Show commands:
SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 203280.gl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.gl1 | 203280a1 | \([0, 1, 0, -68405, 6863250]\) | \(1248870793216/42525\) | \(1205370104400\) | \([2]\) | \(672000\) | \(1.4098\) | \(\Gamma_0(N)\)-optimal |
| 203280.gl2 | 203280a2 | \([0, 1, 0, -65380, 7500920]\) | \(-68150496976/14467005\) | \(-6561070552270080\) | \([2]\) | \(1344000\) | \(1.7564\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.gl have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.gl do not have complex multiplication.Modular form 203280.2.a.gl
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.
