Show commands:
SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 162450ea
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162450.bw2 | 162450ea1 | \([1, -1, 0, -1692, -65133284]\) | \(-1/3420\) | \(-1832716399868437500\) | \([2]\) | \(3317760\) | \(2.1832\) | \(\Gamma_0(N)\)-optimal |
162450.bw1 | 162450ea2 | \([1, -1, 0, -2438442, -1441897034]\) | \(2992209121/54150\) | \(29018009664583593750\) | \([2]\) | \(6635520\) | \(2.5298\) |
Rank
sage: E.rank()
The elliptic curves in class 162450ea have rank \(1\).
Complex multiplication
The elliptic curves in class 162450ea do not have complex multiplication.Modular form 162450.2.a.ea
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.