Show commands:
SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 162240do
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162240.q2 | 162240do1 | \([0, -1, 0, -2721, -57279]\) | \(-3869893/300\) | \(-172779110400\) | \([2]\) | \(184320\) | \(0.90382\) | \(\Gamma_0(N)\)-optimal |
162240.q1 | 162240do2 | \([0, -1, 0, -44321, -3576639]\) | \(16718302693/90\) | \(51833733120\) | \([2]\) | \(368640\) | \(1.2504\) |
Rank
sage: E.rank()
The elliptic curves in class 162240do have rank \(1\).
Complex multiplication
The elliptic curves in class 162240do do not have complex multiplication.Modular form 162240.2.a.do
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 Cremona 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 Cremona labels.