Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 33600.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.bv1 | 33600ei1 | \([0, -1, 0, -533, -1563]\) | \(1048576/525\) | \(8400000000\) | \([2]\) | \(18432\) | \(0.59708\) | \(\Gamma_0(N)\)-optimal |
33600.bv2 | 33600ei2 | \([0, -1, 0, 1967, -14063]\) | \(3286064/2205\) | \(-564480000000\) | \([2]\) | \(36864\) | \(0.94365\) |
Rank
sage: E.rank()
The elliptic curves in class 33600.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 33600.bv do not have complex multiplication.Modular form 33600.2.a.bv
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.