Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 162288.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.bb1 | 162288l1 | \([0, 0, 0, -15145851, -20930933590]\) | \(3188856056959/274710528\) | \(33101306838453074264064\) | \([2]\) | \(14450688\) | \(3.0621\) | \(\Gamma_0(N)\)-optimal |
| 162288.bb2 | 162288l2 | \([0, 0, 0, 16465029, -96828656470]\) | \(4096768048001/35984932992\) | \(-4336012591877677313949696\) | \([2]\) | \(28901376\) | \(3.4087\) |
Rank
sage: E.rank()
The elliptic curves in class 162288.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 162288.bb do not have complex multiplication.Modular form 162288.2.a.bb
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.
