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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 1680.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1680.r1 | 1680s1 | \([0, 1, 0, -565, -5362]\) | \(1248870793216/42525\) | \(680400\) | \([2]\) | \(480\) | \(0.21089\) | \(\Gamma_0(N)\)-optimal |
| 1680.r2 | 1680s2 | \([0, 1, 0, -540, -5832]\) | \(-68150496976/14467005\) | \(-3703553280\) | \([2]\) | \(960\) | \(0.55747\) |
Rank
sage: E.rank()
The elliptic curves in class 1680.r have rank \(0\).
Complex multiplication
The elliptic curves in class 1680.r do not have complex multiplication.Modular form 1680.2.a.r
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.
