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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 457776z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 457776.z2 | 457776z1 | \([0, 0, 0, -22744011, 40850504314]\) | \(18052771191337/444958272\) | \(32070098180291132915712\) | \([2]\) | \(37158912\) | \(3.1023\) | \(\Gamma_0(N)\)-optimal |
| 457776.z1 | 457776z2 | \([0, 0, 0, -51042891, -81055410950]\) | \(204055591784617/78708537864\) | \(5672870234729880768774144\) | \([2]\) | \(74317824\) | \(3.4488\) |
Rank
sage: E.rank()
The elliptic curves in class 457776z have rank \(1\).
Complex multiplication
The elliptic curves in class 457776z do not have complex multiplication.Modular form 457776.2.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 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.
