Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3920.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3920.b1 | 3920t1 | \([0, 0, 0, -103243, -12768518]\) | \(-5154200289/20\) | \(-472252497920\) | \([]\) | \(20160\) | \(1.4533\) | \(\Gamma_0(N)\)-optimal |
3920.b2 | 3920t2 | \([0, 0, 0, 719957, 121149658]\) | \(1747829720511/1280000000\) | \(-30224159866880000000\) | \([]\) | \(141120\) | \(2.4262\) |
Rank
sage: E.rank()
The elliptic curves in class 3920.b have rank \(0\).
Complex multiplication
The elliptic curves in class 3920.b do not have complex multiplication.Modular form 3920.2.a.b
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.