Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 217800bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 217800.dx3 | 217800bw1 | \([0, 0, 0, -335775, -72206750]\) | \(810448/33\) | \(170473771908000000\) | \([2]\) | \(1966080\) | \(2.0722\) | \(\Gamma_0(N)\)-optimal |
| 217800.dx2 | 217800bw2 | \([0, 0, 0, -880275, 221278750]\) | \(3650692/1089\) | \(22502537891856000000\) | \([2, 2]\) | \(3932160\) | \(2.4188\) | |
| 217800.dx1 | 217800bw3 | \([0, 0, 0, -12859275, 17746555750]\) | \(5690357426/891\) | \(36822334732128000000\) | \([2]\) | \(7864320\) | \(2.7654\) | |
| 217800.dx4 | 217800bw4 | \([0, 0, 0, 2386725, 1479073750]\) | \(36382894/43923\) | \(-1815204723276384000000\) | \([2]\) | \(7864320\) | \(2.7654\) |
Rank
sage: E.rank()
The elliptic curves in class 217800bw have rank \(0\).
Complex multiplication
The elliptic curves in class 217800bw do not have complex multiplication.Modular form 217800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
