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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 169650.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169650.cf1 | 169650ef1 | \([1, -1, 0, -112167, -14402259]\) | \(13701674594089/31758480\) | \(361748936250000\) | \([2]\) | \(1081344\) | \(1.6742\) | \(\Gamma_0(N)\)-optimal |
| 169650.cf2 | 169650ef2 | \([1, -1, 0, -71667, -24972759]\) | \(-3573857582569/21617820900\) | \(-246240491189062500\) | \([2]\) | \(2162688\) | \(2.0208\) |
Rank
sage: E.rank()
The elliptic curves in class 169650.cf have rank \(1\).
Complex multiplication
The elliptic curves in class 169650.cf do not have complex multiplication.Modular form 169650.2.a.cf
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.
