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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 270480cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.cs1 | 270480cs1 | \([0, -1, 0, -494965, 134189812]\) | \(7124261256822784/475453125\) | \(894985355250000\) | \([2]\) | \(3317760\) | \(1.9246\) | \(\Gamma_0(N)\)-optimal |
| 270480.cs2 | 270480cs2 | \([0, -1, 0, -464340, 151486812]\) | \(-367624742361424/115740505125\) | \(-3485889199987488000\) | \([2]\) | \(6635520\) | \(2.2711\) |
Rank
sage: E.rank()
The elliptic curves in class 270480cs have rank \(1\).
Complex multiplication
The elliptic curves in class 270480cs do not have complex multiplication.Modular form 270480.2.a.cs
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.
