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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 470925.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
470925.bm1 | 470925bm1 | \([0, 0, 1, -9829650, -11861925719]\) | \(-9221261135586623488/121324931\) | \(-1381966792171875\) | \([]\) | \(11197440\) | \(2.4636\) | \(\Gamma_0(N)\)-optimal* |
470925.bm2 | 470925bm2 | \([0, 0, 1, -9273900, -13262313344]\) | \(-7743965038771437568/2189290237869371\) | \(-24937384115730804046875\) | \([]\) | \(33592320\) | \(3.0129\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 470925.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 470925.bm do not have complex multiplication.Modular form 470925.2.a.bm
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.