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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 117600.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117600.bb1 | 117600br1 | \([0, -1, 0, -45008378, -116206948248]\) | \(10713357105862263488/137781\) | \(129678374952000\) | \([2]\) | \(5308416\) | \(2.7218\) | \(\Gamma_0(N)\)-optimal |
117600.bb2 | 117600br2 | \([0, -1, 0, -45007153, -116213591423]\) | \(-167382537005851712/18983603961\) | \(-1143501835472736768000\) | \([2]\) | \(10616832\) | \(3.0684\) |
Rank
sage: E.rank()
The elliptic curves in class 117600.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 117600.bb do not have complex multiplication.Modular form 117600.2.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.