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SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 203280.gw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.gw1 | 203280er1 | \([0, 1, 0, -14560, 660548]\) | \(188183524/3465\) | \(6285781877760\) | \([2]\) | \(552960\) | \(1.2504\) | \(\Gamma_0(N)\)-optimal |
| 203280.gw2 | 203280er2 | \([0, 1, 0, -40, 1932500]\) | \(-2/444675\) | \(-1613350681958400\) | \([2]\) | \(1105920\) | \(1.5970\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.gw have rank \(1\).
Complex multiplication
The elliptic curves in class 203280.gw do not have complex multiplication.Modular form 203280.2.a.gw
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.
