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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 286110.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.w1 | 286110w2 | \([1, -1, 0, -787741515, -8460957084219]\) | \(625326874420056353/4132697500800\) | \(357274021380937268890550400\) | \([2]\) | \(140378112\) | \(3.9304\) | |
| 286110.w2 | 286110w1 | \([1, -1, 0, -80269515, 54600390981]\) | \(661618760280353/367994880000\) | \(31813364176725916477440000\) | \([2]\) | \(70189056\) | \(3.5839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286110.w have rank \(1\).
Complex multiplication
The elliptic curves in class 286110.w do not have complex multiplication.Modular form 286110.2.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.
