Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 4400.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4400.bb1 | 4400f2 | \([0, -1, 0, -2208, 32912]\) | \(595508/121\) | \(242000000000\) | \([2]\) | \(6400\) | \(0.90003\) | |
| 4400.bb2 | 4400f1 | \([0, -1, 0, 292, 2912]\) | \(5488/11\) | \(-5500000000\) | \([2]\) | \(3200\) | \(0.55346\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4400.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 4400.bb do not have complex multiplication.Modular form 4400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
