Show commands:
SageMath
E = EllipticCurve("gc1")
E.isogeny_class()
Elliptic curves in class 33600.gc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.gc1 | 33600gn1 | \([0, 1, 0, -56533, -5192437]\) | \(1248870793216/42525\) | \(680400000000\) | \([2]\) | \(92160\) | \(1.3622\) | \(\Gamma_0(N)\)-optimal |
| 33600.gc2 | 33600gn2 | \([0, 1, 0, -54033, -5669937]\) | \(-68150496976/14467005\) | \(-3703553280000000\) | \([2]\) | \(184320\) | \(1.7088\) |
Rank
sage: E.rank()
The elliptic curves in class 33600.gc have rank \(0\).
Complex multiplication
The elliptic curves in class 33600.gc do not have complex multiplication.Modular form 33600.2.a.gc
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.
