Show commands:
SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 18480bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.w1 | 18480bz1 | \([0, -1, 0, -2696, 46320]\) | \(529278808969/88704000\) | \(363331584000\) | \([2]\) | \(23040\) | \(0.93928\) | \(\Gamma_0(N)\)-optimal |
| 18480.w2 | 18480bz2 | \([0, -1, 0, 4984, 255216]\) | \(3342032927351/8893500000\) | \(-36427776000000\) | \([2]\) | \(46080\) | \(1.2859\) |
Rank
sage: E.rank()
The elliptic curves in class 18480bz have rank \(0\).
Complex multiplication
The elliptic curves in class 18480bz do not have complex multiplication.Modular form 18480.2.a.bz
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.
