Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 39600.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.bw1 | 39600db1 | \([0, 0, 0, -3675, 234250]\) | \(-117649/440\) | \(-20528640000000\) | \([]\) | \(69120\) | \(1.2401\) | \(\Gamma_0(N)\)-optimal |
39600.bw2 | 39600db2 | \([0, 0, 0, 32325, -5561750]\) | \(80062991/332750\) | \(-15524784000000000\) | \([]\) | \(207360\) | \(1.7894\) |
Rank
sage: E.rank()
The elliptic curves in class 39600.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 39600.bw do not have complex multiplication.Modular form 39600.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.