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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 66240.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66240.f1 | 66240m2 | \([0, 0, 0, -2508, 43632]\) | \(246491883/26450\) | \(187210137600\) | \([2]\) | \(73728\) | \(0.89715\) | |
| 66240.f2 | 66240m1 | \([0, 0, 0, -588, -4752]\) | \(3176523/460\) | \(3255828480\) | \([2]\) | \(36864\) | \(0.55057\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66240.f have rank \(2\).
Complex multiplication
The elliptic curves in class 66240.f do not have complex multiplication.Modular form 66240.2.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.
