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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 11858be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11858.bg2 | 11858be1 | \([1, -1, 1, -173053, 28219909]\) | \(-2749884201/54208\) | \(-11298160379864512\) | \([2]\) | \(138240\) | \(1.8733\) | \(\Gamma_0(N)\)-optimal |
| 11858.bg1 | 11858be2 | \([1, -1, 1, -2781813, 1786524149]\) | \(11422548526761/4312\) | \(898717302943768\) | \([2]\) | \(276480\) | \(2.2199\) |
Rank
sage: E.rank()
The elliptic curves in class 11858be have rank \(0\).
Complex multiplication
The elliptic curves in class 11858be do not have complex multiplication.Modular form 11858.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
