Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 344760.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
344760.bx1 | 344760bx2 | \([0, 1, 0, -121736, 16305264]\) | \(20183398562/3825\) | \(37811290982400\) | \([2]\) | \(1505280\) | \(1.6065\) | |
344760.bx2 | 344760bx1 | \([0, 1, 0, -6816, 308400]\) | \(-7086244/4335\) | \(-21426398223360\) | \([2]\) | \(752640\) | \(1.2599\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 344760.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 344760.bx do not have complex multiplication.Modular form 344760.2.a.bx
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.