Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 4650.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4650.bg1 | 4650x2 | \([1, 1, 1, -50313, -1542969]\) | \(901456690969801/457629750000\) | \(7150464843750000\) | \([2]\) | \(46080\) | \(1.7346\) | |
| 4650.bg2 | 4650x1 | \([1, 1, 1, 11687, -178969]\) | \(11298232190519/7472736000\) | \(-116761500000000\) | \([2]\) | \(23040\) | \(1.3881\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4650.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 4650.bg do not have complex multiplication.Modular form 4650.2.a.bg
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.
