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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 285912.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 285912.c1 | 285912c1 | \([0, 0, 0, -26045067, -51160663690]\) | \(55635379958596/24057\) | \(844871302624453632\) | \([2]\) | \(18579456\) | \(2.7822\) | \(\Gamma_0(N)\)-optimal |
| 285912.c2 | 285912c2 | \([0, 0, 0, -25915107, -51696488770]\) | \(-27403349188178/578739249\) | \(-40650137854472962050048\) | \([2]\) | \(37158912\) | \(3.1288\) |
Rank
sage: E.rank()
The elliptic curves in class 285912.c have rank \(0\).
Complex multiplication
The elliptic curves in class 285912.c do not have complex multiplication.Modular form 285912.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
