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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 14490.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.bu1 | 14490bv1 | \([1, -1, 1, -2586677, -1006001971]\) | \(2625564132023811051529/918925030195200000\) | \(669896347012300800000\) | \([2]\) | \(576000\) | \(2.6976\) | \(\Gamma_0(N)\)-optimal |
14490.bu2 | 14490bv2 | \([1, -1, 1, 7735243, -7038132019]\) | \(70213095586874240921591/69970703040000000000\) | \(-51008642516160000000000\) | \([2]\) | \(1152000\) | \(3.0441\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.bu do not have complex multiplication.Modular form 14490.2.a.bu
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.