Show commands:
SageMath
sage: E = EllipticCurve("bwy1")
sage: E.isogeny_class()
Elliptic curves in class 705600.bwy
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.bwy1 | \([0, 0, 0, -216300, -27538000]\) | \(2185454/625\) | \(320060160000000000\) | \([2]\) | \(7077888\) | \(2.0655\) |
| 705600.bwy2 | \([0, 0, 0, 35700, -2842000]\) | \(19652/25\) | \(-6401203200000000\) | \([2]\) | \(3538944\) | \(1.7189\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bwy have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.bwy do not have complex multiplication.Modular form 705600.2.a.bwy
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.
