Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 338130.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.bj1 | 338130bj2 | \([1, -1, 0, -9999, -381807]\) | \(30870492353/50700\) | \(181585953900\) | \([2]\) | \(524288\) | \(1.0568\) | |
338130.bj2 | 338130bj1 | \([1, -1, 0, -819, -1755]\) | \(16974593/9360\) | \(33523560720\) | \([2]\) | \(262144\) | \(0.71019\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338130.bj have rank \(2\).
Complex multiplication
The elliptic curves in class 338130.bj do not have complex multiplication.Modular form 338130.2.a.bj
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.