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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 42432.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42432.u1 | 42432bu1 | \([0, -1, 0, -1697, 26817]\) | \(8251733668/232713\) | \(15251079168\) | \([2]\) | \(57344\) | \(0.73281\) | \(\Gamma_0(N)\)-optimal |
| 42432.u2 | 42432bu2 | \([0, -1, 0, 383, 86305]\) | \(47279806/24649677\) | \(-3230882463744\) | \([2]\) | \(114688\) | \(1.0794\) |
Rank
sage: E.rank()
The elliptic curves in class 42432.u have rank \(1\).
Complex multiplication
The elliptic curves in class 42432.u do not have complex multiplication.Modular form 42432.2.a.u
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.
