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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 58950ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58950.a2 | 58950ba1 | \([1, -1, 0, -8892, -320234]\) | \(6826561273/7074\) | \(80577281250\) | \([]\) | \(131328\) | \(1.0105\) | \(\Gamma_0(N)\)-optimal |
| 58950.a1 | 58950ba2 | \([1, -1, 0, -32517, 1924141]\) | \(333822098953/53954184\) | \(614571877125000\) | \([]\) | \(393984\) | \(1.5598\) |
Rank
sage: E.rank()
The elliptic curves in class 58950ba have rank \(1\).
Complex multiplication
The elliptic curves in class 58950ba do not have complex multiplication.Modular form 58950.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
