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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 72450cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.ec2 | 72450cz1 | \([1, -1, 1, -2377055, 1418107447]\) | \(-38638468208943/219395344\) | \(-8434294054593750000\) | \([2]\) | \(2211840\) | \(2.4736\) | \(\Gamma_0(N)\)-optimal |
| 72450.ec1 | 72450cz2 | \([1, -1, 1, -38084555, 90472612447]\) | \(158909194494247023/5080516\) | \(195312102398437500\) | \([2]\) | \(4423680\) | \(2.8202\) |
Rank
sage: E.rank()
The elliptic curves in class 72450cz have rank \(0\).
Complex multiplication
The elliptic curves in class 72450cz do not have complex multiplication.Modular form 72450.2.a.cz
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.
