Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 7056.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.bw1 | 7056ca2 | \([0, 0, 0, -1281, 17647]\) | \(406749952\) | \(571536\) | \([]\) | \(2160\) | \(0.34427\) | |
| 7056.bw2 | 7056ca1 | \([0, 0, 0, -21, 7]\) | \(1792\) | \(571536\) | \([]\) | \(720\) | \(-0.20503\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 7056.bw do not have complex multiplication.Modular form 7056.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
