Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 54096.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54096.bg1 | 54096bv2 | \([0, -1, 0, -2623672, 1429824880]\) | \(4144806984356137/568114785504\) | \(273769006693417353216\) | \([2]\) | \(2211840\) | \(2.6484\) | |
54096.bg2 | 54096bv1 | \([0, -1, 0, 261448, 118826352]\) | \(4101378352343/15049939968\) | \(-7252420146361270272\) | \([2]\) | \(1105920\) | \(2.3019\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54096.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 54096.bg do not have complex multiplication.Modular form 54096.2.a.bg
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.