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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 254898.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254898.bq1 | 254898bq2 | \([1, -1, 0, -366795, -88618811]\) | \(-6329617441/279936\) | \(-241365886671176064\) | \([]\) | \(3311616\) | \(2.1004\) | |
254898.bq2 | 254898bq1 | \([1, -1, 0, -2655, 122107]\) | \(-2401/6\) | \(-5173308613494\) | \([]\) | \(473088\) | \(1.1274\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254898.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 254898.bq do not have complex multiplication.Modular form 254898.2.a.bq
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.