Show commands:
SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 9408.df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.df1 | 9408dd2 | \([0, 1, 0, -7121, -233073]\) | \(20720464/63\) | \(121436356608\) | \([2]\) | \(18432\) | \(0.99554\) | |
| 9408.df2 | 9408dd1 | \([0, 1, 0, -261, -6693]\) | \(-16384/147\) | \(-17709468672\) | \([2]\) | \(9216\) | \(0.64897\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9408.df have rank \(0\).
Complex multiplication
The elliptic curves in class 9408.df do not have complex multiplication.Modular form 9408.2.a.df
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.
