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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 203280.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.p1 | 203280eb1 | \([0, -1, 0, -326256, -60346944]\) | \(529278808969/88704000\) | \(643664064282624000\) | \([2]\) | \(2764800\) | \(2.1382\) | \(\Gamma_0(N)\)-optimal |
| 203280.p2 | 203280eb2 | \([0, -1, 0, 603024, -342104640]\) | \(3342032927351/8893500000\) | \(-64534027278336000000\) | \([2]\) | \(5529600\) | \(2.4848\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.p have rank \(1\).
Complex multiplication
The elliptic curves in class 203280.p do not have complex multiplication.Modular form 203280.2.a.p
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.
