Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 18480.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.be1 | 18480ce1 | \([0, -1, 0, -2245, -83975]\) | \(-4890195460096/9282994875\) | \(-2376446688000\) | \([]\) | \(31104\) | \(1.0645\) | \(\Gamma_0(N)\)-optimal |
| 18480.be2 | 18480ce2 | \([0, -1, 0, 19355, 1788745]\) | \(3132137615458304/7250937873795\) | \(-1856240095691520\) | \([]\) | \(93312\) | \(1.6138\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.be have rank \(0\).
Complex multiplication
The elliptic curves in class 18480.be do not have complex multiplication.Modular form 18480.2.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 LMFDB 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 LMFDB labels.
