Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 4650.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.bw1 | 4650bq2 | \([1, 0, 0, -1188, 14742]\) | \(11867954041/778410\) | \(12162656250\) | \([2]\) | \(4608\) | \(0.68486\) | |
4650.bw2 | 4650bq1 | \([1, 0, 0, 62, 992]\) | \(1685159/27900\) | \(-435937500\) | \([2]\) | \(2304\) | \(0.33829\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4650.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 4650.bw do not have complex multiplication.Modular form 4650.2.a.bw
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.