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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 203280.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203280.bm1 | 203280dg2 | \([0, -1, 0, -288141, -163466895]\) | \(-5833703071744/22107421875\) | \(-10026149479500000000\) | \([]\) | \(3732480\) | \(2.3316\) | |
203280.bm2 | 203280dg1 | \([0, -1, 0, 31299, 5325201]\) | \(7476617216/31444875\) | \(-14260867635168000\) | \([]\) | \(1244160\) | \(1.7823\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203280.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.bm do not have complex multiplication.Modular form 203280.2.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.