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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 166410.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.w1 | 166410bo1 | \([1, -1, 0, -2571492474, -50063735170332]\) | \(408076159454905367161/1190206406250000\) | \(5484796835123686006406250000\) | \([2]\) | \(156119040\) | \(4.1931\) | \(\Gamma_0(N)\)-optimal |
166410.w2 | 166410bo2 | \([1, -1, 0, -1531429974, -90933823157832]\) | \(-86193969101536367161/725294740213012500\) | \(-3342356649033695281120357012500\) | \([2]\) | \(312238080\) | \(4.5397\) |
Rank
sage: E.rank()
The elliptic curves in class 166410.w have rank \(0\).
Complex multiplication
The elliptic curves in class 166410.w do not have complex multiplication.Modular form 166410.2.a.w
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.