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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 35280.dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.dr1 | 35280dl2 | \([0, 0, 0, -2667, -37926]\) | \(55306341/15625\) | \(592704000000\) | \([2]\) | \(49152\) | \(0.96587\) | |
35280.dr2 | 35280dl1 | \([0, 0, 0, -987, 11466]\) | \(2803221/125\) | \(4741632000\) | \([2]\) | \(24576\) | \(0.61929\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.dr have rank \(2\).
Complex multiplication
The elliptic curves in class 35280.dr do not have complex multiplication.Modular form 35280.2.a.dr
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.