Show commands:
SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 296240.df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296240.df1 | 296240df2 | \([0, -1, 0, -212615856, -867539143744]\) | \(1753007192038126081/478174101507200\) | \(289943257962064248425676800\) | \([2]\) | \(113541120\) | \(3.7854\) | |
| 296240.df2 | 296240df1 | \([0, -1, 0, -77191856, 250196382656]\) | \(83890194895342081/3958384640000\) | \(2400186323707268956160000\) | \([2]\) | \(56770560\) | \(3.4389\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 296240.df have rank \(0\).
Complex multiplication
The elliptic curves in class 296240.df do not have complex multiplication.Modular form 296240.2.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.
