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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 4200.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4200.w1 | 4200bc1 | \([0, 1, 0, -708, 5088]\) | \(78608/21\) | \(10500000000\) | \([2]\) | \(2560\) | \(0.63122\) | \(\Gamma_0(N)\)-optimal |
| 4200.w2 | 4200bc2 | \([0, 1, 0, 1792, 35088]\) | \(318028/441\) | \(-882000000000\) | \([2]\) | \(5120\) | \(0.97779\) |
Rank
sage: E.rank()
The elliptic curves in class 4200.w have rank \(0\).
Complex multiplication
The elliptic curves in class 4200.w do not have complex multiplication.Modular form 4200.2.a.w
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.
