Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 254898.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254898.bw1 | 254898bw1 | \([1, -1, 0, -96821412, 346425963344]\) | \(9869198625/614656\) | \(6251556868511793737455872\) | \([2]\) | \(53477376\) | \(3.5093\) | \(\Gamma_0(N)\)-optimal |
| 254898.bw2 | 254898bw2 | \([1, -1, 0, 76509228, 1450923467552]\) | \(4869777375/92236816\) | \(-938124252581051047726971792\) | \([2]\) | \(106954752\) | \(3.8559\) |
Rank
sage: E.rank()
The elliptic curves in class 254898.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 254898.bw do not have complex multiplication.Modular form 254898.2.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.
