373654528/441045\) | \(-27570494778750000\) | \([2]\) | \(3096576\) | \(1.9055\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485100.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 485100.dv do not have complex multiplication.Modular form 485100.2.a.dv
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.