Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 53361.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53361.bv1 | 53361m2 | \([1, -1, 0, -98940, 11937393]\) | \(19034163/121\) | \(680915915750763\) | \([2]\) | \(345600\) | \(1.6832\) | |
53361.bv2 | 53361m1 | \([1, -1, 0, -10005, -68832]\) | \(19683/11\) | \(61901446886433\) | \([2]\) | \(172800\) | \(1.3366\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53361.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 53361.bv do not have complex multiplication.Modular form 53361.2.a.bv
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.