Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 134640.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
134640.bw1 | 134640ci2 | \([0, 0, 0, -1693443, 847722242]\) | \(179865548102096641/119964240000\) | \(358211301212160000\) | \([2]\) | \(2064384\) | \(2.3071\) | |
134640.bw2 | 134640ci1 | \([0, 0, 0, -126723, 7646978]\) | \(75370704203521/35157196800\) | \(104978827129651200\) | \([2]\) | \(1032192\) | \(1.9605\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 134640.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 134640.bw do not have complex multiplication.Modular form 134640.2.a.bw
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.