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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 88725cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88725.bo2 | 88725cf1 | \([0, 1, 1, 38264417, -130798773881]\) | \(19444740423680/34451725707\) | \(-10977863691666150291796875\) | \([3]\) | \(16848000\) | \(3.4897\) | \(\Gamma_0(N)\)-optimal |
| 88725.bo1 | 88725cf2 | \([0, 1, 1, -1296413083, -18035831105756]\) | \(-756218111874334720/3363432789843\) | \(-1071740411989715572969921875\) | \([]\) | \(50544000\) | \(4.0390\) |
Rank
sage: E.rank()
The elliptic curves in class 88725cf have rank \(0\).
Complex multiplication
The elliptic curves in class 88725cf do not have complex multiplication.Modular form 88725.2.a.cf
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
