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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 40560.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.f1 | 40560bj1 | \([0, -1, 0, -13576, -605840]\) | \(-2365581049/6750\) | \(-789654528000\) | \([]\) | \(72576\) | \(1.1545\) | \(\Gamma_0(N)\)-optimal |
| 40560.f2 | 40560bj2 | \([0, -1, 0, 26984, -3136784]\) | \(18573478391/46875000\) | \(-5483712000000000\) | \([]\) | \(217728\) | \(1.7038\) |
Rank
sage: E.rank()
The elliptic curves in class 40560.f have rank \(0\).
Complex multiplication
The elliptic curves in class 40560.f do not have complex multiplication.Modular form 40560.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
