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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 215950.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215950.bc1 | 215950j2 | \([1, 1, 1, -84013, 8386531]\) | \(4197043674447625/467985555968\) | \(7312274312000000\) | \([2]\) | \(1741824\) | \(1.7771\) | |
215950.bc2 | 215950j1 | \([1, 1, 1, -20013, -957469]\) | \(56733768015625/7925399552\) | \(123834368000000\) | \([2]\) | \(870912\) | \(1.4305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215950.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 215950.bc do not have complex multiplication.Modular form 215950.2.a.bc
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.