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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 213444.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 213444.z1 | 213444u2 | \([0, 0, 0, -2365671, -1297466786]\) | \(109744/9\) | \(120073860573959077632\) | \([2]\) | \(7526400\) | \(2.5954\) | |
| 213444.z2 | 213444u1 | \([0, 0, 0, -498036, 111850585]\) | \(16384/3\) | \(2501538761957480784\) | \([2]\) | \(3763200\) | \(2.2489\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 213444.z have rank \(1\).
Complex multiplication
The elliptic curves in class 213444.z do not have complex multiplication.Modular form 213444.2.a.z
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.
