Show commands:
SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 34650.em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34650.em1 | 34650cq1 | \([1, -1, 1, -59105, 5544397]\) | \(74246873427/16940\) | \(5209844062500\) | \([2]\) | \(147456\) | \(1.4319\) | \(\Gamma_0(N)\)-optimal |
| 34650.em2 | 34650cq2 | \([1, -1, 1, -52355, 6853897]\) | \(-51603494067/35870450\) | \(-11031844802343750\) | \([2]\) | \(294912\) | \(1.7785\) |
Rank
sage: E.rank()
The elliptic curves in class 34650.em have rank \(0\).
Complex multiplication
The elliptic curves in class 34650.em do not have complex multiplication.Modular form 34650.2.a.em
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.
