Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 10080.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10080.bw1 | 10080cc1 | \([0, 0, 0, -237, 1384]\) | \(31554496/525\) | \(24494400\) | \([2]\) | \(3072\) | \(0.21632\) | \(\Gamma_0(N)\)-optimal |
10080.bw2 | 10080cc2 | \([0, 0, 0, -12, 3904]\) | \(-64/2205\) | \(-6584094720\) | \([2]\) | \(6144\) | \(0.56289\) |
Rank
sage: E.rank()
The elliptic curves in class 10080.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 10080.bw do not have complex multiplication.Modular form 10080.2.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.