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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 400064.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 400064.f1 | 400064f1 | \([0, 1, 0, -337, 975]\) | \(259108432/118769\) | \(1945911296\) | \([2]\) | \(157696\) | \(0.47728\) | \(\Gamma_0(N)\)-optimal |
| 400064.f2 | 400064f2 | \([0, 1, 0, 1183, 8575]\) | \(2791456412/2056579\) | \(-134779961344\) | \([2]\) | \(315392\) | \(0.82385\) |
Rank
sage: E.rank()
The elliptic curves in class 400064.f have rank \(1\).
Complex multiplication
The elliptic curves in class 400064.f do not have complex multiplication.Modular form 400064.2.a.f
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.
