Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 28560.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28560.cj1 | 28560dh2 | \([0, 1, 0, -8296, -217036]\) | \(15417797707369/4080067320\) | \(16711955742720\) | \([2]\) | \(55296\) | \(1.2458\) | |
28560.cj2 | 28560dh1 | \([0, 1, 0, 1304, -21196]\) | \(59822347031/83966400\) | \(-343926374400\) | \([2]\) | \(27648\) | \(0.89927\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28560.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 28560.cj do not have complex multiplication.Modular form 28560.2.a.cj
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.