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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 270480.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.v1 | 270480v1 | \([0, -1, 0, -128396, 17311680]\) | \(22659965872/642735\) | \(6639788952357120\) | \([2]\) | \(2580480\) | \(1.8146\) | \(\Gamma_0(N)\)-optimal |
| 270480.v2 | 270480v2 | \([0, -1, 0, 29384, 56946016]\) | \(67898372/33953175\) | \(-1403016274280678400\) | \([2]\) | \(5160960\) | \(2.1612\) |
Rank
sage: E.rank()
The elliptic curves in class 270480.v have rank \(0\).
Complex multiplication
The elliptic curves in class 270480.v do not have complex multiplication.Modular form 270480.2.a.v
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.
