Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8550.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.f1 | 8550e2 | \([1, -1, 0, -4471992, 3641708916]\) | \(-1389310279182025/267418692\) | \(-1903791274101562500\) | \([]\) | \(288000\) | \(2.5080\) | |
8550.f2 | 8550e1 | \([1, -1, 0, 42948, -214704]\) | \(480705753733655/279172334592\) | \(-5087915797939200\) | \([]\) | \(57600\) | \(1.7033\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.f have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.f do not have complex multiplication.Modular form 8550.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.