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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 249090.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.bd1 | 249090bd2 | \([1, 0, 1, -41884, -3169054]\) | \(172715635009/7935000\) | \(373309065735000\) | \([2]\) | \(1382400\) | \(1.5578\) | |
249090.bd2 | 249090bd1 | \([1, 0, 1, 1436, -188638]\) | \(6967871/331200\) | \(-15581595787200\) | \([2]\) | \(691200\) | \(1.2112\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 249090.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 249090.bd do not have complex multiplication.Modular form 249090.2.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.