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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 166782.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166782.bd1 | 166782bo2 | \([1, 0, 1, -2687653, -1695722608]\) | \(45637459887836881/13417633152\) | \(631244372570646912\) | \([2]\) | \(9580032\) | \(2.3946\) | |
166782.bd2 | 166782bo1 | \([1, 0, 1, -146213, -33620848]\) | \(-7347774183121/6119866368\) | \(-287914504884830208\) | \([2]\) | \(4790016\) | \(2.0480\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166782.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 166782.bd do not have complex multiplication.Modular form 166782.2.a.bd
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.