Show commands:
SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 202160.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202160.cm1 | 202160by2 | \([0, -1, 0, -1031136, 420141440]\) | \(-1742943169/85750\) | \(-5965170814016512000\) | \([]\) | \(3545856\) | \(2.3642\) | |
| 202160.cm2 | 202160by1 | \([0, -1, 0, 66304, 1358336]\) | \(463391/280\) | \(-19478108780462080\) | \([]\) | \(1181952\) | \(1.8149\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202160.cm have rank \(0\).
Complex multiplication
The elliptic curves in class 202160.cm do not have complex multiplication.Modular form 202160.2.a.cm
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
