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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 409101.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.bd1 | 409101bd1 | \([0, 1, 1, -1798463, -929107294]\) | \(-62992384000/14283\) | \(-145867945885748163\) | \([]\) | \(5806080\) | \(2.2856\) | \(\Gamma_0(N)\)-optimal* |
409101.bd2 | 409101bd2 | \([0, 1, 1, 691717, -3232399285]\) | \(3584000000/444107667\) | \(-4535536871623739075787\) | \([]\) | \(17418240\) | \(2.8349\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 409101.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 409101.bd do not have complex multiplication.Modular form 409101.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.