Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 102080.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102080.bw1 | 102080m1 | \([0, -1, 0, -3504005, 2525783525]\) | \(4646415367355940880384/38478378125\) | \(39401859200000\) | \([2]\) | \(1505280\) | \(2.1965\) | \(\Gamma_0(N)\)-optimal |
| 102080.bw2 | 102080m2 | \([0, -1, 0, -3501585, 2529444017]\) | \(-289799689905740628304/835751962890625\) | \(-13692960160000000000\) | \([2]\) | \(3010560\) | \(2.5431\) |
Rank
sage: E.rank()
The elliptic curves in class 102080.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 102080.bw do not have complex multiplication.Modular form 102080.2.a.bw
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.
