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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 60840bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60840.l1 | 60840bm1 | \([0, 0, 0, -1443, -16562]\) | \(202612/45\) | \(73802327040\) | \([2]\) | \(55296\) | \(0.79864\) | \(\Gamma_0(N)\)-optimal |
60840.l2 | 60840bm2 | \([0, 0, 0, 3237, -101738]\) | \(1143574/2025\) | \(-6642209433600\) | \([2]\) | \(110592\) | \(1.1452\) |
Rank
sage: E.rank()
The elliptic curves in class 60840bm have rank \(0\).
Complex multiplication
The elliptic curves in class 60840bm do not have complex multiplication.Modular form 60840.2.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.