Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 18240.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18240.n1 | 18240bw2 | \([0, -1, 0, -25441, -1551359]\) | \(6947097508441/10687500\) | \(2801664000000\) | \([2]\) | \(36864\) | \(1.2878\) | |
| 18240.n2 | 18240bw1 | \([0, -1, 0, -1121, -38655]\) | \(-594823321/2166000\) | \(-567803904000\) | \([2]\) | \(18432\) | \(0.94121\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18240.n have rank \(1\).
Complex multiplication
The elliptic curves in class 18240.n do not have complex multiplication.Modular form 18240.2.a.n
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.
