Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 117117.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.bb1 | 117117k2 | \([0, 0, 1, -1560, 20790]\) | \(3407872000/456533\) | \(56245322133\) | \([]\) | \(82944\) | \(0.79029\) | |
| 117117.bb2 | 117117k1 | \([0, 0, 1, -390, -2961]\) | \(53248000/77\) | \(9486477\) | \([]\) | \(27648\) | \(0.24099\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117117.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 117117.bb do not have complex multiplication.Modular form 117117.2.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.
