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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 19950.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19950.bb1 | 19950bb2 | \([1, 0, 1, -9144951, 10643612548]\) | \(43304971114320697781/296432262\) | \(578969261718750\) | \([2]\) | \(552960\) | \(2.4326\) | |
19950.bb2 | 19950bb1 | \([1, 0, 1, -571201, 166490048]\) | \(-10552599539268821/27662978028\) | \(-54029253960937500\) | \([2]\) | \(276480\) | \(2.0861\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19950.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 19950.bb do not have complex multiplication.Modular form 19950.2.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.