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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 357390u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 357390.u1 | 357390u1 | \([1, -1, 0, -38115, -2695275]\) | \(1224699562099/76665600\) | \(383344176441600\) | \([2]\) | \(1720320\) | \(1.5496\) | \(\Gamma_0(N)\)-optimal |
| 357390.u2 | 357390u2 | \([1, -1, 0, 30285, -11354715]\) | \(614341775501/11479715280\) | \(-57400998619924080\) | \([2]\) | \(3440640\) | \(1.8962\) |
Rank
sage: E.rank()
The elliptic curves in class 357390u have rank \(0\).
Complex multiplication
The elliptic curves in class 357390u do not have complex multiplication.Modular form 357390.2.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 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.
