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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 66240fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66240.h2 | 66240fe1 | \([0, 0, 0, 95892, -5756848]\) | \(510273943271/370215360\) | \(-70749257056911360\) | \([2]\) | \(516096\) | \(1.9215\) | \(\Gamma_0(N)\)-optimal |
66240.h1 | 66240fe2 | \([0, 0, 0, -434028, -48786352]\) | \(47316161414809/22001657400\) | \(4204582206072422400\) | \([2]\) | \(1032192\) | \(2.2681\) |
Rank
sage: E.rank()
The elliptic curves in class 66240fe have rank \(0\).
Complex multiplication
The elliptic curves in class 66240fe do not have complex multiplication.Modular form 66240.2.a.fe
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 Cremona 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 Cremona labels.