Show commands:
SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 35280.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.bz1 | 35280d2 | \([0, 0, 0, -54243, 4834242]\) | \(3721734/25\) | \(118563085670400\) | \([2]\) | \(138240\) | \(1.5353\) | |
35280.bz2 | 35280d1 | \([0, 0, 0, -1323, 166698]\) | \(-108/5\) | \(-11856308567040\) | \([2]\) | \(69120\) | \(1.1887\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.bz do not have complex multiplication.Modular form 35280.2.a.bz
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.