Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 8550.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.w1 | 8550bd2 | \([1, -1, 1, -5248355, 4629200397]\) | \(1403607530712116449/39475350\) | \(449648908593750\) | \([2]\) | \(215040\) | \(2.3221\) | |
8550.w2 | 8550bd1 | \([1, -1, 1, -327605, 72585897]\) | \(-341370886042369/1817528220\) | \(-20702782380937500\) | \([2]\) | \(107520\) | \(1.9755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.w have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.w do not have complex multiplication.Modular form 8550.2.a.w
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.