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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 283920.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.a1 | 283920a2 | \([0, -1, 0, -314396, 67947996]\) | \(2781352607056/429975\) | \(531304243142400\) | \([2]\) | \(2709504\) | \(1.8372\) | |
| 283920.a2 | 283920a1 | \([0, -1, 0, -17801, 1273440]\) | \(-8077950976/4312035\) | \(-333013909541040\) | \([2]\) | \(1354752\) | \(1.4906\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 283920.a have rank \(0\).
Complex multiplication
The elliptic curves in class 283920.a do not have complex multiplication.Modular form 283920.2.a.a
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.
