Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 8550c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.p2 | 8550c1 | \([1, -1, 0, 18183, -656659]\) | \(2161700757/1848320\) | \(-568445040000000\) | \([2]\) | \(46080\) | \(1.5188\) | \(\Gamma_0(N)\)-optimal |
8550.p1 | 8550c2 | \([1, -1, 0, -89817, -5732659]\) | \(260549802603/104256800\) | \(32063853037500000\) | \([2]\) | \(92160\) | \(1.8653\) |
Rank
sage: E.rank()
The elliptic curves in class 8550c have rank \(0\).
Complex multiplication
The elliptic curves in class 8550c do not have complex multiplication.Modular form 8550.2.a.c
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 Cremona 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 Cremona labels.