Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 9360.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9360.bw1 | 9360bu1 | \([0, 0, 0, -732, 731]\) | \(3718856704/2132325\) | \(24871438800\) | \([2]\) | \(6144\) | \(0.68442\) | \(\Gamma_0(N)\)-optimal |
9360.bw2 | 9360bu2 | \([0, 0, 0, 2913, 5834]\) | \(14647977776/8555625\) | \(-1596684960000\) | \([2]\) | \(12288\) | \(1.0310\) |
Rank
sage: E.rank()
The elliptic curves in class 9360.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 9360.bw do not have complex multiplication.Modular form 9360.2.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.