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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 166410.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.bb1 | 166410bq2 | \([1, -1, 0, -15504, 735560]\) | \(7111117467/125000\) | \(7245075375000\) | \([2]\) | \(354816\) | \(1.2640\) | |
166410.bb2 | 166410bq1 | \([1, -1, 0, -24, 32768]\) | \(-27/8000\) | \(-463684824000\) | \([2]\) | \(177408\) | \(0.91743\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166410.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 166410.bb do not have complex multiplication.Modular form 166410.2.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.