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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 287490bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
287490.bb2 | 287490bb1 | \([1, 1, 0, -8016892, -9692793956]\) | \(-438456365173/58344300\) | \(-7582526735125911011100\) | \([2]\) | \(30689280\) | \(2.9310\) | \(\Gamma_0(N)\)-optimal |
287490.bb1 | 287490bb2 | \([1, 1, 0, -132116742, -584548119126]\) | \(1962373936020373/28934010\) | \(3760314278848155868770\) | \([2]\) | \(61378560\) | \(3.2776\) |
Rank
sage: E.rank()
The elliptic curves in class 287490bb have rank \(0\).
Complex multiplication
The elliptic curves in class 287490bb do not have complex multiplication.Modular form 287490.2.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.