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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 207368z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 207368.r2 | 207368z1 | \([0, 0, 0, -1529339, 826309638]\) | \(-22180932/3703\) | \(-66040282881301076992\) | \([2]\) | \(3244032\) | \(2.5301\) | \(\Gamma_0(N)\)-optimal |
| 207368.r1 | 207368z2 | \([0, 0, 0, -25376659, 49202982990]\) | \(50668941906/1127\) | \(40198433058183264256\) | \([2]\) | \(6488064\) | \(2.8766\) |
Rank
sage: E.rank()
The elliptic curves in class 207368z have rank \(1\).
Complex multiplication
The elliptic curves in class 207368z do not have complex multiplication.Modular form 207368.2.a.z
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.
