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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 3920p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3920.p2 | 3920p1 | \([0, -1, 0, 1944, -2960]\) | \(34391/20\) | \(-472252497920\) | \([]\) | \(4032\) | \(0.92951\) | \(\Gamma_0(N)\)-optimal |
| 3920.p1 | 3920p2 | \([0, -1, 0, -25496, 1709296]\) | \(-77626969/8000\) | \(-188900999168000\) | \([]\) | \(12096\) | \(1.4788\) |
Rank
sage: E.rank()
The elliptic curves in class 3920p have rank \(0\).
Complex multiplication
The elliptic curves in class 3920p do not have complex multiplication.Modular form 3920.2.a.p
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
