Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 38720bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38720.k2 | 38720bc1 | \([0, 1, 0, -13185, -872225]\) | \(-726572699/512000\) | \(-178643795968000\) | \([2]\) | \(138240\) | \(1.4347\) | \(\Gamma_0(N)\)-optimal |
| 38720.k1 | 38720bc2 | \([0, 1, 0, -238465, -44891937]\) | \(4298149261979/1000000\) | \(348913664000000\) | \([2]\) | \(276480\) | \(1.7813\) |
Rank
sage: E.rank()
The elliptic curves in class 38720bc have rank \(0\).
Complex multiplication
The elliptic curves in class 38720bc do not have complex multiplication.Modular form 38720.2.a.bc
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 Cremona 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 Cremona labels.
