Show commands:
SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 58800.ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.ej1 | 58800hh1 | \([0, -1, 0, -653, 6252]\) | \(131072/9\) | \(2117682000\) | \([2]\) | \(27648\) | \(0.53770\) | \(\Gamma_0(N)\)-optimal |
| 58800.ej2 | 58800hh2 | \([0, -1, 0, 572, 25852]\) | \(5488/81\) | \(-304946208000\) | \([2]\) | \(55296\) | \(0.88428\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.ej do not have complex multiplication.Modular form 58800.2.a.ej
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.
