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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 74970ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74970.ee2 | 74970ed1 | \([1, -1, 1, 971293, 2653707039]\) | \(1181569139409959/36161310937500\) | \(-3101415369384248437500\) | \([2]\) | \(5898240\) | \(2.8039\) | \(\Gamma_0(N)\)-optimal |
| 74970.ee1 | 74970ed2 | \([1, -1, 1, -23834957, 42710839539]\) | \(17460273607244690041/918397653311250\) | \(78767404260008718161250\) | \([2]\) | \(11796480\) | \(3.1504\) |
Rank
sage: E.rank()
The elliptic curves in class 74970ed have rank \(0\).
Complex multiplication
The elliptic curves in class 74970ed do not have complex multiplication.Modular form 74970.2.a.ed
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.
