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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 69360.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69360.r1 | 69360ca2 | \([0, -1, 0, -39536, -2624064]\) | \(339630096833/47239200\) | \(950625032601600\) | \([2]\) | \(307200\) | \(1.6005\) | |
| 69360.r2 | 69360ca1 | \([0, -1, 0, 3984, -221760]\) | \(347428927/1244160\) | \(-25037037895680\) | \([2]\) | \(153600\) | \(1.2539\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 69360.r have rank \(0\).
Complex multiplication
The elliptic curves in class 69360.r do not have complex multiplication.Modular form 69360.2.a.r
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.
