Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 166635.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166635.bu1 | 166635bl1 | \([1, -1, 0, -1095129, -378770472]\) | \(1345938541921/203765625\) | \(21990011949051890625\) | \([2]\) | \(3244032\) | \(2.4354\) | \(\Gamma_0(N)\)-optimal |
| 166635.bu2 | 166635bl2 | \([1, -1, 0, 1880496, -2080232847]\) | \(6814692748079/21258460125\) | \(-2294173966620685645125\) | \([2]\) | \(6488064\) | \(2.7820\) |
Rank
sage: E.rank()
The elliptic curves in class 166635.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 166635.bu do not have complex multiplication.Modular form 166635.2.a.bu
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.
