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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 54978bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54978.bs1 | 54978bo1 | \([1, 1, 1, -44297, -3578569]\) | \(81706955619457/744505344\) | \(87590309216256\) | \([2]\) | \(322560\) | \(1.4975\) | \(\Gamma_0(N)\)-optimal |
54978.bs2 | 54978bo2 | \([1, 1, 1, -12937, -8508361]\) | \(-2035346265217/264305213568\) | \(-31095244071061632\) | \([2]\) | \(645120\) | \(1.8441\) |
Rank
sage: E.rank()
The elliptic curves in class 54978bo have rank \(0\).
Complex multiplication
The elliptic curves in class 54978bo do not have complex multiplication.Modular form 54978.2.a.bo
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.