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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 1920.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1920.r1 | 1920g1 | \([0, 1, 0, -606, -5850]\) | \(192596360288/3796875\) | \(486000000\) | \([2]\) | \(960\) | \(0.45885\) | \(\Gamma_0(N)\)-optimal |
| 1920.r2 | 1920g2 | \([0, 1, 0, 19, -16725]\) | \(43904/7381125\) | \(-120932352000\) | \([2]\) | \(1920\) | \(0.80543\) |
Rank
sage: E.rank()
The elliptic curves in class 1920.r have rank \(0\).
Complex multiplication
The elliptic curves in class 1920.r do not have complex multiplication.Modular form 1920.2.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.
