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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 1950.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1950.z1 | 1950ba2 | \([1, 0, 0, -4013, -16983]\) | \(3659383421/2056392\) | \(4016390625000\) | \([2]\) | \(3840\) | \(1.1086\) | |
| 1950.z2 | 1950ba1 | \([1, 0, 0, 987, -1983]\) | \(54439939/32448\) | \(-63375000000\) | \([2]\) | \(1920\) | \(0.76201\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1950.z have rank \(0\).
Complex multiplication
The elliptic curves in class 1950.z do not have complex multiplication.Modular form 1950.2.a.z
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.
