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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 9702.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.q1 | 9702q2 | \([1, -1, 0, -472131, -124745643]\) | \(46546832455691959/748268928\) | \(187102400639616\) | \([2]\) | \(86016\) | \(1.8714\) | |
| 9702.q2 | 9702q1 | \([1, -1, 0, -28611, -2068011]\) | \(-10358806345399/1445216256\) | \(-361371989164032\) | \([2]\) | \(43008\) | \(1.5249\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.q have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.q do not have complex multiplication.Modular form 9702.2.a.q
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.
