Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 53550.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53550.k1 | 53550be2 | \([1, -1, 0, -116667, -11270259]\) | \(15417797707369/4080067320\) | \(46474516816875000\) | \([2]\) | \(442368\) | \(1.9067\) | |
53550.k2 | 53550be1 | \([1, -1, 0, 18333, -1145259]\) | \(59822347031/83966400\) | \(-956429775000000\) | \([2]\) | \(221184\) | \(1.5601\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53550.k have rank \(1\).
Complex multiplication
The elliptic curves in class 53550.k do not have complex multiplication.Modular form 53550.2.a.k
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.