Show commands for:
SageMath
sage: E = EllipticCurve("64974.bw1")
sage: E.isogeny_class()
Elliptic curves in class 64974.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
64974.bw1 | 64974bx2 | [1, 0, 0, -87674406, 422770263012] | [7] | 14620032 | |
64974.bw2 | 64974bx1 | [1, 0, 0, -2226316, -1477144936] | [] | 2088576 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64974.bw have rank \(1\).
Modular form 64974.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.