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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 154800bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154800.k1 | 154800bm1 | \([0, 0, 0, -687675, 202374250]\) | \(770842973809/66873600\) | \(3120054681600000000\) | \([2]\) | \(2949120\) | \(2.2895\) | \(\Gamma_0(N)\)-optimal |
154800.k2 | 154800bm2 | \([0, 0, 0, 752325, 938214250]\) | \(1009328859791/8734528080\) | \(-407518142100480000000\) | \([2]\) | \(5898240\) | \(2.6360\) |
Rank
sage: E.rank()
The elliptic curves in class 154800bm have rank \(1\).
Complex multiplication
The elliptic curves in class 154800bm do not have complex multiplication.Modular form 154800.2.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 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.