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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1920.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1920.e1 | 1920a2 | \([0, -1, 0, -41, -39]\) | \(953312/405\) | \(3317760\) | \([2]\) | \(256\) | \(-0.052094\) | |
| 1920.e2 | 1920a1 | \([0, -1, 0, 9, -9]\) | \(281216/225\) | \(-57600\) | \([2]\) | \(128\) | \(-0.39867\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1920.e have rank \(1\).
Complex multiplication
The elliptic curves in class 1920.e do not have complex multiplication.Modular form 1920.2.a.e
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.
