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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 1920.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1920.x1 | 1920x2 | \([0, 1, 0, -25, 23]\) | \(219488/75\) | \(614400\) | \([2]\) | \(384\) | \(-0.18728\) | |
| 1920.x2 | 1920x1 | \([0, 1, 0, 5, 5]\) | \(43904/45\) | \(-11520\) | \([2]\) | \(192\) | \(-0.53386\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1920.x have rank \(0\).
Complex multiplication
The elliptic curves in class 1920.x do not have complex multiplication.Modular form 1920.2.a.x
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.
