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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 457776.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.bb1 | 457776bb2 | \([0, 0, 0, -33043971, -59277654110]\) | \(110725946217794/21954955473\) | \(791195064649826477819904\) | \([2]\) | \(53084160\) | \(3.3020\) | \(\Gamma_0(N)\)-optimal* |
457776.bb2 | 457776bb1 | \([0, 0, 0, -31275291, -67317719654]\) | \(187761599684068/10385793\) | \(187137436333681861632\) | \([2]\) | \(26542080\) | \(2.9554\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 457776.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 457776.bb do not have complex multiplication.Modular form 457776.2.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.