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SageMath
E = EllipticCurve("lz1")
E.isogeny_class()
Elliptic curves in class 463680.lz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 463680.lz1 | 463680lz1 | \([0, 0, 0, -1692, 24624]\) | \(44851536/4025\) | \(48074342400\) | \([2]\) | \(327680\) | \(0.78937\) | \(\Gamma_0(N)\)-optimal |
| 463680.lz2 | 463680lz2 | \([0, 0, 0, 1908, 115344]\) | \(16078716/129605\) | \(-6191975301120\) | \([2]\) | \(655360\) | \(1.1359\) |
Rank
sage: E.rank()
The elliptic curves in class 463680.lz have rank \(1\).
Complex multiplication
The elliptic curves in class 463680.lz do not have complex multiplication.Modular form 463680.2.a.lz
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.
