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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 230640df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230640.df2 | 230640df1 | \([0, 1, 0, 7187960, -2801689612]\) | \(11298232190519/7472736000\) | \(-27165002576450420736000\) | \([2]\) | \(22118400\) | \(2.9935\) | \(\Gamma_0(N)\)-optimal |
| 230640.df1 | 230640df2 | \([0, 1, 0, -30944520, -23225445900]\) | \(901456690969801/457629750000\) | \(1663582567055809536000000\) | \([2]\) | \(44236800\) | \(3.3400\) |
Rank
sage: E.rank()
The elliptic curves in class 230640df have rank \(1\).
Complex multiplication
The elliptic curves in class 230640df do not have complex multiplication.Modular form 230640.2.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 Cremona 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 Cremona labels.
