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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 42432bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42432.j1 | 42432bs1 | \([0, -1, 0, -1223073, 503634753]\) | \(771864882375147625/29358565696512\) | \(7696171845946441728\) | \([2]\) | \(614400\) | \(2.3921\) | \(\Gamma_0(N)\)-optimal |
| 42432.j2 | 42432bs2 | \([0, -1, 0, 507487, 1812976449]\) | \(55138849409108375/5449537181735712\) | \(-1428563474968926486528\) | \([2]\) | \(1228800\) | \(2.7387\) |
Rank
sage: E.rank()
The elliptic curves in class 42432bs have rank \(1\).
Complex multiplication
The elliptic curves in class 42432bs do not have complex multiplication.Modular form 42432.2.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 Cremona 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 Cremona labels.
