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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 443760.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.bb1 | 443760bb2 | \([0, -1, 0, -473960, -115080048]\) | \(909513218/83205\) | \(1077184537583708160\) | \([2]\) | \(6623232\) | \(2.1992\) | |
443760.bb2 | 443760bb1 | \([0, -1, 0, -104160, 10947792]\) | \(19307236/3225\) | \(20875669333017600\) | \([2]\) | \(3311616\) | \(1.8526\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443760.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 443760.bb do not have complex multiplication.Modular form 443760.2.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 LMFDB 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 LMFDB labels.