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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 18240bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18240.br2 | 18240bb1 | \([0, 1, 0, -1, -1441]\) | \(-1/3420\) | \(-896532480\) | \([2]\) | \(9216\) | \(0.39672\) | \(\Gamma_0(N)\)-optimal |
18240.br1 | 18240bb2 | \([0, 1, 0, -1921, -32545]\) | \(2992209121/54150\) | \(14195097600\) | \([2]\) | \(18432\) | \(0.74329\) |
Rank
sage: E.rank()
The elliptic curves in class 18240bb have rank \(0\).
Complex multiplication
The elliptic curves in class 18240bb do not have complex multiplication.Modular form 18240.2.a.bb
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.