Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 360672bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360672.bw1 | 360672bw1 | \([0, 1, 0, -4142, -83628]\) | \(5088448/1053\) | \(1626679050048\) | \([2]\) | \(655360\) | \(1.0583\) | \(\Gamma_0(N)\)-optimal |
| 360672.bw2 | 360672bw2 | \([0, 1, 0, 8863, -491985]\) | \(778688/1521\) | \(-150377441071104\) | \([2]\) | \(1310720\) | \(1.4049\) |
Rank
sage: E.rank()
The elliptic curves in class 360672bw have rank \(0\).
Complex multiplication
The elliptic curves in class 360672bw do not have complex multiplication.Modular form 360672.2.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 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.
