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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 53550bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53550.bd2 | 53550bi1 | \([1, -1, 0, 495558, -967306784]\) | \(1181569139409959/36161310937500\) | \(-411899932397460937500\) | \([2]\) | \(2949120\) | \(2.6356\) | \(\Gamma_0(N)\)-optimal |
| 53550.bd1 | 53550bi2 | \([1, -1, 0, -12160692, -15559963034]\) | \(17460273607244690041/918397653311250\) | \(10461123269748457031250\) | \([2]\) | \(5898240\) | \(2.9822\) |
Rank
sage: E.rank()
The elliptic curves in class 53550bi have rank \(1\).
Complex multiplication
The elliptic curves in class 53550bi do not have complex multiplication.Modular form 53550.2.a.bi
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.
