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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 414736bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.bw2 | 414736bw1 | \([0, -1, 0, -1667584, -761454336]\) | \(7189057/644\) | \(45941066352209444864\) | \([2]\) | \(14598144\) | \(2.5126\) | \(\Gamma_0(N)\)-optimal* |
414736.bw1 | 414736bw2 | \([0, -1, 0, -5814944, 4537212800]\) | \(304821217/51842\) | \(3698255841352860311552\) | \([2]\) | \(29196288\) | \(2.8592\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414736bw have rank \(0\).
Complex multiplication
The elliptic curves in class 414736bw do not have complex multiplication.Modular form 414736.2.a.bw
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 Cremona 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 Cremona labels.