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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 88725.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88725.x1 | 88725a2 | \([0, -1, 1, -51856523, -144265906237]\) | \(-756218111874334720/3363432789843\) | \(-68591386367341796670075\) | \([]\) | \(10108800\) | \(3.2343\) | |
| 88725.x2 | 88725a1 | \([0, -1, 1, 1530577, -1047002422]\) | \(19444740423680/34451725707\) | \(-702583276266633618675\) | \([]\) | \(3369600\) | \(2.6849\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88725.x have rank \(1\).
Complex multiplication
The elliptic curves in class 88725.x do not have complex multiplication.Modular form 88725.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
