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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1920.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1920.d1 | 1920k2 | \([0, -1, 0, -281, -1719]\) | \(300605792/675\) | \(5529600\) | \([2]\) | \(384\) | \(0.17595\) | |
| 1920.d2 | 1920k1 | \([0, -1, 0, -11, -45]\) | \(-628864/3645\) | \(-933120\) | \([2]\) | \(192\) | \(-0.17063\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1920.d have rank \(0\).
Complex multiplication
The elliptic curves in class 1920.d do not have complex multiplication.Modular form 1920.2.a.d
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.
