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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 23184.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23184.bo1 | 23184bq2 | \([0, 0, 0, -2019, -29342]\) | \(304821217/51842\) | \(154799382528\) | \([2]\) | \(27648\) | \(0.86776\) | |
23184.bo2 | 23184bq1 | \([0, 0, 0, -579, 4930]\) | \(7189057/644\) | \(1922973696\) | \([2]\) | \(13824\) | \(0.52119\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23184.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 23184.bo do not have complex multiplication.Modular form 23184.2.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 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.