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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 304200bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304200.bq2 | 304200bq1 | \([0, 0, 0, -12675, -356463250]\) | \(-4/975\) | \(-54892402671600000000\) | \([2]\) | \(6193152\) | \(2.4665\) | \(\Gamma_0(N)\)-optimal |
304200.bq1 | 304200bq2 | \([0, 0, 0, -7617675, -7969068250]\) | \(434163602/7605\) | \(856321481676960000000\) | \([2]\) | \(12386304\) | \(2.8131\) |
Rank
sage: E.rank()
The elliptic curves in class 304200bq have rank \(1\).
Complex multiplication
The elliptic curves in class 304200bq do not have complex multiplication.Modular form 304200.2.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 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.