Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 47610e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47610.e2 | 47610e1 | \([1, -1, 0, -33236640, 93568332800]\) | \(-1015884369980369163/358196480000000\) | \(-1431700227543709440000000\) | \([2]\) | \(9934848\) | \(3.3461\) | \(\Gamma_0(N)\)-optimal |
47610.e1 | 47610e2 | \([1, -1, 0, -570531360, 5245042649216]\) | \(5138442430700033888523/413281250000000\) | \(1651872345771093750000000\) | \([2]\) | \(19869696\) | \(3.6927\) |
Rank
sage: E.rank()
The elliptic curves in class 47610e have rank \(0\).
Complex multiplication
The elliptic curves in class 47610e do not have complex multiplication.Modular form 47610.2.a.e
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.