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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 350064.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.s1 | 350064s2 | \([0, 0, 0, -24831, 1245086]\) | \(244964195971056/44871740771\) | \(310153472209152\) | \([2]\) | \(1081344\) | \(1.4992\) | |
| 350064.s2 | 350064s1 | \([0, 0, 0, 3054, 112955]\) | \(7292006774784/16978743353\) | \(-7334817128496\) | \([2]\) | \(540672\) | \(1.1527\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350064.s have rank \(2\).
Complex multiplication
The elliptic curves in class 350064.s do not have complex multiplication.Modular form 350064.2.a.s
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.
