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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 107712.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107712.bs1 | 107712ff1 | \([0, 0, 0, -520716, 143483920]\) | \(81706955619457/744505344\) | \(142277186886303744\) | \([2]\) | \(1720320\) | \(2.1136\) | \(\Gamma_0(N)\)-optimal |
| 107712.bs2 | 107712ff2 | \([0, 0, 0, -152076, 342696976]\) | \(-2035346265217/264305213568\) | \(-50509512885160378368\) | \([2]\) | \(3440640\) | \(2.4602\) |
Rank
sage: E.rank()
The elliptic curves in class 107712.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 107712.bs do not have complex multiplication.Modular form 107712.2.a.bs
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.
