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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 27584.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27584.s1 | 27584i1 | \([0, 1, 0, -157441, 23998303]\) | \(-1646417855125441/451936256\) | \(-118472377892864\) | \([]\) | \(122880\) | \(1.6830\) | \(\Gamma_0(N)\)-optimal |
| 27584.s2 | 27584i2 | \([0, 1, 0, 984319, -55448737]\) | \(402337908227545919/237961300338416\) | \(-62380127115913723904\) | \([]\) | \(614400\) | \(2.4877\) |
Rank
sage: E.rank()
The elliptic curves in class 27584.s have rank \(0\).
Complex multiplication
The elliptic curves in class 27584.s do not have complex multiplication.Modular form 27584.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
