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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 177870.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177870.bm1 | 177870hk1 | \([1, 1, 0, -1817, 10641]\) | \(1092727/540\) | \(328128528420\) | \([2]\) | \(268800\) | \(0.90281\) | \(\Gamma_0(N)\)-optimal |
177870.bm2 | 177870hk2 | \([1, 1, 0, 6653, 90259]\) | \(53582633/36450\) | \(-22148675668350\) | \([2]\) | \(537600\) | \(1.2494\) |
Rank
sage: E.rank()
The elliptic curves in class 177870.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 177870.bm do not have complex multiplication.Modular form 177870.2.a.bm
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.