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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 87514.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87514.f1 | 87514c1 | \([1, -1, 0, -15836, -758948]\) | \(3733252610697/23278724\) | \(2738718599876\) | \([2]\) | \(161280\) | \(1.2244\) | \(\Gamma_0(N)\)-optimal |
| 87514.f2 | 87514c2 | \([1, -1, 0, -6526, -1650846]\) | \(-261284780457/9875692358\) | \(-1161865330226342\) | \([2]\) | \(322560\) | \(1.5709\) |
Rank
sage: E.rank()
The elliptic curves in class 87514.f have rank \(1\).
Complex multiplication
The elliptic curves in class 87514.f do not have complex multiplication.Modular form 87514.2.a.f
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.
