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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 67280a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67280.y2 | 67280a1 | \([0, -1, 0, -43171, 1406370]\) | \(934979584/453125\) | \(4312469077250000\) | \([2]\) | \(322560\) | \(1.6936\) | \(\Gamma_0(N)\)-optimal |
| 67280.y1 | 67280a2 | \([0, -1, 0, -568796, 165191120]\) | \(133649126224/105125\) | \(16007885214752000\) | \([2]\) | \(645120\) | \(2.0401\) |
Rank
sage: E.rank()
The elliptic curves in class 67280a have rank \(1\).
Complex multiplication
The elliptic curves in class 67280a do not have complex multiplication.Modular form 67280.2.a.a
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.
