Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 53550.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53550.l1 | 53550j2 | \([1, -1, 0, -57492, 5058416]\) | \(398525769279/22204448\) | \(1170937687500000\) | \([2]\) | \(307200\) | \(1.6465\) | |
53550.l2 | 53550j1 | \([1, -1, 0, 2508, 318416]\) | \(33076161/852992\) | \(-44982000000000\) | \([2]\) | \(153600\) | \(1.2999\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53550.l have rank \(0\).
Complex multiplication
The elliptic curves in class 53550.l do not have complex multiplication.Modular form 53550.2.a.l
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.