Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 5782.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5782.j1 | 5782h1 | \([1, 0, 0, -1226, -17116]\) | \(-1732323601/60416\) | \(-7107881984\) | \([]\) | \(3960\) | \(0.66325\) | \(\Gamma_0(N)\)-optimal |
5782.j2 | 5782h2 | \([1, 0, 0, 5634, 867824]\) | \(168105213359/2859697196\) | \(-336440515412204\) | \([]\) | \(19800\) | \(1.4680\) |
Rank
sage: E.rank()
The elliptic curves in class 5782.j have rank \(0\).
Complex multiplication
The elliptic curves in class 5782.j do not have complex multiplication.Modular form 5782.2.a.j
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.