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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 66654.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66654.bd1 | 66654bu2 | \([1, -1, 1, -345272, -19576695]\) | \(42180533641/22862322\) | \(2467259794006334082\) | \([2]\) | \(1622016\) | \(2.2201\) | |
66654.bd2 | 66654bu1 | \([1, -1, 1, 83218, -2437095]\) | \(590589719/365148\) | \(-39406101412700988\) | \([2]\) | \(811008\) | \(1.8735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66654.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 66654.bd do not have complex multiplication.Modular form 66654.2.a.bd
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.