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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 40898bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40898.bd2 | 40898bx1 | \([1, -1, 1, -54957, -7570923]\) | \(-2146689/1664\) | \(-14228841667204736\) | \([]\) | \(470400\) | \(1.7983\) | \(\Gamma_0(N)\)-optimal |
40898.bd1 | 40898bx2 | \([1, -1, 1, -4349247, 3831524337]\) | \(-1064019559329/125497034\) | \(-1073123453419356633866\) | \([]\) | \(3292800\) | \(2.7712\) |
Rank
sage: E.rank()
The elliptic curves in class 40898bx have rank \(1\).
Complex multiplication
The elliptic curves in class 40898bx do not have complex multiplication.Modular form 40898.2.a.bx
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.