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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 8550.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.bh1 | 8550bc2 | \([1, -1, 1, -6755, 211997]\) | \(2992209121/54150\) | \(616802343750\) | \([2]\) | \(18432\) | \(1.0576\) | |
| 8550.bh2 | 8550bc1 | \([1, -1, 1, -5, 9497]\) | \(-1/3420\) | \(-38955937500\) | \([2]\) | \(9216\) | \(0.71102\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.bh do not have complex multiplication.Modular form 8550.2.a.bh
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.
