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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 414736.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.bd1 | 414736bd2 | \([0, 0, 0, -366275, -84554302]\) | \(926859375/9604\) | \(56309782193487872\) | \([2]\) | \(2654208\) | \(2.0312\) | \(\Gamma_0(N)\)-optimal* |
414736.bd2 | 414736bd1 | \([0, 0, 0, -5635, -3266046]\) | \(-3375/784\) | \(-4596716913754112\) | \([2]\) | \(1327104\) | \(1.6846\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414736.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 414736.bd do not have complex multiplication.Modular form 414736.2.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.