Show commands:
SageMath
E = EllipticCurve("jl1")
E.isogeny_class()
Elliptic curves in class 388080.jl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.jl1 | 388080jl1 | \([0, 0, 0, -296352, -40387221]\) | \(226492416/75625\) | \(961078856363010000\) | \([2]\) | \(5160960\) | \(2.1532\) | \(\Gamma_0(N)\)-optimal |
388080.jl2 | 388080jl2 | \([0, 0, 0, 861273, -278626446]\) | \(347482224/366025\) | \(-74425946636751494400\) | \([2]\) | \(10321920\) | \(2.4997\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.jl have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.jl do not have complex multiplication.Modular form 388080.2.a.jl
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.