Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 286110.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286110.bb1 | 286110bb1 | \([1, -1, 0, -2655, -143195]\) | \(-117649/440\) | \(-7742366632440\) | \([]\) | \(604800\) | \(1.1588\) | \(\Gamma_0(N)\)-optimal |
286110.bb2 | 286110bb2 | \([1, -1, 0, 23355, 3409771]\) | \(80062991/332750\) | \(-5855164765782750\) | \([]\) | \(1814400\) | \(1.7081\) |
Rank
sage: E.rank()
The elliptic curves in class 286110.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 286110.bb do not have complex multiplication.Modular form 286110.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.