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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 5184bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5184.d2 | 5184bb1 | \([0, 0, 0, 36, 144]\) | \(432\) | \(-11943936\) | \([]\) | \(1152\) | \(0.042015\) | \(\Gamma_0(N)\)-optimal |
5184.d1 | 5184bb2 | \([0, 0, 0, -1404, 20304]\) | \(-316368\) | \(-967458816\) | \([]\) | \(3456\) | \(0.59132\) |
Rank
sage: E.rank()
The elliptic curves in class 5184bb have rank \(2\).
Complex multiplication
The elliptic curves in class 5184bb do not have complex multiplication.Modular form 5184.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.